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diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/README.md b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/README.md index 4de6c1d..9115c78 100644 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/README.md +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/README.md @@ -3,11 +3,12 @@ FSF2020--Somnath Pandit # **Topics:**
## Double Integral
-
+Check the note [here](https://math.animations.fossee.in/contents/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals)
## Fubini's Theorem
-
+Check the note [here](https://math.animations.fossee.in/contents/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's-theorem)
## Line Integrals
-
+Check the note [here](https://math.animations.fossee.in/contents/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals)
## Fundamental Theorem of Line integrals
-
+Check the note [here](https://math.animations.fossee.in/contents/calculus-of-several-variables/div,-grad,-curl-and-all-that/the-fundamental-theorem-of-line-integrals)
## Vector Fields
+Check the note [here](https://math.animations.fossee.in/contents/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields)
diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/README.md b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/README.md index 5fa2146..f86f7e3 100644 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/README.md +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/README.md @@ -1,21 +1,21 @@ **file1_area_under_func** - + **file2_volume_under_surface** - + **file3_y_limit_dependent_on_x** - + **file4_non_rect_region** - + **file5_elementary_area** - + **file6_doing_integration** - + **file7_int_process_of_example** - + diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file1_area_under_func.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/gifs/file1_area_under_func.gif Binary files differindex 223218b..223218b 100644 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file1_area_under_func.gif +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/gifs/file1_area_under_func.gif diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file2_volume_under_surface.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/gifs/file2_volume_under_surface.gif Binary files differindex 1455573..1455573 100644 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file2_volume_under_surface.gif +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/gifs/file2_volume_under_surface.gif diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file3_y_limit_dependent_on_x.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/gifs/file3_y_limit_dependent_on_x.gif Binary files differindex dcfacb6..dcfacb6 100644 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file3_y_limit_dependent_on_x.gif +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/gifs/file3_y_limit_dependent_on_x.gif diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file4_non_rect_region.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/gifs/file4_non_rect_region.gif Binary files differindex c8e7c8c..c8e7c8c 100644 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file4_non_rect_region.gif +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/gifs/file4_non_rect_region.gif diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file5_elementary_area.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/gifs/file5_elementary_area.gif Binary files differindex 5c9ac03..5c9ac03 100644 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file5_elementary_area.gif +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/gifs/file5_elementary_area.gif diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file6_doing_integration.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/gifs/file6_doing_integration.gif Binary files differindex 7a9271b..7a9271b 100644 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file6_doing_integration.gif +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/gifs/file6_doing_integration.gif diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file7_int_process_of_example.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/gifs/file7_int_process_of_example.gif Binary files differindex 9fbdde8..9fbdde8 100644 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file7_int_process_of_example.gif +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/gifs/file7_int_process_of_example.gif diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's-theorem/README.md b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's-theorem/README.md index c1c6e8e..3aa9be2 100644 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's-theorem/README.md +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's-theorem/README.md @@ -1,14 +1,14 @@ **file1_surface1** - + **file2_surface2** - + **file3_iteration_methods** - + **file4_curvy_limits** - + diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's-theorem/file1_surface1.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's-theorem/gifs/file1_surface1.gif Binary files differindex 8c9fa0a..8c9fa0a 100644 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's-theorem/file1_surface1.gif +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's-theorem/gifs/file1_surface1.gif diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's-theorem/file2_surface2.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's-theorem/gifs/file2_surface2.gif Binary files differindex 37c4b1d..37c4b1d 100644 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's-theorem/file2_surface2.gif +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's-theorem/gifs/file2_surface2.gif diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's-theorem/file3.o_iteration_methods_checkpoint.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's-theorem/gifs/file3.o_iteration_methods_checkpoint.gif Binary files differindex 2e507f9..2e507f9 100644 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's-theorem/file3.o_iteration_methods_checkpoint.gif +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's-theorem/gifs/file3.o_iteration_methods_checkpoint.gif diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's-theorem/file3_iteration_methods.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's-theorem/gifs/file3_iteration_methods.gif Binary files differindex 4e1611b..4e1611b 100644 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's-theorem/file3_iteration_methods.gif +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's-theorem/gifs/file3_iteration_methods.gif diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's-theorem/file4_curvy_region.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's-theorem/gifs/file4_curvy_region.gif Binary files differindex b0620e5..b0620e5 100644 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's-theorem/file4_curvy_region.gif +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's-theorem/gifs/file4_curvy_region.gif diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/README.md b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/README.md index aa8c7f8..3cdddae 100644 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/README.md +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/README.md @@ -1,9 +1,9 @@ **file1_grad_of_scalar_function** - + **file2_line_int_independent_of_path** - + **file3_line_int_example** - + diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/file1_grad_of_scalar_function.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/file1_grad_of_scalar_function.gif Binary files differdeleted file mode 100644 index 5a6e102..0000000 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/file1_grad_of_scalar_function.gif +++ /dev/null diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/file1_grad_of_scalar_function.py b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/file1_grad_of_scalar_function.py index c9f479c..fd3d9b5 100644 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/file1_grad_of_scalar_function.py +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/file1_grad_of_scalar_function.py @@ -1,6 +1,6 @@ from manimlib.imports import * -class GradOfScalar(ThreeDScene): +class GradOfScalarFunc(ThreeDScene): CONFIG = { "axes_config": { @@ -27,7 +27,7 @@ class GradOfScalar(ThreeDScene): "num_axis_pieces": 1, }, "default_graph_style": { - "stroke_width": 2, + "stroke_width": 5, "stroke_color": WHITE, }, "default_vector_field_config": { @@ -38,8 +38,8 @@ class GradOfScalar(ThreeDScene): "y_min": -3, "y_max": 3, "min_magnitude": 0, - "max_magnitude": 2, - "colors": [TEAL,GREEN,GREEN,GREEN,YELLOW,RED], + "max_magnitude": 3, + "colors": [TEAL,GREEN,YELLOW,RED], "length_func": lambda norm : norm*np.exp(-.38*norm)/2, "opacity": 1.0, "vector_config": { @@ -49,9 +49,9 @@ class GradOfScalar(ThreeDScene): "default_surface_config": { "fill_opacity": 0.5, "checkerboard_colors": [BLUE_E], - "stroke_width": .5, + "stroke_width": .2, "stroke_color": WHITE, - "stroke_opacity": 0.75, + "stroke_opacity": 0.5, }, } @@ -66,17 +66,24 @@ class GradOfScalar(ThreeDScene): theta=-135 * DEGREES, ) - scalar_fn_text=TexMobject("f(x,y,z)=","xy").set_color(BLUE) + scalar_fn_text=TexMobject("f(x,y)=","xy").set_color(BLUE) scalar_fn_text.to_corner(UR,buff=.6) operator=TexMobject("\\vec\\nabla").next_to( scalar_fn_text,LEFT,buff=.2 ).set_color(GOLD) - grad_text=TexMobject(r"\dfrac{\partial f}{\partial x} \hat i+\dfrac{\partial f}{\partial y} \hat j+\dfrac{\partial f}{\partial z} \hat k").set_color(GOLD) + + grad_text=TexMobject(r"\dfrac{\partial f}{\partial x} \hat i+\dfrac{\partial f}{\partial y} \hat j").set_color(GOLD) grad_text.next_to(scalar_fn_text,DOWN).scale(.9) - VGroup(grad_text[0][1],grad_text[0][9],grad_text[0][17]).set_color(BLUE) - VGroup(grad_text[0][5:8],grad_text[0][13:16],grad_text[0][21:23]).set_color(WHITE) + VGroup( + grad_text[0][1], + grad_text[0][9] + ).set_color(BLUE) + VGroup( + grad_text[0][5:8], + grad_text[0][13:16] + ).set_color(WHITE) vector_field_text=TexMobject("\\vec F=y\hat i+x\hat j").set_color_by_gradient(*self.default_vector_field_config["colors"]) vector_field_text.next_to(scalar_fn_text,DOWN) @@ -108,30 +115,33 @@ class GradOfScalar(ThreeDScene): self.play(Write(grad_text)) self.wait(2) - self.play(FadeOut(grad_text)) - self.add_fixed_in_frame_mobjects(vector_field_text) - show_vec_field=[ + + show_vects=[ FadeIn(v_field1), - Write(vector_field_text), ] self.begin_ambient_camera_rotation(rate=.2) self.move_camera( # distance=20, phi=60 * DEGREES, - added_anims=show_vec_field, + added_anims=show_vects, run_time=4.5 ) - + + self.play(FadeOut(grad_text)) self.wait(2) self.stop_ambient_camera_rotation() - fadeout= [FadeOut(s_field1)] + self.add_fixed_in_frame_mobjects(vector_field_text) + vector_field= [ + FadeOut(s_field1), + Write(vector_field_text), + ] self.move_camera( # distance=20, phi=0 * DEGREES, theta=-90 * DEGREES, - added_anims=fadeout, + added_anims=vector_field, run_time=2 ) self.wait(2) @@ -165,6 +175,7 @@ class GradOfScalar(ThreeDScene): config.update(self.default_vector_field_config) config.update(kwargs) vector_field= VectorField(func,**config) + vector_field.move_to(self.axes.c2p(0,0,0)) self.vector_field=vector_field if on_surface: @@ -175,15 +186,14 @@ class GradOfScalar(ThreeDScene): def get_vectors_on_surface(self): - config = dict() - config.update(self.default_vector_field_config["vector_config"]) vectors_on_surface = VGroup(*[ - self.vector_field.get_vector(point,**config) + self.vector_field.get_vector(point) for point in self.surface_points ]) return vectors_on_surface - + + def get_surface(self, func, **kwargs): axes=self.axes @@ -305,4 +315,3 @@ class GradOfScalar(ThreeDScene): - diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/file2_line_int_independent_of_path.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/file2_line_int_independent_of_path.gif Binary files differdeleted file mode 100644 index 29c6d02..0000000 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/file2_line_int_independent_of_path.gif +++ /dev/null diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/file2_line_int_independent_of_path.py b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/file2_line_int_independent_of_path.py index b9597b6..b8f7cfa 100644 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/file2_line_int_independent_of_path.py +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/file2_line_int_independent_of_path.py @@ -95,7 +95,7 @@ class LineIntegration(GraphScene): def get_endpoints_of_curve(self): points=[[-3,0],[2,2]] - point_labels= ["P_i","P_f"] + point_labels= ["P_f","P_i"] for point,label in zip(points,point_labels): dot=Dot(self.coords_to_point(*point)).set_color(RED) dot_label=TexMobject(label) diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/gifs/file1_grad_of_scalar_function.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/gifs/file1_grad_of_scalar_function.gif Binary files differnew file mode 100644 index 0000000..1fd2e15 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/gifs/file1_grad_of_scalar_function.gif diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/gifs/file2_line_int_independent_of_path.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/gifs/file2_line_int_independent_of_path.gif Binary files differnew file mode 100644 index 0000000..8d375bb --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/gifs/file2_line_int_independent_of_path.gif diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/file3_line_int_example.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/gifs/file3_line_int_example.gif Binary files differindex 20ed081..20ed081 100644 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/file3_line_int_example.gif +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/gifs/file3_line_int_example.gif diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/README.md b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/README.md index 17077b6..7e4299d 100644 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/README.md +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/README.md @@ -1,14 +1,15 @@ **file1_scalar_line_int_as_sum** - + **file2_scalar_line_integral** - + **file3_vector_line_int_as_sum** - + +**file4_vector_line_integral** + - -**file4_helix** - +**file5_helix** + diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file1_scalar_line_int_as_sum.py b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file1_scalar_line_int_as_sum.py index e3f3574..af32ebf 100644 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file1_scalar_line_int_as_sum.py +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file1_scalar_line_int_as_sum.py @@ -155,17 +155,13 @@ class LineIntegrationAsSum(GraphScene): sum_up_text.set_color_by_tex("summed",PURPLE) sum_up_text.next_to(multiply_text,DOWN) - dot.set_color(ORANGE).scale(1.2) self.play(FadeIn(VGroup( point_coord,dot ))) self.play(Write(self.evaluate_text)) self.play(Write(func_val)) - self.play(FadeIn(VGroup(*[ - dot.set_color(ORANGE).scale(1.4) - for dot in dots ] - ))) + self.wait(2) self.remove(point_coord) self.get_ds(dots,index) @@ -182,7 +178,11 @@ class LineIntegrationAsSum(GraphScene): func_val, RIGHT,buff=.2 )) self.play(Write(sum_up_text)) - + dot.set_color(ORANGE).scale(1.2) + self.play(FadeIn(VGroup(*[ + dot.set_color(ORANGE).scale(1.4) + for dot in dots ] + ))) self.func_val=func_val self.sum_text_group=VGroup(multiply_text,sum_up_text) diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file2_scalar_line_integral.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file2_scalar_line_integral.gif Binary files differdeleted file mode 100644 index 71c97d6..0000000 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file2_scalar_line_integral.gif +++ /dev/null diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file2_scalar_line_integral.py b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file2_scalar_line_integral.py index 996ead1..200f768 100644 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file2_scalar_line_integral.py +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file2_scalar_line_integral.py @@ -47,8 +47,8 @@ class LineIntegrationProcess(SpecialThreeDScene): axes=self.axes self.set_camera_orientation(distance=35, - phi=65 * DEGREES, - theta=-65 * DEGREES, + phi=60 * DEGREES, + theta=-60 * DEGREES, ) fn_text=TextMobject("$z=2+x^2y$").set_color(BLUE) @@ -86,7 +86,14 @@ class LineIntegrationProcess(SpecialThreeDScene): self.play(Write(area_text)) self.play(Write(self.area),run_time=2) self.play(FadeOut(VGroup(surface,fn_text))) - self.wait() + self.move_camera( + # distance=20, + phi=90 * DEGREES, + # theta=-90 * DEGREES, + # added_anims=into_graph, + run_time=2 + ) + self.wait(2) self.stop_ambient_camera_rotation() # self.get_lines() @@ -307,7 +314,8 @@ class LineIntegrationProcess(SpecialThreeDScene): line=DashedLine(start,end,color=color) return line - + +#------------------------------------------------------- #customize 3D axes def get_three_d_axes(self, include_labels=True, include_numbers=True, **kwargs): config = dict(self.axes_config) @@ -417,5 +425,3 @@ class LineIntegrationProcess(SpecialThreeDScene): #uploaded by Somnath Pandit.FSF2020_Line_Integrals - - diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file4_vector_line_integral.py b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file4_vector_line_integral.py new file mode 100644 index 0000000..6730820 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file4_vector_line_integral.py @@ -0,0 +1,374 @@ +from manimlib.imports import * + +class LineIntegrationProcess(GraphScene): + + CONFIG = { + "x_min" : -0, + "x_max" : 1, + "y_min" : -0, + "y_max" : 1, + "axes_color":WHITE, + "graph_origin": ORIGIN+6.3*LEFT+3*DOWN, + "x_axis_width": 5.5, + "y_axis_height": 5.5, + "x_tick_frequency": 1, + "y_tick_frequency": 1, + "default_vector_field_config": { + "delta_x": .5, + "delta_y": .5, + "min_magnitude": 0, + "max_magnitude": 15, + "colors": [BLUE], + "length_func": lambda norm : norm/35, + "opacity": 1.0, + "vector_config": { + "stroke_width":2 + }, + }, + "default_graph_style": { + "stroke_width": 2, + "stroke_color": WHITE, + }, + } + + + def construct(self): + X = RIGHT*self.x_axis_width/(self.x_max- self.x_min) + Y = UP*self.y_axis_height/(self.y_max- self.y_min) + self.X=X ;self.Y=Y + + self.setup_axes(animate=False) + + fn_text=TexMobject( + r"\vec F = x^2\hat i-xy\hat j", + stroke_width=2.5 + ).set_color_by_gradient( + *self.default_vector_field_config["colors"] + ) + fn_text.to_edge(TOP,buff=.1).shift(2*LEFT) + + origin=self.graph_origin + v_field=self.get_vector_field( + lambda v: np.array([ + (v[0]-origin[0])**2, + -(v[0]-origin[0])*(v[1]-origin[1]), + 0, + ]), + x_min= -.001+origin[0], + x_max= 5.4+origin[0], + y_min= -0+origin[1], + y_max= 5.5+origin[1], + ) + + self.add(v_field, fn_text) + self.play(Write(fn_text)) + self.wait(2) + self.get_line_of_int() + self.get_dot_product_values() + self.wait(2) + self.remove(v_field,fn_text) + self.write_area_as_intgral_value() + self.wait(2) + + + def get_vector_field(self,func,**kwargs): + config = dict() + config.update(self.default_vector_field_config) + config.update(kwargs) + vector_field= VectorField(func,**config) + self.vector_field=vector_field + + return vector_field + + def get_line_of_int(self): + line_of_int_text=TextMobject( + r"Line of integration is\\", + "$\\vec r(t)=\cos(t)\hat i+\sin(t)\hat j$" + ) + line_of_int_text[1].set_color(PINK) + line_of_int_text.to_corner(UR,buff=.8) + + + line_of_int= self.get_graph( + lambda x : np.sqrt(1-x**2), + x_min=1, + x_max=0, + ) + line_of_int.set_style( + stroke_width=3, + stroke_color=PINK, + ) + + self.play(Write(line_of_int_text)) + self.wait(.5) + self.play(ShowCreation(line_of_int),run_time=2) + # self.add(line_of_int) + + self.line_of_int=line_of_int + self.line_of_int_text=line_of_int_text + + + def get_dot_product_values(self): + t_tracker = ValueTracker(0) + self.t_tracker = t_tracker + self.get_vector_and_tangent() + self.get_dot_product_graph() + self.wait(1.5) + self.play(ApplyMethod( + self.t_tracker.set_value, PI/6, + rate_func=linear, + run_time=2.5, + ) + ) + self.wait(1) + self.play(ApplyMethod( + self.t_tracker.set_value, PI/2, + rate_func=linear, + run_time=4, + ) + ) + self.dot_prod_graph.suspend_updating() + + def get_vector_and_tangent(self): + vect_tangent_text=TextMobject( + "Get the"," vector",r" and\\"," tangent", + " on the"," line" + ) + vect_tangent_text.set_color_by_tex_to_color_map({ + "tangent": ORANGE, "vector": YELLOW, "line":PINK + }) + vect_tangent_text.to_corner(UR,buff=.8) + self.vect_tangent_text= vect_tangent_text + + self.play(FadeOut(self.axes)) + self.remove(self.line_of_int_text) + self.play(Write(vect_tangent_text)) + self.show_vector() + self.show_tangent() + self.wait(1.3) + + def show_vector(self): + t = self.t_tracker.get_value + vect_label=TextMobject( + "$\\vec F(x_i,y_i)$", + color=YELLOW, + stroke_width=2 + ).scale(.8) + + vector = always_redraw( lambda: + self.vector_field.get_vector( + self.coords_to_point( + np.cos(t()), np.sin(t()) + ), + stroke_width=6, + max_stroke_width_to_length_ratio= 8, + ).set_color(YELLOW), + ) + + vect_label.next_to(vector,RIGHT,buff=.1) + vector_group= VGroup(vector,vect_label) + + # self.add(vector_group) + self.play(Write(vector_group),run_time=1) + self.wait(.4) + + self.vect_label = vect_label + self.vector_group= vector_group + + def show_tangent(self): + tangent_label=TextMobject( + "$\\vec T(x_i,y_i)$", + color=ORANGE, + stroke_width=2 + ).scale(.8) + + t = self.t_tracker.get_value + + tangent = always_redraw(lambda: + Vector( + color=ORANGE, + stroke_width=6, + ).scale(1).next_to( + self.coords_to_point( + np.cos(t()), np.sin(t()) + ),DR,buff=-.1 + ).rotate( + self.angle_of_tangent( + np.cos(t()), + self.line_of_int, + dx=-0.00001 + ), + about_point=self.coords_to_point( + np.cos(t()), np.sin(t()) + ) + ) + ) + tangent_label.next_to(tangent,UP,buff=.1) + tangent_group=VGroup(tangent,tangent_label) + + # self.add(tangent_group) + self.play(Write(tangent_group)) + self.wait(.6) + + self.tangent_label=tangent_label + self.tangent_group=tangent_group + + def get_dot_product_graph(self): + t = self.t_tracker.get_value + + self.start_x= 1.3 ; self.end_x=2.3 + + t_axis= self.get_graph( + lambda x : 2.0/5, + x_min= self.start_x, + x_max= self.end_x, + ).set_style( + stroke_width=4, + ) + + dot_prod_axis= Vector(3*UP).next_to( + t_axis,LEFT,buff=-.1 + ).set_color(GREEN) + dot_prod_label=TexMobject( + "\\vec F","\\cdot","\\vec T", + stroke_width= 1.5, + ).next_to(dot_prod_axis,UP).scale(.8) + dot_prod_label[0].set_color(YELLOW) + dot_prod_label[2].set_color(ORANGE) + + dot_prod_graph_axes= VGroup(t_axis,dot_prod_axis) + + self.write_about_graph() + self.wait(1) + # self.add(dot_prod_graph_axes) + self.play(Write(dot_prod_graph_axes)) + self.show_the_parameter(t,t_axis) + self.wait(.6) + self.play(ReplacementTransform( + self.vect_label,dot_prod_label[0] + )) + self.play(ReplacementTransform( + self.tangent_label,dot_prod_label[1:3] + )) + self.show_graph_area(t_axis) + + self.dot_prod_graph_axes= dot_prod_graph_axes + self.dot_prod_label= dot_prod_label + + def write_about_graph(self): + graph_text=TextMobject( + "Graph",r" of the "," vector",r" $-$\\ ", + r"tangent",r" dot product\\", + " with the parameter ","$t$" + ) + graph_text.set_color_by_tex_to_color_map({ + "Graph":GREEN, "vector": YELLOW, + "tangent":ORANGE, "$t$":RED + }) + graph_text.to_corner(UR,buff=.5) + self.graph_text=graph_text + + self.remove(self.vect_tangent_text) + self.play(Write(graph_text),run_time=4) + + def show_the_parameter(self,t,t_axis): + t_dot=Dot(color=RED).next_to(t_axis,LEFT,buff=0) + t_dot.add_updater(lambda obj : + obj.move_to(self.c2g([t(),0]) + )) + t_text=TextMobject("$t$=").next_to(t_dot,UP,buff=.25) + t_val=always_redraw( + lambda: DecimalNumber( + t()/PI, + color=GOLD + ).next_to(t_text,RIGHT,buff=0).scale(.8) + ) + t_label=VGroup( + t_text,t_val + ).set_color(RED) + + + pi = TexMobject( + "\\pi ", + color=GOLD, + ).next_to(t_val,RIGHT,buff=0.05) + t_label.add(pi) + + t_label.add_updater(lambda label : + label.next_to(t_dot,UP) + ) + + t_group=VGroup(t_dot,t_label) + + # self.add(t_group) + self.play(Write(t_group)) + + self.t_group= t_group + + + def show_graph_area(self,t_axis): + t = self.t_tracker.get_value + dot_prod_graph= always_redraw(lambda: Polygon( + *[ + self.c2g([t,-2*np.cos(t)**2*np.sin(t)]) + for t in np.arange(0,t(),0.01) + ], + *[ + self.c2g([t,0]) + for t in [ t(),0 ] + ], + stroke_width=2.5, + fill_color=TEAL_D, + fill_opacity=.6, + )) + + self.add(dot_prod_graph) + + self.dot_prod_graph=dot_prod_graph + + def c2g(self,coord): + """ get points for the dot product graph + from its coordinates""" + + return self.coords_to_point( + self.start_x+coord[0]/(PI/2), + 2.0/5+coord[1]/2, + ) + + + def write_area_as_intgral_value(self): + area_text=TextMobject( + "Value of the "," line"," integral in the", + r"Vector field\\", + "is equal to this ","area" + ) + area_text.set_color_by_tex_to_color_map({ + "Vector field": BLUE, "line":PINK, "area":TEAL_C + }) + area_text.to_edge(TOP,buff=MED_SMALL_BUFF) + + + self.play(FadeOut(VGroup( + self.line_of_int, + self.vector_group, + self.tangent_group, + self.t_group, + self.dot_prod_graph_axes, + self.dot_prod_label, + self.graph_text + ) + )) + area= self.dot_prod_graph.copy().scale(1.3) + area.next_to(area_text,DOWN,buff=1.5) + + # self.add(area_text) + self.play(Write(area_text),run_time=4) + self.play(ReplacementTransform( + self.dot_prod_graph, + area + )) + self.wait(.5) + + #uploaded by Somnath Pandit.FSF2020_Line_Integrals + + diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file4_helix.py b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file5_helix.py index 50aeb33..50aeb33 100644 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file4_helix.py +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file5_helix.py diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file1_scalar_line_int_as_sum.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/gifs/file1_scalar_line_int_as_sum.gif Binary files differindex 1984b08..17ea3f0 100644 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file1_scalar_line_int_as_sum.gif +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/gifs/file1_scalar_line_int_as_sum.gif diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/gifs/file2_scalar_line_integral.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/gifs/file2_scalar_line_integral.gif Binary files differnew file mode 100644 index 0000000..f9a8f98 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/gifs/file2_scalar_line_integral.gif diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file3_vector_line_int_as_sum.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/gifs/file3_vector_line_int_as_sum.gif Binary files differindex 46b35bc..46b35bc 100644 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file3_vector_line_int_as_sum.gif +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/gifs/file3_vector_line_int_as_sum.gif diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/gifs/file4_vector_line_integral.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/gifs/file4_vector_line_integral.gif Binary files differnew file mode 100644 index 0000000..1be7e1e --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/gifs/file4_vector_line_integral.gif diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file4_helix.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/gifs/file5_helix.gif Binary files differindex ceedb1f..ceedb1f 100644 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file4_helix.gif +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/gifs/file5_helix.gif diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/README.md b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/README.md new file mode 100644 index 0000000..d8c0956 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/README.md @@ -0,0 +1,11 @@ +**file1_vector_fields** + + +**file2_grad_of_scalar_function** + + +**file3_constructing_vector_field** + + +**file4_slope_field** + diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/file1_vector_fields.py b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/file1_vector_fields.py new file mode 100644 index 0000000..6b1b686 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/file1_vector_fields.py @@ -0,0 +1,350 @@ +from manimlib.imports import * + +class VectorFields(ThreeDScene): + + CONFIG = { + "axes_config": { + "x_min": -4, + "x_max": 4, + "y_min": -4, + "y_max": 4, + "z_min": -3, + "z_max": 3, + "a":-4 ,"b": 4, "c":-4 , "d":4, + "axes_shift": ORIGIN+2*LEFT, + "x_axis_config": { + "tick_frequency": 1, + # "include_tip": False, + }, + "y_axis_config": { + "tick_frequency": 1, + # "include_tip": False, + }, + "z_axis_config": { + "tick_frequency": 1, + # "include_tip": False, + }, + "num_axis_pieces": 10, + }, + "default_graph_style": { + "stroke_width": 2, + "stroke_color": WHITE, + }, + "default_vector_field_config": { + "delta_x": .5, + "delta_y": .5, + "x_min": -3, + "x_max": 3, + "y_min": -3, + "y_max": 3, + "min_magnitude": 0, + "max_magnitude": 4, + "colors": [BLUE,GREEN,ORANGE,RED], + "length_func": lambda norm : .45*sigmoid(norm), + "opacity": 1.0, + "vector_config": { + "stroke_width":3.5, + "max_tip_length_to_length_ratio": 0.35, + "max_stroke_width_to_length_ratio": 8, + }, + }, + + } + + + def construct(self): + + self.setup_axes() + axes=self.axes + + self.set_camera_orientation(distance=35, + phi=0 * DEGREES, + theta=-90 * DEGREES, + ) + self.move_camera(frame_center=axes.c2p(0,0,0)) + + self.show_2d_field() + self.wait(3) + + self.show_3d_field() + self.begin_ambient_camera_rotation(rate=-.3,) + self.wait(1.5) + axes.x_axis.rotate( + -90 * DEGREES, LEFT, + about_point=axes.c2p(0, 0, 0), + ), + axes.y_axis.rotate( + 90 * DEGREES, UP, + about_point=axes.c2p(0, 0, 0), + ), + self.move_camera( + # distance=20, + phi=85 * DEGREES, + rate_func=linear, + run_time=8 + ) + self.wait(5) + + + def show_2d_field(self): + d2_field_text=TexMobject( + r"\vec F(x,y)=-y\hat i+x\hat j", + stroke_width=1.5 + ).set_color_by_gradient( + *self.default_vector_field_config["colors"] + ) + d2_field_text.to_corner(UR,buff=.5) + + d2_field = self.get_vector_field( + lambda v: np.array([ + -v[1], + v[0], + 0 + ]), + ) + self.add_fixed_in_frame_mobjects(d2_field_text) + # self.add(d2_field) + self.play(Write(d2_field_text)) + self.play(FadeIn(d2_field)) + + self.d2_field=d2_field + self.d2_field_text=d2_field_text + + def show_3d_field(self): + d3_field_text=TexMobject( + r"\vec F(x,y,z)=-y\hat i+x\hat j+0 \hat k", + stroke_width=1.5 + ).set_color_by_gradient( + *self.default_vector_field_config["colors"] + ) + d3_field_text.to_corner(UR,buff=.5) + + d3_field= self.get_vector_field( + lambda v: np.array([ + -v[1], + v[0], + 0 + # v[0]*v[2] + ]), + z_min=-2, + z_max= 2, + delta_x= 1, + delta_y= 1, + delta_z= 1, + length_func=lambda norm : .5*sigmoid(norm), + opacity= 1, + ThreeD=True + ) + + self.remove(self.d2_field,self.d2_field_text) + self.add_fixed_in_frame_mobjects(d3_field_text) + # self.add(d3_field) + self.play(Write(d3_field_text)) + self.play(FadeIn(d3_field)) + + def get_vector_field(self,func,ThreeD=False,**kwargs): + config = dict() + config.update(self.default_vector_field_config) + config.update(kwargs) + if ThreeD: + vector_field= VectorField3D(func,**config) + else: + vector_field= VectorField(func,**config) + + vector_field.move_to(self.axes.c2p(0,0,0)) + self.vector_field=vector_field + + return vector_field + + + +#------------------------------------------------------- + #customize 3D axes + def get_three_d_axes(self, include_labels=True, include_numbers=False, **kwargs): + config = dict(self.axes_config) + config.update(kwargs) + axes = ThreeDAxes(**config) + axes.set_stroke(width=2) + self.axes=axes + + if include_numbers: + self.add_axes_numbers(axes) + + if include_labels: + self.add_axes_labels(axes) + + # Adjust axis orientation + axes.x_axis.rotate( + -0 * DEGREES, LEFT, + about_point=axes.c2p(0, 0, 0), + ) + axes.y_axis.rotate( + 0 * DEGREES, UP, + about_point=axes.c2p(0, 0, 0), + ) + + return axes + + + def setup_axes(self): + axes = self.get_three_d_axes(include_labels=True) + axes.scale(1) + # axes.center() + axes.shift(axes.axes_shift) + + self.add(axes) + self.axes = axes + + def add_axes_numbers(self, axes): + x_axis = axes.x_axis + y_axis = axes.y_axis + tex_vals_x = [ + + ("1", axes.b), + ] + tex_vals_y=[ + + ("1", axes.d) + ] + x_labels = VGroup() + y_labels = VGroup() + for tex, val in tex_vals_x: + label = TexMobject(tex) + label.scale(1) + label.next_to(x_axis.n2p(val), DOWN) + # label.rotate(180 * DEGREES) + x_labels.add(label) + x_axis.add(x_labels) + x_axis.numbers = x_labels + + for tex, val in tex_vals_y: + label = TexMobject(tex) + label.scale(1) + label.next_to(y_axis.n2p(val), LEFT) + label.rotate(90 * DEGREES) + y_labels.add(label) + + y_axis.add(y_labels) + y_axis.numbers = y_labels + + return axes + + def add_axes_labels(self, axes): + x_label = TexMobject("x") + x_label.next_to(axes.x_axis.get_end(), RIGHT) + axes.x_axis.label = x_label + + y_label = TextMobject("y") + y_label.rotate(90 * DEGREES, OUT) + y_label.next_to(axes.y_axis.get_end(), UP) + axes.y_axis.label = y_label + + z_label = TextMobject("z") + z_label.rotate(90 * DEGREES, RIGHT) + z_label.next_to(axes.z_axis.get_zenith(), LEFT) + axes.z_axis.label = z_label + for axis in axes: + axis.add(axis.label) + return axes + +#----------------------------------------------------------- + +class VectorField3D(VGroup): + CONFIG = { + "delta_x": 1, + "delta_y": 1, + "delta_z": 1, + "x_min": int(np.floor(-FRAME_WIDTH / 2)), + "x_max": int(np.ceil(FRAME_WIDTH / 2)), + "y_min": int(np.floor(-FRAME_HEIGHT / 2)), + "y_max": int(np.ceil(FRAME_HEIGHT / 2)), + "z_min":-1, + "z_max": 1, + "min_magnitude": 0, + "max_magnitude": 4, + "colors": DEFAULT_SCALAR_FIELD_COLORS, + # Takes in actual norm, spits out displayed norm + "length_func": lambda norm: 0.45 * sigmoid(norm), + "opacity": 1.0, + "vector_config": {}, + } + '''Position of the tip of vector to be fixed''' + def __init__(self, func, **kwargs): + VGroup.__init__(self, **kwargs) + self.func = func + self.rgb_gradient_function = get_rgb_gradient_function( + self.min_magnitude, + self.max_magnitude, + self.colors, + flip_alphas=False + ) + x_range = np.arange( + self.x_min, + self.x_max + self.delta_x, + self.delta_x + ) + y_range = np.arange( + self.y_min, + self.y_max + self.delta_y, + self.delta_y + ) + z_range = np.arange( + self.z_min, + self.z_max + self.delta_z, + self.delta_z + ) + for x, y, z in it.product(x_range, y_range, z_range): + point = x * RIGHT + y * UP + z * OUT + # print(point) + self.add(self.get_vector(point)) + self.set_opacity(self.opacity) + + def get_vector(self, point, **kwargs): + output = np.array(self.func(point)) + norm = get_norm(output) + if norm == 0: + output *= 0 + else: + output *= self.length_func(norm) / norm + # norm=np.linalg.norm(output) + vector_config = dict(self.vector_config) + vector_config.update(kwargs) + + vect = Vector( + output, + **vector_config + ) + vect_perp=vect.copy().rotate(PI/2, axis=output) + vect= VGroup(vect,vect_perp) + # vect= self.position_vector(vect,point,output,norm) + vect.shift(point) + fill_color = rgb_to_color( + self.rgb_gradient_function(np.array([norm]))[0] + ) + vect.set_color(fill_color) + return vect + + '''def position_vector(self,vect,point,output,norm): + theta,phi=self.get_theta_phi(output,norm) + vect.rotate(PI-phi, axis=RIGHT) + vect.rotate(theta, axis=IN) + # or apply rotation matrix? + return vect + + def get_theta_phi(self,output,norm): + if norm==0: + phi,theta=0,0 + else: + phi= np.arccos(output[-1]/norm) + if output[0]!=0: + theta= np.arccos(output[0]/(norm*np.sin(phi))) + else: + theta= 0 + return phi,theta''' + + + + #uploaded by Somnath Pandit. FSF2020_Vector_fields + + + diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/file2_grad_of_scalar_function.py b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/file2_grad_of_scalar_function.py new file mode 100644 index 0000000..231b15c --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/file2_grad_of_scalar_function.py @@ -0,0 +1,320 @@ +from manimlib.imports import * + +class GradOfScalarFunc(ThreeDScene): + + CONFIG = { + "axes_config": { + "x_min": -3, + "x_max": 3, + "y_min": -3, + "y_max": 3, + "z_min": 0, + "z_max": 3, + "a":-3 ,"b": 3, "c":-3 , "d":3, + "axes_shift": ORIGIN+IN+LEFT, + "x_axis_config": { + "tick_frequency": 1, + # "include_tip": False, + }, + "y_axis_config": { + "tick_frequency": 1, + # "include_tip": False, + }, + "z_axis_config": { + "tick_frequency": 1, + # "include_tip": False, + }, + "num_axis_pieces": 1, + }, + "default_graph_style": { + "stroke_width": 2, + "stroke_color": WHITE, + }, + "default_vector_field_config": { + "delta_x": .5, + "delta_y": .5, + "x_min": -3, + "x_max": 3, + "y_min": -3, + "y_max": 3, + "min_magnitude": 0, + "max_magnitude": 2, + "colors": [BLUE,GREEN,GREEN,ORANGE,RED], + "length_func": lambda norm : .45*sigmoid(norm), + "opacity": 1.0, + "vector_config": { + "stroke_width":6 + }, + }, + "default_surface_config": { + "fill_opacity": 0.5, + "checkerboard_colors": [BLUE_D], + "stroke_width": .5, + "stroke_color": WHITE, + "stroke_opacity": 0.2, + }, + } + + + def construct(self): + + self.setup_axes() + axes=self.axes + + self.set_camera_orientation(distance=35, + phi=80 * DEGREES, + theta=-80 * DEGREES, + ) + + scalar_fn_text=TexMobject("f(x,y)=","\cos(xy)").set_color(BLUE) + scalar_fn_text.to_corner(UR,buff=.6) + + operator=TexMobject("\\vec\\nabla").next_to( + scalar_fn_text,LEFT,buff=.2 + ).set_color(GOLD) + + grad_text=TexMobject(r"\dfrac{\partial f}{\partial x} \hat i+\dfrac{\partial f}{\partial y} \hat j+\dfrac{\partial f}{\partial z} \hat k").set_color(GOLD) + grad_text.next_to(scalar_fn_text,DOWN).scale(.9) + + VGroup( + grad_text[0][1], + grad_text[0][9], + grad_text[0][17] + ).set_color(BLUE) + VGroup( + grad_text[0][5:8], + grad_text[0][13:16], + grad_text[0][21:23] + ).set_color(WHITE) + + vector_field_text=TexMobject( + r"\vec F&=-y\sin(xy)\hat i\\ &-x\sin(xy)\hat j" + ).set_color_by_gradient( + *self.default_vector_field_config["colors"] + ) + vector_field_text.next_to(scalar_fn_text,DOWN) + + + '''always generate the scalar field first''' + s_field=self.get_scalar_field( + func= lambda x ,y : np.cos(x*y/2), + dn=.25 + ) + v_field=self.get_vector_field( + lambda v: np.array([ + -(v[1]-axes.c2p(0,0,0)[1])*np.sin((v[0]-axes.c2p(0,0,0)[0])*(v[1]-axes.c2p(0,0,0)[1])), + -(v[0]-axes.c2p(0,0,0)[0])*np.sin((v[0]-axes.c2p(0,0,0)[0])*(v[1]-axes.c2p(0,0,0)[1])), + 0, + ]), + on_surface=True, + ) + + self.add_fixed_in_frame_mobjects(scalar_fn_text) + + self.begin_ambient_camera_rotation(rate=.2) + self.play(Write(s_field),run_time=2) + self.wait(4) + self.stop_ambient_camera_rotation() + + self.add_fixed_in_frame_mobjects(operator) + self.play(Write(operator),FadeOut(scalar_fn_text[1])) + self.add_fixed_in_frame_mobjects(grad_text) + self.play(Write(grad_text)) + self.wait(1.5) + + self.play(FadeOut(grad_text)) + self.add_fixed_in_frame_mobjects(vector_field_text) + show_vec_field=[ + FadeIn(v_field), + Write(vector_field_text), + ] + # self.play(*show_vec_field,run_time=.5) + self.begin_ambient_camera_rotation(rate=.2) + self.move_camera( + # distance=20, + phi=50 * DEGREES, + added_anims=show_vec_field, + run_time=3 + ) + + self.wait(5) + self.stop_ambient_camera_rotation() + + fadeout= [FadeOut(s_field)] + # self.play(*fadeout) + self.move_camera( + # distance=20, + phi=0 * DEGREES, + theta=-90 * DEGREES, + added_anims=fadeout, + run_time=2 + ) + self.wait(2) + + + + + + def get_scalar_field(self,func,dn=.5): + surface= self.get_surface( + lambda x , y: + func(x,y), + ) + + self.surface_points=self.get_points(func,dn) + return surface + + def get_points(self,func,dn): + axes=self.axes + + x_vals=np.arange(axes.a,axes.b,dn) + y_vals=np.arange(axes.c,axes.d,dn) + points=[] + for x_val in x_vals: + for y_val in y_vals: + points+=[axes.c2p(x_val,y_val,func(x_val,y_val)+.05)] + return points + + def get_vector_field(self,func,on_surface=True,**kwargs): + config = dict() + config.update(self.default_vector_field_config) + config.update(kwargs) + vector_field= VectorField(func,**config) + vector_field.move_to(self.axes.c2p(0,0,0)) + self.vector_field=vector_field + + if on_surface: + vector_field=self.get_vectors_on_surface() + + return vector_field + + + + def get_vectors_on_surface(self): + vectors_on_surface = VGroup(*[ + self.vector_field.get_vector(point) + for point in self.surface_points + ]) + + return vectors_on_surface + + + def get_surface(self, func, **kwargs): + axes=self.axes + config = { + "u_min": axes.a, + "u_max": axes.b, + "v_min": axes.c, + "v_max": axes.d, + "resolution": ( + 4*(axes.y_max - axes.y_min) // axes.y_axis.tick_frequency, + 4*(axes.x_max - axes.x_min) // axes.x_axis.tick_frequency, + ), + } + + config.update(self.default_surface_config) + config.update(kwargs) + return ParametricSurface( + lambda x,y : axes.c2p( + x, y, func(x, y) + ), + **config + ) + + +#------------------------------------------------------- + #customize 3D axes + def get_three_d_axes(self, include_labels=True, include_numbers=False, **kwargs): + config = dict(self.axes_config) + config.update(kwargs) + axes = ThreeDAxes(**config) + axes.set_stroke(width=2) + self.axes=axes + + if include_numbers: + self.add_axes_numbers(axes) + + if include_labels: + self.add_axes_labels(axes) + + # Adjust axis orientation + axes.x_axis.rotate( + -90 * DEGREES, LEFT, + about_point=axes.c2p(0, 0, 0), + ) + axes.y_axis.rotate( + 90 * DEGREES, UP, + about_point=axes.c2p(0, 0, 0), + ) + + return axes + + + def setup_axes(self): + axes = self.get_three_d_axes(include_labels=True) + axes.scale(1) + # axes.center() + axes.shift(axes.axes_shift) + + self.add(axes) + self.axes = axes + + def add_axes_numbers(self, axes): + x_axis = axes.x_axis + y_axis = axes.y_axis + tex_vals_x = [ + + ("1", axes.b), + ("-1", axes.a), + ] + tex_vals_y=[ + + ("1", axes.d) + ] + x_labels = VGroup() + y_labels = VGroup() + for tex, val in tex_vals_x: + label = TexMobject(tex) + label.scale(1) + label.next_to(x_axis.n2p(val), DOWN) + # label.rotate(180 * DEGREES) + x_labels.add(label) + x_axis.add(x_labels) + x_axis.numbers = x_labels + + for tex, val in tex_vals_y: + label = TexMobject(tex) + label.scale(1) + label.next_to(y_axis.n2p(val), LEFT) + label.rotate(90 * DEGREES) + y_labels.add(label) + + y_axis.add(y_labels) + y_axis.numbers = y_labels + + return axes + + def add_axes_labels(self, axes): + x_label = TexMobject("x") + x_label.next_to(axes.x_axis.get_end(), RIGHT) + axes.x_axis.label = x_label + + y_label = TextMobject("y") + y_label.rotate(90 * DEGREES, OUT) + y_label.next_to(axes.y_axis.get_end(), UP) + axes.y_axis.label = y_label + + z_label = TextMobject("z") + z_label.rotate(90 * DEGREES, RIGHT) + z_label.next_to(axes.z_axis.get_zenith(), LEFT) + axes.z_axis.label = z_label + for axis in axes: + axis.add(axis.label) + return axes + + + + #uploaded by Somnath Pandit. FSF2020_Vector_fields + + + diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/file3_constructing_vector_field.py b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/file3_constructing_vector_field.py new file mode 100644 index 0000000..fc56306 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/file3_constructing_vector_field.py @@ -0,0 +1,196 @@ +from manimlib.imports import * + + +class VectorFields(GraphScene): + CONFIG = { + "x_min" : -4, + "x_max" : 4, + "y_min" : -4, + "y_max" : 4, + "graph_origin": ORIGIN+2.5*LEFT, + "x_axis_width": 7, + "y_axis_height": 7, + "x_tick_frequency": 1, + "y_tick_frequency": 1, + "default_vector_field_config": { + "delta_x": .5, + "delta_y": .5, + "min_magnitude": 0, + "max_magnitude": 4, + "colors": [GREEN,GREEN,YELLOW,RED], + "length_func": lambda n: n/2.5, + "opacity": .75, + "vector_config": { + "stroke_width":6, + "max_stroke_width_to_length_ratio":4 + }, + }, + + "a":-3.5 ,"b": 4, "c": -3.5 ,"d": 4, + } + + def construct(self): + X = RIGHT*self.x_axis_width/(self.x_max- self.x_min) + Y = UP*self.y_axis_height/(self.y_max- self.y_min) + self.X=X ;self.Y=Y + + self.setup_axes(animate=False) + vector_function = lambda v: np.array([ + (v[0]-self.graph_origin[0])*(v[1]-self.graph_origin[1]), + -(v[0]-self.graph_origin[0]), + 0, + ]) + + vector_field=self.get_vector_field( + vector_function, + colors= [GREEN] + ) + + self.show_points() + self.wait(.5) + self.show_func_machine() + self.wait(1) + self.produce_vectors(vector_field) + self.wait(.5) + self.scale_down_vectors(vector_function) + self.wait(2) + + + + def show_points(self): + dn=1 + x_vals=np.arange(self.a,self.b,dn) + y_vals=np.arange(self.c,self.d,dn) + dots=VGroup() + for x_val in x_vals: + for y_val in y_vals: + dot=Dot( + self.coords_to_point(x_val,y_val), + radius=.05, + color=TEAL, + ) + dots.add(dot) + self.play(ShowCreation(dots, run_time=1)) + self.dots=dots + + def show_func_machine(self): + machine=RoundedRectangle( + height=2, + width=3.5, + color=PURPLE, + stroke_width=8 + ).to_edge(RIGHT, buff=.4) + + machine_label=TexMobject( + r"\vec F=xy\hat i-x\hat j", + stroke_width=1.5, + ).set_color_by_gradient( + *self.default_vector_field_config["colors"] + ).next_to(machine,IN) + + machine=VGroup(machine,machine_label) + self.add(machine) + + self.func_machine=machine + + + def produce_vectors(self,vector_field): + count,i=3,0 + self.run_time=1 + non_scaled_vectors=VGroup() + for dot in self.dots: + if i==count: + self.run_time=.05 + position=dot.get_center() + vect= vector_field.get_vector(position) + self.go_to_machine(dot) + self.take_vec_from_machine(vect,position) + non_scaled_vectors.add(vect) + i+=1 + + self.non_scaled_vectors=non_scaled_vectors + + def go_to_machine(self,dot): + if self.run_time>.5: + self.play(ApplyMethod( + dot.next_to, + self.func_machine,4*UP, + ), + run_time=self.run_time + ) + self.dot=dot + + def take_vec_from_machine(self,vect,position): + vect.next_to(self.func_machine,DOWN,buff=.1) + + if self.run_time>.5: + point_coord=TexMobject( + "(x_i,y_i)" + ).next_to(self.dot,RIGHT,buff= .01).scale(.75) + input_point=VGroup(point_coord, self.dot) + self.play( + ApplyMethod( + input_point.shift,DOWN, + run_time=self.run_time + )), + self.play( + FadeOut(input_point), + run_time=.2 + ) + self.play( + FadeIn(vect), + run_time=.4 + ) + else: + self.remove(self.dot) + self.add(vect) + self.wait(1.0/15) + + self.play( + vect.move_to,position, + run_time=self.run_time + ) + + def scale_down_vectors(self,vector_function): + scale_down_text=TextMobject( + r"Vectors are rescaled\\ for clarity\\ and \\", + r"colors are used to \\ indicate magnitudes", + stroke_width=1.2 + ) + scale_down_text[0][:7].set_color(BLUE) + scale_down_text[1].set_color_by_gradient( + *self.default_vector_field_config["colors"] + ) + scale_down_text.to_corner(UR).shift(DOWN) + scaled_vector_field= self.get_vector_field( + vector_function, + length_func= lambda norm : .75*sigmoid(norm) + ) + for vector in self.non_scaled_vectors: + scaled_vect= scaled_vector_field.get_vector(vector.get_center()) + vector.target= scaled_vect + + self.play(FadeOut(self.func_machine)) + self.play(Write(scale_down_text)) + self.wait(1.2) + self.play(LaggedStartMap( + MoveToTarget, self.non_scaled_vectors, + run_time=3 + )) + + def get_vector_field(self,func,**kwargs): + config = dict() + config.update(self.default_vector_field_config) + config.update(kwargs) + vector_field= VectorField(func,**config) + + return vector_field + + + + + +#uploaded by Somnath Pandit. FSF2020_Vector_fields + + + diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/file4_slope_field.py b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/file4_slope_field.py new file mode 100644 index 0000000..8ebb6f5 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/file4_slope_field.py @@ -0,0 +1,247 @@ +from manimlib.imports import * + + +class SlopeFields(GraphScene): + CONFIG = { + "x_min" : -2, + "x_max" : 2, + "y_min" : -2, + "y_max" : 2, + "graph_origin": ORIGIN+2.5*LEFT, + "x_axis_width": 7, + "y_axis_height": 7, + "x_tick_frequency": 1, + "y_tick_frequency": 1, + "default_slope_field_config": { + "delta_x": .2, + "delta_y": .2, + "opacity": 1, + "color": BLUE_A, + "slope_length_factor": .2, + "line_config": { + "stroke_width":2.5, + }, + }, + + "a":-1.9 ,"b": 2, "c": -1.9 ,"d": 2, + } + + def construct(self): + X = RIGHT*self.x_axis_width/(self.x_max- self.x_min) + Y = UP*self.y_axis_height/(self.y_max- self.y_min) + self.X=X ;self.Y=Y + + self.setup_axes(animate=False) + + slope_field=self.get_slope_field( + lambda x,y:-2.0*(x-self.graph_origin[0])*(y-self.graph_origin[1]), + x_min=self.graph_origin[0]+self.a, + x_max=self.graph_origin[0]+self.b, + y_min=self.graph_origin[1]+self.c, + y_max=self.graph_origin[1]+self.d, + color= GREEN_B + ) + + self.show_points() + self.wait(.5) + self.show_func_machine() + self.wait(1) + self.produce_slopes(slope_field) + # self.add(slope_field) + self.glimpse_of_solutions() + self.wait(2) + + + + + def show_points(self): + dn=1.0/5 + x_vals=np.arange(self.a,self.b,dn) + y_vals=np.arange(self.c,self.d,dn) + dots=VGroup() + for x_val in x_vals: + for y_val in y_vals: + dot=Dot( + self.coords_to_point(x_val,y_val), + radius=.04, + color=TEAL, + ) + dots.add(dot) + self.play(ShowCreation(dots, run_time=1)) + self.dots=dots + + def show_func_machine(self): + machine=RoundedRectangle( + height=3, + width=4, + color=PURPLE, + stroke_width=8 + ).to_edge(RIGHT, buff=.4) + + machine_label=TextMobject( + r"Line segment\\ with slope\\"," $y'=-2xy$", + stroke_width=1.2, + color=BLUE + ).next_to(machine,IN) + machine_label[1].set_color(GREEN) + machine=VGroup(machine, machine_label) + self.play(FadeIn(machine)) + + self.func_machine = machine + + + def produce_slopes(self,slope_field): + count,i=3,0 + self.run_time=1 + for dot in self.dots: + if i==count: + self.run_time=.05 + position=dot.get_center() + line= slope_field.get_slope(position) + self.go_to_machine(dot) + self.take_line_from_machine(line,position) + i+=1 + + def go_to_machine(self,dot): + if self.run_time>.5: + self.play(ApplyMethod( + dot.next_to, + self.func_machine,4*UP, + ), + run_time=self.run_time + ) + self.dot=dot + + def take_line_from_machine(self,vect,position): + + if self.run_time>.5: + vect.next_to(self.func_machine,DOWN,buff=.1) + self.play( + ApplyMethod( + self.dot.shift,DOWN, + run_time=self.run_time + )), + self.play( + FadeOut(self.dot), + run_time=.2 + ) + self.play( + FadeIn(vect), + run_time=.4 + ) + self.play( + ApplyMethod( + vect.move_to,position + ), + run_time=self.run_time + ) + else: + self.remove(self.dot) + self.add(vect) + vect.move_to(position) + + + def get_slope_field(self,func,**kwargs): + config = dict() + config.update(self.default_slope_field_config) + config.update(kwargs) + slope_field= SlopeField(func,**config) + + return slope_field + + def glimpse_of_solutions(self): + sol_text= TextMobject( + r"The solution curves\\ seem to be like...", + color= BLUE, + stroke_width=1.2 + ) + sol_text.to_corner(UR, buff=1) + condition_text= TextMobject( + r"for different\\ initial conditions", + color= GOLD, + stroke_width=1.1 + ) + condition_text.next_to(sol_text,DOWN,buff=1) + solution1 = self.get_graph( + lambda x : np.exp(-x**2), + x_min = self.a, + x_max = self.b, + color = PINK) + solution2 = self.get_graph( + lambda x : .5*np.exp(-x**2), + x_min = self.a, + x_max = self.b, + color = YELLOW) + solution3 = self.get_graph( + lambda x : 1.5*np.exp(-x**2), + x_min = self.a, + x_max = self.b, + color = BLUE) + solution4 = self.get_graph( + lambda x : -np.exp(-x**2), + x_min = self.a, + x_max = self.b, + color = RED_E) + + self.play(FadeOut(self.func_machine)) + self.play(Write(sol_text)) + self.wait(.6) + self.play(ShowCreation(solution1)) + self.play(Write(condition_text)) + self.play(ShowCreation(solution2)) + self.wait(.5) + self.play(ShowCreation(solution3)) + self.wait(.5) + self.play(ShowCreation(solution4)) + + +class SlopeField(VGroup): + CONFIG = { + "delta_x": 0.5, + "delta_y": 0.5, + "x_min": int(np.floor(-FRAME_WIDTH / 2)), + "x_max": int(np.ceil(FRAME_WIDTH / 2)), + "y_min": int(np.floor(-FRAME_HEIGHT / 2)), + "y_max": int(np.ceil(FRAME_HEIGHT / 2)), + "opacity": 1.0, + "color": WHITE, + "slope_length_factor": .25, + "line_config": {}, + } + + def __init__(self, func, **kwargs): + VGroup.__init__(self, **kwargs) + self.func = func + + x_range = np.arange( + self.x_min, + self.x_max + self.delta_x, + self.delta_x + ) + y_range = np.arange( + self.y_min, + self.y_max + self.delta_y, + self.delta_y + ) + for x, y in it.product(x_range, y_range): + point = x * RIGHT + y * UP + self.add(self.get_slope(point)) + self.set_opacity(self.opacity) + + def get_slope(self, point, **kwargs): + slope = self.func(*point[:2]) + line_config = dict(self.line_config) + line_config.update(kwargs) + line = Line(ORIGIN,self.slope_length_factor*RIGHT, **line_config) + line.move_to(point).rotate(np.arctan(slope/3.2)) + + line.set_color(self.color) + return line + + + + +#uploaded by Somnath Pandit. FSF2020_Vector_fields + + + diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/gifs/file1_vector_fields.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/gifs/file1_vector_fields.gif Binary files differnew file mode 100644 index 0000000..96e50ac --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/gifs/file1_vector_fields.gif diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/gifs/file2_grad_of_scalar_function.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/gifs/file2_grad_of_scalar_function.gif Binary files differnew file mode 100644 index 0000000..c1ab66a --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/gifs/file2_grad_of_scalar_function.gif diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/gifs/file3_constructing_vector_field.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/gifs/file3_constructing_vector_field.gif Binary files differnew file mode 100644 index 0000000..6a57cab --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/gifs/file3_constructing_vector_field.gif diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/gifs/file4_slope_field.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/gifs/file4_slope_field.gif Binary files differnew file mode 100644 index 0000000..c39ec54 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/gifs/file4_slope_field.gif diff --git a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/divergence-gauss-theorem/README.md b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/divergence-gauss-theorem/README.md index e69de29..17fcde0 100644 --- a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/divergence-gauss-theorem/README.md +++ b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/divergence-gauss-theorem/README.md @@ -0,0 +1,4 @@ +**file1_flux@_various_points.py**
+
+**file2_different_valuesof_Div.py**
+
diff --git a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/divergence-gauss-theorem/file1_flux@_various_points.gif b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/divergence-gauss-theorem/file1_flux@_various_points.gif Binary files differnew file mode 100644 index 0000000..6c32b94 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/divergence-gauss-theorem/file1_flux@_various_points.gif diff --git a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/divergence-gauss-theorem/file1_flux@_various_points.py b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/divergence-gauss-theorem/file1_flux@_various_points.py new file mode 100644 index 0000000..6727982 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/divergence-gauss-theorem/file1_flux@_various_points.py @@ -0,0 +1,60 @@ +from manimlib.imports import * +def pendulum_vector_field_func(point): + #theta, omega = point[:2] + return np.array([ + 5*point[0]+point[1], + 3*point[1]+3*point[1], + 0, + ]) +class SF(Scene): + CONFIG = { + #"func": cylinder_flow_vector_field, + "flow_time": 5, + } + def initialize_vector_field(self): + self.vector_field = VectorField( + pendulum_vector_field_func, + ) + self.vector_field.sort(get_norm) + def construct(self): + # plane = NumberPlane(color=RED) + # plane.add(plane.get_axis_labels()) + # self.add(plane) + + A=TextMobject("The net flux through the green circular region is zero",tex_to_color_map={"green": GREEN}) + B=TextMobject("The net flux through the blue circular region is non-zero",tex_to_color_map={"blue": BLUE}) + + c1=Circle(color=GREEN, radius=1.5) + c1.shift(4*LEFT+2.2*UP) + c2=Circle(color=BLUE, radius=1.5) + + + + + self.play(ShowCreation(A)) + self.wait(0.5) + self.play(ApplyMethod(A.shift, (0.8*UP+0.2*LEFT))) + self.play(ShowCreation(B)) + # self.play(ApplyMethod(B.shift, (2*UP))) + self.wait(2) + self.play(FadeOut(A),FadeOut(B)) + self.initialize_vector_field() + field = self.vector_field + self.play(ShowCreation(field), run_time=4) + self.play(ShowCreation(c1)) + self.play(ShowCreation(c2)) + self.wait(1) + lines = StreamLines( + pendulum_vector_field_func, + virtual_time=3, + min_magnitude=0, + max_magnitude=2, + ) + self.add(AnimatedStreamLines( + lines, + line_anim_class=ShowPassingFlash + )) + self.wait(2) + phase_point = VectorizedPoint(1*UP+1*RIGHT) + self.add(move_along_vector_field(phase_point, pendulum_vector_field_func)) + self.wait(2) diff --git a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/divergence-gauss-theorem/file2_different_valuesof_Div.gif b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/divergence-gauss-theorem/file2_different_valuesof_Div.gif Binary files differnew file mode 100644 index 0000000..477c311 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/divergence-gauss-theorem/file2_different_valuesof_Div.gif diff --git a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/divergence-gauss-theorem/file2_different_valuesof_Div.py b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/divergence-gauss-theorem/file2_different_valuesof_Div.py new file mode 100644 index 0000000..921047d --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/divergence-gauss-theorem/file2_different_valuesof_Div.py @@ -0,0 +1,91 @@ +from manimlib.imports import * +class Div(Scene): + def construct(self): + one=TextMobject(r"Div$ \vec{F} < 0$ ").set_color(RED) + two=TextMobject(r"Div$ \vec{F} = 0$ ").set_color(BLUE) + three=TextMobject(r"Div$ \vec{F} > 0$ ").set_color(YELLOW) + + one.shift(2.3*DOWN) + two.shift(2.3*DOWN) + three.shift(2.3*DOWN) + + + a=Dot(color=RED) + a.shift(0.1*LEFT) + b=Dot(color=BLUE) + b.shift(0.1*LEFT) + c=Dot(color=YELLOW) + c.shift(0.1*LEFT) + + rot=[0*DEGREES,45*DEGREES,90*DEGREES,135*DEGREES,180*DEGREES,225*DEGREES,270*DEGREES,315*DEGREES] + rot2=[180*DEGREES,180*DEGREES,180*DEGREES,180*DEGREES,180*DEGREES,180*DEGREES,180*DEGREES,180*DEGREES] + shift=[RIGHT,0.7*RIGHT+0.7*UP,UP,0.7*LEFT+0.7*UP,LEFT,0.7*LEFT+0.7*DOWN,DOWN,0.7*RIGHT+0.7*DOWN] + shift2=[RIGHT,RIGHT+UP,RIGHT+DOWN,UP,DOWN,LEFT,LEFT+UP,LEFT+DOWN] + + + + u=[Vector(color=RED),Vector(color=RED),Vector(color=RED),Vector(color=RED), + Vector(color=RED),Vector(color=RED),Vector(color=RED),Vector(color=RED)] + + + [u[i].rotate(rot[i]) for i in range(8) ] + [u[i].rotate(rot2[i]) for i in range(8) ] + [u[i].shift(shift[i]) for i in range(8) ] + + + divone=VGroup(*u) + divone.shift(0.6*LEFT) + + + v=[Vector(color=BLUE),Vector(color=BLUE),Vector(color=BLUE),Vector(color=BLUE), + Vector(color=BLUE),Vector(color=BLUE),Vector(color=BLUE),Vector(color=BLUE)] + + + [v[i].rotate(45*DEGREES) for i in range(8)] + [v[i].shift(shift2[i]) for i in range(8) ] + + divtwo=VGroup(*v) + divtwo.shift(0.6*LEFT) + + + w=[Vector(color=YELLOW),Vector(color=YELLOW),Vector(color=YELLOW),Vector(color=YELLOW), + Vector(color=YELLOW),Vector(color=YELLOW),Vector(color=YELLOW),Vector(color=YELLOW)] + + + [w[i].rotate(rot[i]) for i in range(8)] + [w[i].shift(shift[i]) for i in range(8) ] + + + divthree=VGroup(*w) + divthree.shift(0.6*LEFT) + + + + + self.play(ShowCreation(a),ShowCreation(divone)) + self.play(ShowCreation(one)) + self.wait(1) + self.play(FadeOut(a),FadeOut(divone),FadeOut(one)) + + self.play(ShowCreation(b),ShowCreation(divtwo)) + self.play(ShowCreation(two)) + self.wait(1) + self.play(FadeOut(b),FadeOut(divtwo),FadeOut(two)) + + + self.play(ShowCreation(c),ShowCreation(divthree)) + self.play(ShowCreation(three)) + self.wait(1) + self.play(FadeOut(c),FadeOut(divthree),FadeOut(three)) + self.wait(0.5) + + + + + + + + + + + diff --git a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/README.md b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/README.md index 0af7aa1..97d6d10 100644 --- a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/README.md +++ b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/README.md @@ -1,7 +1,5 @@ -**file1_flux_through_sphere.py** - -**file2_mobius_strip.py** - +**file1_flux_through_circle.py** + **file3_normal_vector.py**  **file4_cube_surface.py** diff --git a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file1_flux_through_circle.gif b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file1_flux_through_circle.gif Binary files differnew file mode 100644 index 0000000..c00076b --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file1_flux_through_circle.gif diff --git a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file1_flux_through_circle.py b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file1_flux_through_circle.py new file mode 100644 index 0000000..e418a96 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file1_flux_through_circle.py @@ -0,0 +1,43 @@ +from manimlib.imports import * +def pendulum_vector_field_func(point): + #theta, omega = point[:2] + return np.array([ + point[0], + point[1], + point[2], + ]) +class F2D(Scene): + CONFIG = { + # "func": cylinder_flow_vec or_field, + "flow_time": 5, + } + def initialize_vector_field(self): + self.vector_field = VectorField( + pendulum_vector_field_func, + ) + self.vector_field.sort(get_norm) + def construct(self): + # plane = NumberPlane(color=RED) + # plane.add(plane.get_axis_labels()) + # self.add(plane) + self.initialize_vector_field() + + field = self.vector_field + c1=Circle(radius=3,color=BLUE) + self.play(ShowCreation(field), run_time=7) + self.play(ShowCreation(c1)) + self.wait(3) + lines = StreamLines( + pendulum_vector_field_func, + virtual_time=3, + min_magnitude=0, + max_magnitude=2, + ) + self.add(AnimatedStreamLines( + lines, + line_anim_class=ShowPassingFlash + )) + self.wait(2) + phase_point = VectorizedPoint(1*UP+1*RIGHT) + self.add(move_along_vector_field(phase_point, pendulum_vector_field_func)) + self.wait(2) diff --git a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file1_flux_through_sphere.gif b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file1_flux_through_sphere.gif Binary files differdeleted file mode 100644 index 43327bf..0000000 --- a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file1_flux_through_sphere.gif +++ /dev/null diff --git a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file1_flux_through_sphere.py b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file1_flux_through_sphere.py deleted file mode 100644 index e07715e..0000000 --- a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file1_flux_through_sphere.py +++ /dev/null @@ -1,50 +0,0 @@ -from manimlib.imports import * -class fluxsphere(ThreeDScene): - - - def construct(self): - s = Sphere(checkerboard_colors=[BLUE_D,BLUE_D]) - s.scale(2.3) - - n = VGroup( - *[self.n(*self.func(u, v)) - for u in np.arange(0, PI, 0.4) - for v in np.arange(0, TAU, 0.8)] - ) - - - - self.move_camera(0.8 * PI / 2, -0.45 * PI) - self.play(Write(s)) - # self.play(Write(f)) - self.play(ShowCreation(n), run_time=4) - # self.add(n) - self.begin_ambient_camera_rotation(rate=0.1) - self.wait(5) - - - def func(self, u, v): - return [ - np.cos(v) * np.sin(u), - np.sin(v) * np.sin(u), - np.cos(u) - ] - - def vect(self, x, y, z): - return np.array([ - x, y, z - ]) - - def n(self, x, y, z): - vect = np.array([ - x, - y, - z - ]) - - mag = math.sqrt(vect[0] ** 2 + vect[1] ** 2 + vect[2] ** 2) - v = Vector( - (1.5/mag) * vect, - color=RED_B, - stroke_width=4).shift(2*x * RIGHT + 2*y * UP + 2*z * OUT) - return v diff --git a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file2_mobius_strip.py b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file2_mobius_strip.py deleted file mode 100644 index 31b1990..0000000 --- a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file2_mobius_strip.py +++ /dev/null @@ -1,81 +0,0 @@ -from manimlib.imports import * - -class Mobius(ThreeDScene): - def construct(self): - axes=ThreeDAxes() - - - - R=2.5 - - - mobius = ParametricSurface( - lambda u, v: np.array([ - (R+u*np.cos(v/2))*np.cos(v), - (R+u*np.cos(v/2))*np.sin( v), - u*np.sin(v/2) - ]), - u_min = -0.5, u_max = 0.5, v_min = 0, v_max = 2*PI, - - resolution=(6, 32)).fade(0.5) #Resolution of the surfaces - circle=Circle(radius=2.5, color=BLUE) - - - - mobius.rotate(PI/2, axis=RIGHT) - mobius.rotate(PI/2, axis=OUT) - # # mobius.shift(RIGHT+OUT+DOWN) - - - - - - along = ParametricSurface( - lambda u, v: np.array([ - (R+u*np.cos(v/2))*np.cos(v), - (R+u*np.cos(v/2))*np.sin(v), - 0 - ]), - u_min = -0.5, u_max = 0.5, v_min = 0, v_max = 2*PI, - - resolution=(6, 32)).fade(0.5) #Resolution of the surfaces - circle=Circle(radius=2.5, color=BLUE) - - - - - - - - - - - - - - - - - - - - - - - - self.set_camera_orientation(phi=75 * DEGREES,theta=-75*DEGREES) - - self.play(Write(mobius)) - - self.wait(1) - self.begin_ambient_camera_rotation(rate=0.65) - - self.wait(10) - self.stop_ambient_camera_rotation() - self.wait(1) - - - - - - diff --git a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file4_cube_surface.gif b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file4_cube_surface.gif Binary files differindex c6101cf..001edb8 100644 --- a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file4_cube_surface.gif +++ b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file4_cube_surface.gif diff --git a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file4_cube_surface.py b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file4_cube_surface.py index 9301a00..146d955 100644 --- a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file4_cube_surface.py +++ b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file4_cube_surface.py @@ -1,7 +1,4 @@ from manimlib.imports import* - - - class cuber(ThreeDScene): def construct(self): @@ -41,6 +38,7 @@ class cuber(ThreeDScene): n1=TextMobject(r"$\vec{n}$",color=YELLOW) n1.scale(0.8) n1.rotate(PI/2,axis=RIGHT) + n1.rotate(PI,axis=OUT) n1.shift(3*RIGHT+1.3*OUT+DOWN) spaceloc = [[0,0,2],[1,0,2],[-1,0,2],[2,0,2],[-2,0,2],[3,0,2],[-3,0,2], @@ -59,158 +57,128 @@ class cuber(ThreeDScene): [0,3,2],[1,3,2],[-1,3,2],[2,3,2],[-2,3,2],[3,3,2],[-3,3,2]] - veclist1=[Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E)] + veclist1=[Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY)] - [veclist1[i].rotate(PI/4,axis=RIGHT) for i in range(10,30,1)] - [veclist1[i].rotate(PI/4,axis=RIGHT) for i in range(40,80,2)] - [veclist1[i].rotate(PI/6,axis=OUT) for i in range(98)] - [veclist1[i].rotate(PI/8,axis=DOWN) for i in range(98)] + [veclist1[i].rotate(PI/4,axis=RIGHT) for i in range(42)] + [veclist1[i].rotate(PI/6,axis=OUT) for i in range(42)] + [veclist1[i].rotate(PI/8,axis=DOWN) for i in range(42)] vectorfield1=VGroup(*veclist1) - [veclist1[i].shift(spaceloc[i]) for i in range(98)] + [veclist1[i].shift(spaceloc[i]) for i in range(42)] - veclist2=[Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E)] + veclist2=[Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY)] - [veclist2[i].rotate(PI/4,axis=RIGHT) for i in range(10,30,1)] - [veclist2[i].rotate(PI/4,axis=RIGHT) for i in range(40,80,2)] - [veclist2[i].rotate(PI/6,axis=OUT) for i in range(98)] - [veclist2[i].rotate(PI/8,axis=DOWN) for i in range(98)] + [veclist2[i].rotate(PI/4,axis=RIGHT) for i in range(42)] + [veclist2[i].rotate(PI/4,axis=RIGHT) for i in range(42)] + [veclist2[i].rotate(PI/6,axis=OUT) for i in range(42)] + [veclist2[i].rotate(PI/8,axis=DOWN) for i in range(42)] vectorfield2=VGroup(*veclist2) - [veclist2[i].shift(spaceloc[i]) for i in range(98)] + [veclist2[i].shift(spaceloc[i]) for i in range(42)] - veclist3=[Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector()] + veclist3=[Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY)] - [veclist3[i].rotate(PI/4,axis=RIGHT) for i in range(10,30,1)] - [veclist3[i].rotate(PI/4,axis=RIGHT) for i in range(40,80,2)] - [veclist3[i].rotate(PI/6,axis=OUT) for i in range(98)] - [veclist3[i].rotate(PI/8,axis=DOWN) for i in range(98)] + [veclist3[i].rotate(PI/4,axis=RIGHT) for i in range(42)] + [veclist3[i].rotate(PI/4,axis=RIGHT) for i in range(42)] + [veclist3[i].rotate(PI/6,axis=OUT) for i in range(42)] + [veclist3[i].rotate(PI/8,axis=DOWN) for i in range(42)] vectorfield3=VGroup(*veclist3) - [veclist3[i].shift(spaceloc[i]) for i in range(98)] + [veclist3[i].shift(spaceloc[i]) for i in range(42)] - veclist4=[Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector()] + veclist4=[Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY)] - [veclist4[i].rotate(PI/4,axis=RIGHT) for i in range(10,30,1)] - [veclist4[i].rotate(PI/4,axis=RIGHT) for i in range(40,80,2)] - [veclist4[i].rotate(PI/6,axis=OUT) for i in range(98)] - [veclist4[i].rotate(PI/8,axis=DOWN) for i in range(98)] + [veclist4[i].rotate(PI/4,axis=RIGHT) for i in range(42)] + [veclist4[i].rotate(PI/4,axis=RIGHT) for i in range(42)] + [veclist4[i].rotate(PI/6,axis=OUT) for i in range(42)] + [veclist4[i].rotate(PI/8,axis=DOWN) for i in range(42)] vectorfield4=VGroup(*veclist4) - [veclist4[i].shift(spaceloc[i]) for i in range(98)] + [veclist4[i].shift(spaceloc[i]) for i in range(42)] vectorfield1.shift(1.5*DOWN) vectorfield2.shift(IN+1.5*DOWN) vectorfield3.shift(2*IN+1.5*DOWN) - vectorfield4.shift(3*IN+1.5*DOWN) + vectorfield4.shift(3*IN+1.5*DOWN) + vectors=[vectorfield1,vectorfield2,vectorfield3,vectorfield4] vectorfield=VGroup(*vectors) - vectorfield.scale(1.25) + vectorfield.scale(1.3) + - fv=[Vector(color=ORANGE),Vector(color=ORANGE),Vector(color=ORANGE),Vector(color=ORANGE), - Vector(color=ORANGE),Vector(color=ORANGE),Vector(color=ORANGE),Vector(color=ORANGE), - Vector(color=ORANGE),Vector(color=ORANGE),Vector(color=ORANGE),Vector(color=ORANGE), - Vector(color=ORANGE),Vector(color=ORANGE),Vector(color=ORANGE),Vector(color=ORANGE), + fv=[Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY) ] - spaceloc2 = [[1.5,0.5,0.5],[1.5,1,0.5],[1.5,1.5,0.5],[1.5,2,0.5], - [1.5,0.5,1],[1.5,1,1],[1.5,1.5,1],[1.5,2,1], - [1.5,0.5,1.5],[1.5,1,1.5],[1.5,1.5,1.5],[1.5,2,1.5], - [1.5,0.5,2],[1.5,1,2],[1.5,1.5,2],[1.5,2,2]] - - [fv[i].rotate(PI/4,axis=RIGHT) for i in range(1)] - [fv[i].rotate(PI/6,axis=OUT) for i in range(16)] - [fv[i].rotate(PI/8,axis=DOWN) for i in range(16)] - [fv[i].shift(spaceloc2[i]) for i in range(16)] + spaceloc2 = [[1.5,0.5,0.5],[1.5,1,0.5],[1.5,1.5,0.5], + [1.5,0.5,1],[1.5,1,1],[1.5,1.5,1], + [1.5,0.5,1.5],[1.5,1,1.5],[1.5,1.5,1.5] + ] + [fv[i].rotate(PI/4,axis=RIGHT) for i in range(9)] + [fv[i].rotate(PI/6,axis=OUT) for i in range(9)] + [fv[i].rotate(PI/8,axis=DOWN) for i in range(9)] + [fv[i].shift(spaceloc2[i]) for i in range(9)] fvfield=VGroup(*fv) - fvfield.shift(0.5*IN+2*DOWN) + fvfield.shift(2*DOWN) + fvfield.scale(1.3) - flux=TextMobject("Flux through one side of the cube").set_color(ORANGE) - flux.shift(3*UP+1.5*LEFT) + flux=TextMobject("Flux through one side of the cube").set_color(GOLD) + flux.shift(3.5*UP+0.5*LEFT) + alll=[vectorfield1,vectorfield2,vectorfield3,vectorfield4,fvfield] + alllvectors=VGroup(*alll) self.set_camera_orientation(phi=70 * DEGREES,theta=-75*DEGREES) self.play(ShowCreation(axes),ShowCreation(axis_label)) - self.play(ShowCreation(vectorfield)) - self.add(fvfield) - self.begin_ambient_camera_rotation(rate=0.01) + self.begin_ambient_camera_rotation(rate=0.2) + self.play(ShowCreation(alllvectors)) + # self.add(fvfield) self.play(ShowCreation(cube, run_time=1)) @@ -223,6 +191,6 @@ class cuber(ThreeDScene): # self.play(ShowCreation(flux)) self.wait(1) self.play(ShowCreation(v1),ShowCreation(n1)) - self.wait(6) - # self.stop_ambient_camera_rotation() - + self.wait(5) + self.stop_ambient_camera_rotation() + self.wait(1) diff --git a/FSF-2020/calculus/intro-to-calculus/introderivative/derivative1.py b/FSF-2020/calculus/intro-to-calculus/introderivative/derivative1.py new file mode 100644 index 0000000..79a6fc6 --- /dev/null +++ b/FSF-2020/calculus/intro-to-calculus/introderivative/derivative1.py @@ -0,0 +1,55 @@ +from manimlib.imports import * +class derivative1(GraphScene, Scene): + def setup(self): + GraphScene.setup(self) + CONFIG = { + "y_max" : 4, + "y_min" : -2, + "x_max" : 4, + "x_min" : -2, + "y_tick_frequency" : 1, + "x_tick_frequency" : 1, + "axes_color" : WHITE, + "num_graph_anchor_points": 3000, #this is the number of points that graph manim + "graph_origin" : ORIGIN+2*DOWN+4*LEFT, + "x_labeled_nums": list(range(-2,5)), + "y_labeled_nums": list(range(-2,5)), + "x_axis_label":"$x$", + "y_axis_label":r"$f(x)=y= 3-\frac { 3 }{ 2 } x$", + "x_axis_width": 5, + "y_axis_height": 5, + } + def construct(self): + #XTD = self.x_axis_width/(self.x_max - self.x_min) + #YTD = self.y_axis_height/(self.y_max - self.y_min) + + text1 = TextMobject("") + text2 = TexMobject("{y}_{2}-{y}_{1}") + text2 = TexMobject("{x}_{2}-{x}_{1}") + text3 = TexMobject(r"m\quad =\frac { { y }_{ 2 }-{ y }_{ 1 } }{ { x }_{ 2 }-{ x }_{ 1 } }").move_to(np.array([3,0,0])) + text4 = TexMobject(r"m\quad =\frac { 3 }{ -2 }").move_to(np.array([3,0,0])) + text5 = TexMobject(r"m\quad =\quad -1.5").move_to(np.array([3,0,0])) + self.setup_axes() + graph_1 = self.get_graph(lambda x : 3-1.5*x, color = GREEN_SCREEN, x_min = -1, x_max = 3) + graph_2 = self.get_graph(lambda x : 3.1-1.5*x, color = ORANGE, x_min = 0, x_max = 2) + dot1 = Dot() + dot2 = SmallDot(self.graph_origin+1.7*RIGHT, color = PINK) + dot3 = SmallDot(self.graph_origin+2.5*UP, color = RED_B) + vec1 = Vector(2.5*DOWN, color = PINK).shift(self.graph_origin+2.5*UP) + vec2 = Vector(1.7*RIGHT, color = RED_B).shift(self.graph_origin) + brace1 = Brace(vec1, LEFT) + brace2 = Brace(vec2, DOWN) + br1text = brace1.get_text(r"${y}_{2}-{y}_{1}$").next_to(brace1, LEFT) + br2text = brace2.get_text(r"${x}_{2}-{x}_{1}$").next_to(brace2, DOWN) + self.play(ShowCreation(graph_1), ShowCreation(dot2), ShowCreation(dot3)) + self.play(MoveAlongPath(dot1, graph_2), ShowCreation(vec1), ShowCreation(vec2), run_time = 3) + self.wait(1) + self.play(ShowCreation(brace1), ShowCreation(brace2)) + self.play(ShowCreation(br1text), ShowCreation(br2text)) + self.wait(2) + self.play(GrowFromCenter(text3)) + self.wait(2.5) + self.play(ReplacementTransform(text3, text4)) + self.wait(2) + self.play(ReplacementTransform(text4, text5)) + self.wait(2) diff --git a/FSF-2020/calculus/intro-to-calculus/introderivative/derivative2.py b/FSF-2020/calculus/intro-to-calculus/introderivative/derivative2.py new file mode 100644 index 0000000..d6aab15 --- /dev/null +++ b/FSF-2020/calculus/intro-to-calculus/introderivative/derivative2.py @@ -0,0 +1,78 @@ +from manimlib.imports import * +class derivative2(GraphScene, MovingCameraScene): + def setup(self): + GraphScene.setup(self) + MovingCameraScene.setup(self) + CONFIG = { + "y_max" : 100, + "y_min" : 0, + "x_max" : 10, + "x_min" : 0, + "y_tick_frequency" : 100, + "x_tick_frequency" : 10, + "axes_color" : WHITE, + "num_graph_anchor_points": 3000, #this is the number of points that graph manim + "graph_origin" : ORIGIN, + "x_labeled_nums": None,#list(range(0,11)), + "y_labeled_nums": None,#list(range(0,101))[::10], + "x_axis_label":"$x$", + "y_axis_label":"$f(x)$", + "x_axis_width": 5, + "y_axis_height": 5, + "start_x" : 2, + "start_dx" : 6, + "df_color" : YELLOW, + "dx_color" : GREEN, + "secant_line_color" : MAROON_B, + "zoomed_camera_frame_starting_position": ORIGIN+2*DOWN+6*LEFT, + } + def construct(self): + self.setup() + self.camera_frame.save_state() + self.graph_origin = ORIGIN+2*DOWN+6*LEFT + self.setup_axes() + graph23 = self.get_graph(lambda x : x**2+7, color = GREEN_SCREEN, x_min = 0, x_max = 10) + graph24 = self.get_graph(lambda x : x**2+7, color = GREEN_SCREEN, x_min = 8, x_max = 2.01) + line_1 = DashedVMobject(Line(np.array([-5,-2,0]), np.array([-5,-1.42,0]))) + textdef = TextMobject("") + text1 = TexMobject("{ x }_{ 0 }").move_to(np.array([-5,-2.2,0])) + text2 = TextMobject("The line becomes tangential to the curve").move_to(self.graph_origin+RIGHT+0.5*UP).scale(0.01) + text3 = TexMobject(r"\frac { df }{ dx } =\frac { f({ x }_{ 0 }+h)-f({ x }_{ 0 }) }{ h-0 }").move_to(2*RIGHT) + text4 = TexMobject(r"\frac { df }{ dx } =\lim _{ h\rightarrow 0 }{ \frac { f({ x }_{ 0 }+h)-f({ x }_{ 0 }) }{ h } }").move_to(2*RIGHT) + squareobj = Square(side_length = 15).move_to(self.graph_origin+RIGHT+0.53*UP) + ss_group = self.get_secant_slope_group( + self.start_x, graph23, + dx = self.start_dx, + dx_label = "h", + df_label = "df", + df_line_color = self.df_color, + dx_line_color = self.dx_color, + secant_line_color = self.secant_line_color, + dot_df_top = True, + dot_dx_start = True, + dot_df_top_label = "Q", + dot_dx_start_label = "P", + secant_line_length = 8 + ) + self.play(ShowCreation(graph23)) + self.wait() + self.play(ShowCreation(ss_group.secant_line)) + self.add(text1) + self.play(ShowCreation(line_1)) + self.wait(3) + self.play(ShowCreation(ss_group.dx_line)) + self.play(ShowCreation(ss_group.dx_label)) + self.play(ShowCreation(ss_group.df_line)) + self.play(Write(ss_group.df_label)) + self.play(ShowCreation(ss_group.dot_df_top), ShowCreation(ss_group.dot_dx_start)) + self.play(ShowCreation(ss_group.dot_df_top_label), ShowCreation(ss_group.dot_dx_start_label)) + self.wait() + self.play(ShowCreation(text3)) + self.wait(2) + self.play(ReplacementTransform(text3, text4)) + self.animate_secant_slope_group_change(ss_group, target_dx = 0.01, run_time = 5) + self.wait(2) + self.play(self.camera_frame.set_width,0.2,self.camera_frame.move_to,squareobj,run_time = 2) + self.wait() + self.play(ShowCreation(text2)) + self.wait(3) diff --git a/FSF-2020/calculus/intro-to-calculus/introderivative/derivative3.py b/FSF-2020/calculus/intro-to-calculus/introderivative/derivative3.py new file mode 100644 index 0000000..ebbacb1 --- /dev/null +++ b/FSF-2020/calculus/intro-to-calculus/introderivative/derivative3.py @@ -0,0 +1,57 @@ +from manimlib.imports import * +class derivative3(GraphScene, Scene): + def setup(self): + Scene.setup(self) + #ZoomedScene.setup(self) + CONFIG = { + "y_max" : 8, + "y_min" : 0, + "x_max" : 11, + "x_min" : 0, + "y_tick_frequency" : 1, + "x_tick_frequency" : 1, + "axes_color" : WHITE, + "num_graph_anchor_points": 3000, #this is the number of points that graph manim + "graph_origin" : ORIGIN+3*DOWN+6.5*LEFT, + "x_labeled_nums": list(range(0,12))[::1], + "y_labeled_nums": list(range(0,9))[::1], + "x_axis_label":"$t$", + "y_axis_label":"$s$", + "x_axis_width": 5, + "y_axis_height": 5, + } + def construct(self): + XTD = self.x_axis_width/(self.x_max - self.x_min) + YTD = self.y_axis_height/(self.y_max - self.y_min) + + self.setup_axes() + graph_1 = self.get_graph(lambda x : -(x-2)**2+4, color = GOLD_A, x_min = 0, x_max = 1.5) + graph_2 = self.get_graph(lambda x : 1*x+2.25, color = GOLD_A, x_min = 1.5, x_max = 5) + graph_3 = self.get_graph(lambda x : 7.25, color = GOLD_A, x_min = 5, x_max = 8) + graph_4 = self.get_graph(lambda x : -3.625*x + 36.25, color = GOLD_A, x_min = 8, x_max = 10) + + self.y_max = 5 + self.x_max = 10 + self.x_min = 0 + self.y_min = -5 + self.x_labeled_nums = list(range(0,11)) + self.y_labeled_nums = list(range(-5,6))[::1] + self.x_axis_label = r"$t$" + self.y_axis_label = r"$v$" + self.y_tick_frequency = 1 + self.x_tick_frequency = 1 + self.graph_origin = ORIGIN+1*RIGHT + self.setup_axes() + graph_5 = self.get_graph(lambda x : 2*(x-2)+4, color = GREEN_SCREEN, x_min = 0, x_max = 1.5) + graph_6 = self.get_graph(lambda x : 3, color = GREEN_SCREEN, x_min = 1.5, x_max = 5) + graph_7 = self.get_graph(lambda x : 0, color = GREEN_SCREEN, x_min = 5, x_max = 8) + graph_8 = self.get_graph(lambda x : -3.625, color = GREEN_SCREEN, x_min = 8, x_max = 10) + line1 = DashedVMobject(Line(self.graph_origin+2.5*RIGHT, self.graph_origin+2.5*RIGHT+1.5*UP)) + line2 = DashedVMobject(Line(self.graph_origin+4*RIGHT, self.graph_origin+4*RIGHT+1.835*DOWN)) + self.play(ShowCreation(graph_1), ShowCreation(graph_5), run_time = 3) + self.play(ShowCreation(graph_2), ShowCreation(graph_6), run_time = 3) + self.add(line1) + self.play(ShowCreation(graph_3), ShowCreation(graph_7), run_time = 3) + self.add(line2) + self.play(ShowCreation(graph_4), ShowCreation(graph_8), run_time = 3) + self.wait(3) diff --git a/FSF-2020/calculus/intro-to-calculus/limit/Test1.py b/FSF-2020/calculus/intro-to-calculus/limit/Test1.py new file mode 100644 index 0000000..bd7d2a6 --- /dev/null +++ b/FSF-2020/calculus/intro-to-calculus/limit/Test1.py @@ -0,0 +1,34 @@ +from manimlib.imports import * +class Test1(GraphScene): + CONFIG = { + "y_max" : 5, + "y_min" : -5, + "x_max" : 5, + "x_min" : -5, + "y_tick_frequency" : 1, + "x_tick_frequency" : 1, + "axes_color" : BLUE, + "num_graph_anchor_points": 3000, #this is the number of points that graph manim + "graph_origin" : ORIGIN, + "x_labeled_nums": list(range(-5,6)), + "y_labeled_nums": list(range(-5,6)), + "x_axis_label":"$x$", + "y_axis_label":"${ f }_{ 1 }(x)$" + } + def construct(self): + self.setup_axes() + cir1 = Circle(radius = 0.1, color = BLUE) + graph_1 = self.get_graph(lambda x : x+2, + color = GREEN, + x_min = -5, # Domain 1 + x_max = +1.9 + ) + graph_2 =self.get_graph(lambda x : x+2, + color = GREEN, + x_min = 2.1, # Domain 2 + x_max = 5 + ) + cir1.move_to(np.array([1,2,0])) + self.play(ShowCreation(graph_1)) + self.play(ShowCreation(cir1)) + self.play(ShowCreation(graph_2)) diff --git a/FSF-2020/calculus/intro-to-calculus/limit/Test2.py b/FSF-2020/calculus/intro-to-calculus/limit/Test2.py new file mode 100644 index 0000000..0efb565 --- /dev/null +++ b/FSF-2020/calculus/intro-to-calculus/limit/Test2.py @@ -0,0 +1,26 @@ +from manimlib.imports import * +class Test2(GraphScene): + CONFIG = { + "y_max" : 5, + "y_min" : -5, + "x_max" : 5, + "x_min" : -5, + "y_tick_frequency" : 1, + "x_tick_frequency" : 1, + "axes_color" : BLUE, + "num_graph_anchor_points": 3000, #this is the number of points that graph manim + "graph_origin" : ORIGIN, + "x_labeled_nums": list(range(-5,6)), + "y_labeled_nums": list(range(-5,6)), + "x_axis_label":"$x$", + "y_axis_label":"${ f }_{ 1 }(x)$" + } + def construct(self): + self.setup_axes() + graph_1 = self.get_graph(lambda x : x+2, + color = GREEN, + x_min = -5, # Domain 1 + x_max = +5 + ) + self.play(ShowCreation(graph_1)) + self.wait() diff --git a/FSF-2020/calculus/intro-to-calculus/limit/limit1.py b/FSF-2020/calculus/intro-to-calculus/limit/limit1.py new file mode 100644 index 0000000..fe5cb1e --- /dev/null +++ b/FSF-2020/calculus/intro-to-calculus/limit/limit1.py @@ -0,0 +1,105 @@ +from manimlib.imports import * +class limit1(GraphScene,MovingCameraScene): + def setup(self): + GraphScene.setup(self) + MovingCameraScene.setup(self) + CONFIG = { + "y_max" : 1, + "y_min" : 0, + "x_max" : 1, + "x_min" : -1, + "y_tick_frequency" : 0.2, + "x_tick_frequency" : 0.2, + "axes_color" : WHITE, + "num_graph_anchor_points": 3000, #this is the number of points that graph manim + "graph_origin" : ORIGIN+3*DOWN, + "x_labeled_nums": list(range(-1,2)), + "y_labeled_nums": list(range(0,2)), + "x_axis_label":"$x$", + "y_axis_label":"$f(x)$", + "x_axis_width": 10, + "y_axis_height": 5, + } + def construct(self): + XTD = self.x_axis_width/(self.x_max - self.x_min) + YTD = self.y_axis_height/(self.y_max - self.y_min) + + dot1 = SmallDot(np.array([0.025,-2.975,0])) + dot2 = SmallDot(np.array([-0.025,-2.975,0])) + sqr = Square(side_length = 15.0).move_to(np.array([0,-3,0])) + brline1 = DashedVMobject(Line(np.array([0.15,-3,0]), np.array([0.15,-2.85,0]))) + brline2 = DashedVMobject(Line(np.array([0.025,-3,0]), np.array([0.025,-2.975,0]))) + brline3 = DashedVMobject(Line(np.array([-0.15,-3,0]), np.array([-0.15,-2.85,0]))) + brline4 = DashedVMobject(Line(np.array([-0.025,-3,0]), np.array([-0.025,-2.975,0]))) + textdef = TextMobject("") + text003 = TextMobject("0.03").move_to(np.array([0.15,-3.05,0])).scale(0.1) + textazero1 = TexMobject(r"\approx 0").move_to(np.array([0.04,-3.05,0])).scale(0.1) + textazero2 = TexMobject(r"\approx 0").move_to(np.array([-0.04,-3.05,0])).scale(0.1) + textm003 = TextMobject("-0.03").move_to(np.array([-0.15,-3.05,0])).scale(0.1) + text2 = TextMobject("Let f(x) = |x|. We'll check neighbourhood of origin") + text3 = TextMobject("h has to be a very small number greater than 0").move_to(np.array([0,-3.3,0])).scale(0.2) + text4 = TextMobject("The point travels through range of neighbourhood").move_to(np.array([0,-3.3,0])).scale(0.19) + text5 = TextMobject("let h be equal to 0.03").move_to(np.array([0,-3.3,0])).scale(0.25) + text6 = TextMobject("Notice how the point never touches the origin").move_to(np.array([0,-3.3,0])).scale(0.2) + text7 = TextMobject("Green line shows the Right hand neighbourhood of origin").move_to(np.array([0,-3.3,0])).scale(0.17) + text8 = TextMobject("The point is approaching (0,0) for the values of x which are positive").move_to(np.array([0,-3.3,0])).scale(0.1) + text9 = TextMobject("Values of x are tending to 0 from positive side").move_to(np.array([0,-3.3,0])).scale(0.19) + text10 = TexMobject(r"\text {Notation for this is }",r"x\rightarrow { 0 }^{ + }").move_to(np.array([0,-3.3,0])).scale(0.25) + text11 = TextMobject("Similar case can be made for negative values of x").move_to(np.array([0,-3.3,0])).scale(0.19) + text12 = TextMobject("The point is approaching (0,0) for the values of x which are negative").move_to(np.array([0,-3.3,0])).scale(0.1) + text13 = TextMobject("Values of x are tending to 0 from negative side").move_to(np.array([0,-3.3,0])).scale(0.19) + text14 = TexMobject(r"\text {Notation for this is }",r"x\rightarrow { 0 }^{ - }").move_to(np.array([0,-3.3,0])).scale(0.25) + + + self.play(FadeIn(text2), run_time = 1.5) + self.wait(2.5) + self.setup_axes() + graph_1 = self.get_graph(lambda x : x, color = RED, x_min = 0, x_max = 1) + graph_2 = self.get_graph(lambda x : -x, color = RED, x_min = 0, x_max = -1) + graph_3 = self.get_graph(lambda x : x,color = RED, x_min = 0.005, x_max = 0.03) + graph_4 = self.get_graph(lambda x : x,color = GREEN_SCREEN, x_min = 0.03, x_max = 0.005) + graph_5 = self.get_graph(lambda x : -x,color = GREEN_SCREEN, x_min = -0.03, x_max = -0.005) + grp1 = VGroup(graph_1,graph_2) + grp2 = VGroup(brline2, textazero1) + grp3 = VGroup(textazero2, textm003, brline3, brline4) + self.play(ShowCreation(grp1)) + self.add(sqr) + self.play(ReplacementTransform(text2, text3)) + self.camera_frame.save_state() + self.play(self.camera_frame.set_width,2.25,self.camera_frame.move_to,sqr,run_time = 2) + self.wait(2.5) + self.play(ReplacementTransform(text3, text4), ShowCreation(dot1)) + self.wait(2.5) + self.play(ReplacementTransform(text4, text5), ShowCreation(brline1), ShowCreation(text003)) + self.wait(2.5) + for i in range(0,3): + self.play(MoveAlongPath(dot1,graph_3), run_time = 0.5) + self.play(MoveAlongPath(dot1,graph_4), run_time = 0.5) + self.play(ReplacementTransform(text5, text6), ShowCreation(grp2)) + self.wait(2) + self.play(FadeOut(dot1)) + self.add(graph_4) + self.play(ReplacementTransform(text6, text7)) + self.wait(2.5) + self.play(ReplacementTransform(text7,text8)) + for i in range(0,3): + self.play(MoveAlongPath(dot1,graph_4), run_time = 0.7) + self.play(ReplacementTransform(text8, text9)) + self.wait(2.5) + self.play(ReplacementTransform(text9, text10)) + self.wait(2.5) + self.play(ShowCreation(grp3), ReplacementTransform(text10, text11), FadeOut(dot1)) + self.add(graph_5) + for i in range(0,3): + self.play(MoveAlongPath(dot2, graph_5), run_time = 0.7) + self.play(ReplacementTransform(text11, text12)) + self.wait(2.5) + self.play(ReplacementTransform(text12, text13)) + self.wait(2.5) + self.play(ReplacementTransform(text13, text14)) + self.wait(2) + self.play(FadeOut(dot2), ReplacementTransform(text14, textdef)) + self.wait(2) + self.play(Restore(self.camera_frame)) + + self.wait(2.5) diff --git a/FSF-2020/calculus/intro-to-calculus/limit/limit3.py b/FSF-2020/calculus/intro-to-calculus/limit/limit3.py new file mode 100644 index 0000000..a4f07d7 --- /dev/null +++ b/FSF-2020/calculus/intro-to-calculus/limit/limit3.py @@ -0,0 +1,95 @@ +from manimlib.imports import * +class limit3(GraphScene, MovingCameraScene): + def setup(self): + GraphScene.setup(self) + MovingCameraScene.setup(self) + CONFIG = { + "y_max" : 10, + "y_min" : 0, + "x_max" : 100, + "x_min" : 0, + "y_tick_frequency" : 1, + "x_tick_frequency" : 10, + "axes_color" : WHITE, + "num_graph_anchor_points": 3000, #this is the number of points that graph manim + "graph_origin" : ORIGIN+3*DOWN+4*LEFT, + "x_labeled_nums": list(range(0,101))[::10], + "y_labeled_nums": list(range(0,11)), + "x_axis_label":"$x$", + "y_axis_label":"$f(x)$", + "x_axis_width": 10, + "y_axis_height": 5, + } + def construct(self): + XTD = self.x_axis_width/(self.x_max - self.x_min) + YTD = self.y_axis_height/(self.y_max - self.y_min) + sqr1 = Square(side_length = 15).move_to(np.array([1,0.5,0])) + sqr2 = Square(side_length = 15).move_to(np.array([-4,-3,0])) + + textdef = TextMobject("") + text20 = TextMobject("f(x) is not defined at x=50").move_to(np.array([1,0.3,0])).scale(0.2) + text21 = TexMobject(r"\text {f(x) is not defined in interval }",r" (-\infty ,\quad 1]").move_to(np.array([-4,-3.2,0])).scale(0.18) + text22 = TextMobject("1").move_to(np.array([-3.9,-3.05,0])).scale(0.2) + text1 = TexMobject(r"\text {Let }" ,r"f\left( x \right) =\begin{cases} \sqrt { x-1 } ,x\in \quad (1,\infty )-50 \end{cases}") + text2 = TextMobject("Graph of f(x) is ") + text3 = TextMobject("Right hand neighbour of 50 will approximately be 50.000001").move_to(np.array([1,0.3,0])).scale(0.15) + text4 = TextMobject("Left hand neighbour of 50 will approximately be 49.999999").move_to(np.array([1,0.3,0])).scale(0.15) + text5 = TexMobject(r"\text {Hence R.H.L }", r"=\lim _{ x\rightarrow { 50 }^{ + } }{ \sqrt { 50.000001 - 1 } } \approx 7.000000071").move_to(np.array([1,0.3,0])).scale(0.13) + text6 = TexMobject(r"\text{Hence L.H.L }", r" = \lim _{ x\rightarrow { 50 }^{ - } }{ \sqrt { 49.999999-1 } }\approx 6.999999929").move_to(np.array([1,0.3,0])).scale(0.13) + text7 = TextMobject("7.000000071").move_to(np.array([1.9,0.25,0])).scale(0.1) + text8 = TextMobject("6.999999929").move_to(np.array([0.1,0.25,0])).scale(0.1) + text9 = TexMobject(r"6.999999929\quad \approx \quad 7.000000071 \quad \approx 7").move_to(np.array([1,0.25,0])).scale(0.2) + text10 = TexMobject(r"\text{Because LHL }" ,r"\approx" ,r"\text{ RHL, Limit exists at x=50 and equals 7").move_to(np.array([1,0.25,0])).scale(0.13) + text11 = TextMobject("There is no Left hand neighbour of x=1").move_to(np.array([-4,-3.2,0])).scale(0.22) + text12 = TexMobject(r"\therefore\quad \lim _{ x\rightarrow 0 }{ f(x) } \quad =\quad \lim _{ x\rightarrow { 0 }^{ + } }{ f(x) } ").move_to(np.array([-4,-3.2,0])).scale(0.25) + text13 = TexMobject(r"\text {R.H.L =}",r" \lim _{ x\rightarrow { 0 }^{ + } }{ \sqrt { 1.000000000001-1 } } \quad \approx 0").move_to(np.array([-4,-3.2,0])).scale(0.13) + text14 = TexMobject(r"\therefore \quad \lim _{ x\rightarrow 0 }{ f(x)\quad =\quad 0 }").move_to(np.array([-4,-3.2,0])).scale(0.13) + self.camera_frame.save_state() + self.play(ShowCreation(text1)) + self.wait(3) + self.play(ReplacementTransform(text1, text2)) + self.wait() + self.play(ReplacementTransform(text2, textdef)) + self.setup_axes() + self.setup() + graph_1 = self.get_graph(lambda x : (x-1)**(1/2),color = PINK, x_min = 1, x_max = 49.9) + graph_2 = self.get_graph(lambda x : (x-1)**(1/2),color = PINK, x_min = 50.1, x_max = 100) + graph_3 = self.get_graph(lambda x : (x-1)**(1/2),color = PINK, x_min = 1.05, x_max = 1.001) + dot1 = SmallDot(color = PURPLE_A) + cir = Circle(radius = 0.01, color = GREEN_SCREEN).move_to(np.array([1,0.5,0])) + grp1 = VGroup(graph_1, graph_2, cir) + grp2 = VGroup(text7, text8) + self.play(ShowCreation(grp1)) + self.wait(2) + self.play(self.camera_frame.set_width,2.25,self.camera_frame.move_to,sqr1,run_time = 2) + self.wait(1) + self.play(ShowCreation(text20)) + self.wait(2) + self.play(ReplacementTransform(text20, text3)) + self.wait(3) + self.play(ReplacementTransform(text3, text5)) + self.wait(3) + self.play(ReplacementTransform(text5, text7), ShowCreation(text4)) + self.wait(4) + self.play(ReplacementTransform(text4, text6)) + self.wait(3) + self.play(ReplacementTransform(text6, text8)) + self.wait(1.5) + self.play(ReplacementTransform(grp2, text9)) + self.wait(1.5) + self.play(ReplacementTransform(text9, text10)) + self.wait(3) + self.play(self.camera_frame.set_width,2.25,self.camera_frame.move_to,sqr2,run_time = 2) + self.play(ShowCreation(text21), ShowCreation(text22)) + self.play(MoveAlongPath(dot1, graph_3), run_time = 3) + self.wait(3) + self.play(ReplacementTransform(text21, text11)) + self.wait(3) + self.play(ReplacementTransform(text11, text12)) + self.wait(3) + self.play(ReplacementTransform(text12, text13)) + self.wait(2) + self.play(ReplacementTransform(text13, text14)) + self.wait(3) + self.play(ReplacementTransform(text14, textdef)) + self.wait(2) diff --git a/FSF-2020/calculus/intro-to-calculus/limit/limitdef.py b/FSF-2020/calculus/intro-to-calculus/limit/limitdef.py new file mode 100644 index 0000000..15f2845 --- /dev/null +++ b/FSF-2020/calculus/intro-to-calculus/limit/limitdef.py @@ -0,0 +1,73 @@ +from manimlib.imports import * +class limitdef(GraphScene, Scene): + CONFIG = { + "y_max" : 5, + "y_min" : 0, + "x_max" : 5, + "x_min" : -5, + "y_tick_frequency" : 1, + "x_tick_frequency" : 1, + "axes_color" : WHITE, + "num_graph_anchor_points": 3000, #this is the number of points that graph manim + "graph_origin" : ORIGIN+2*DOWN, + "x_labeled_nums": None,#list(range(-1,2)), + "y_labeled_nums": None,#list(range(0,2)), + "x_axis_label":"$x$", + "y_axis_label":"$f(x)$", + "x_axis_width": 10, + "y_axis_height": 5, + } + def construct(self): + Ldot = MediumDot(self.graph_origin+2.1*UP).set_color(GREEN_SCREEN) + adot = MediumDot(self.graph_origin+3*RIGHT).set_color(PINK) + epline1 = DashedVMobject(Line(self.graph_origin+1*LEFT+2.5*UP, self.graph_origin+4*RIGHT+2.5*UP)) + epline2 = DashedVMobject(Line(self.graph_origin+1*LEFT+1.7*UP, self.graph_origin+4*RIGHT+1.7*UP)) + epline3 = DashedVMobject(Line(self.graph_origin+3.5*RIGHT+0.5*DOWN, self.graph_origin+3.5*RIGHT+2.5*UP)) + epline4 = DashedVMobject(Line(self.graph_origin+2.5*RIGHT+0.5*DOWN, self.graph_origin+2.5*RIGHT+2.5*UP)) + Lline = Line(self.graph_origin+2.1*UP, self.graph_origin+3*RIGHT+2.1*UP).set_color(GREEN_SCREEN) + aline = Line(self.graph_origin+3*RIGHT, self.graph_origin+3*RIGHT+2.1*UP).set_color(PINK) + vertical_rectangle = Rectangle(width = 1, height = 0.8, color = PINK, fill_opacity = 0.5, fill_color = LIGHT_PINK).move_to(self.graph_origin+3*RIGHT+2.1*UP) + horizontal_rectangle = Rectangle(width = 1, height = 0.8, color = GREEN_SCREEN, fill_opacity = 0.5, fill_color = GREEN).move_to(self.graph_origin+3*RIGHT+2.1*UP) + vec1 = Line(self.graph_origin+2.5*UP, self.graph_origin+2.1*UP) + vec2 = Line(self.graph_origin+2.1*UP, self.graph_origin+1.7*UP) + vec3 = Line(self.graph_origin+2.5*RIGHT, self.graph_origin+3*RIGHT) + vec4 = Line(self.graph_origin+3*RIGHT, self.graph_origin+3.5*RIGHT) + brace1 = Brace(vec1, LEFT) + brace2 = Brace(vec2, LEFT) + brace3 = Brace(vec3, DOWN) + brace4 = Brace(vec4, DOWN) + br1text = brace1.get_text(r"$\epsilon$").next_to(brace1, LEFT) + br2text = brace2.get_text(r"$\epsilon$").next_to(brace2, LEFT) + br3text = brace3.get_text(r"$\delta$").next_to(brace3, DOWN) + br4text = brace4.get_text(r"$\delta$").next_to(brace4, DOWN) + epgrp = VGroup(epline1, epline2, Ldot, adot, Lline, aline, epline4, epline3) + recgrp = VGroup(vertical_rectangle, horizontal_rectangle) + epbrgrp = VGroup(brace1, brace2, br1text, br2text) + delbrgrp = VGroup(brace3, brace4, br3text, br4text) + self.setup_axes() + graph_1 = self.get_graph(lambda x :0.1*(x+1)**2 +0.5, x_min = -5, x_max = 5) + graph_2 = self.get_graph(lambda x : 0.1*(x+1)**2 +0.5, x_min = 2.5, x_max = 3.5, color = YELLOW_A) + graph_2.shift(2.5*LEFT) + self.play(ShowCreation(graph_1)) + self.wait(2) + self.play(ShowCreation(epgrp), ShowCreation(horizontal_rectangle), ShowCreation(vertical_rectangle)) + self.wait(2) + self.play(ShowCreation(epbrgrp)) + self.play(ShowCreation(delbrgrp)) + self.wait(2) + self.play(FadeOut(recgrp)) + self.wait(2) + for i in range(0,1): + self.play(ApplyMethod(graph_2.shift, 2.5*RIGHT)) + self.wait(1) + self.play(ApplyMethod(graph_2.shift, 1.7*DOWN)) + self.play(ApplyMethod(graph_2.shift, 1.7*UP)) + self.wait(1) + self.play(ApplyMethod(graph_2.shift, 2.5*LEFT)) + self.play(ApplyMethod(graph_2.shift, 2.5*RIGHT)) + self.wait(1) + self.play(ApplyMethod(graph_2.shift, 1.7*DOWN)) + self.play(ApplyMethod(graph_2.shift, 1.7*UP)) + self.wait(1) + self.play(ApplyMethod(graph_2.shift, 2.5*LEFT)) + self.wait() diff --git a/FSF-2020/calculus/intro-to-calculus/riemannintegrals/README.md b/FSF-2020/calculus/intro-to-calculus/riemannintegrals/README.md new file mode 100644 index 0000000..a9ad0bb --- /dev/null +++ b/FSF-2020/calculus/intro-to-calculus/riemannintegrals/README.md @@ -0,0 +1,18 @@ +rierect1.gif + + + +rierect2.gif + + + +rierect3.gif + + + +RiemannRectanglesAnimation. + + + +mimi.gif + diff --git a/FSF-2020/calculus/intro-to-calculus/riemannintegrals/RiemannRectanglesAnimation.py b/FSF-2020/calculus/intro-to-calculus/riemannintegrals/RiemannRectanglesAnimation.py new file mode 100644 index 0000000..a278c9d --- /dev/null +++ b/FSF-2020/calculus/intro-to-calculus/riemannintegrals/RiemannRectanglesAnimation.py @@ -0,0 +1,64 @@ +from manimlib.imports import * +class RiemannRectanglesAnimation(GraphScene): + CONFIG = { + "y_max": 5, + "x_max": 6, + "x_min": 0, + "y_min": 0, + "x_axis_width": 5, + "y_axis_height": 5, + "init_dx":0.5, + "graph_origin": ORIGIN+2*DOWN+6*LEFT, + } + def construct(self): + self.setup_axes() + def func(x): + return 0.1*(x)*(x-3)*(x-7)+3 + + graph1=self.get_graph(func,x_min=0,x_max=6) + kwargs = { + "x_min" : 1.5, + "x_max" : 5.5, + "fill_opacity" : 0.75, + "stroke_width" : 0.25, + "input_sample_type": "right", + } + flat_rectangles1 = self.get_riemann_rectangles(self.get_graph(lambda x : 0),dx=self.init_dx,start_color=invert_color(PURPLE),end_color=invert_color(ORANGE),**kwargs) + riemann_rectangles_list1 = self.get_riemann_rectangles_list(graph1,8,max_dx=self.init_dx,power_base=2,start_color=PURPLE,end_color=ORANGE,**kwargs) + self.add(graph1) + self.graph_origin = ORIGIN+2*DOWN+1*RIGHT + self.setup_axes() + graph2=self.get_graph(func,x_min=0,x_max=6) + kwargs = { + "x_min" : 1.5, + "x_max" : 5.5, + "fill_opacity" : 0.75, + "stroke_width" : 0.25, + "input_sample_type": "left", + } + flat_rectangles2 = self.get_riemann_rectangles(self.get_graph(lambda x : 0),dx=self.init_dx,start_color=invert_color(PURPLE),end_color=invert_color(ORANGE),**kwargs) + riemann_rectangles_list2 = self.get_riemann_rectangles_list(graph2,8,max_dx=self.init_dx,power_base=2,start_color=PURPLE,end_color=ORANGE,**kwargs) + self.add(graph2) + text1 = TextMobject("Left Riemann sum").move_to(np.array([-3,-2.5,0])) + text2 = TextMobject("Right Riemann sum").move_to(np.array([4,-2.5,0])) + grp1 = VGroup(text1, text2) + text3 = TexMobject(r"n \rightarrow \infty").move_to(np.array([0, -3, 0])) + text4 = TextMobject("Left and Right Riemann sums are equal").move_to(np.array([0, -3, 0])) + text5 = TextMobject("Hence function is Riemann integrable and value of integral equals area covered").move_to(np.array([0, -3, 0])).scale(0.6) + grp2 = VGroup(text1, text2, text3) + # Show Riemann rectangles + self.play(ReplacementTransform(flat_rectangles1,riemann_rectangles_list1[0]), ReplacementTransform(flat_rectangles2, riemann_rectangles_list2[0])) + self.wait() + self.play(ShowCreation(grp1)) + for r in range(1,len(riemann_rectangles_list1)-5): + self.transform_between_riemann_rects(riemann_rectangles_list1[r-1],riemann_rectangles_list1[r],replace_mobject_with_target_in_scene = True,) + self.transform_between_riemann_rects(riemann_rectangles_list2[r-1],riemann_rectangles_list2[r],replace_mobject_with_target_in_scene = True,) + self.play(ShowCreation(text3)) + for r in range(len(riemann_rectangles_list1)-5,len(riemann_rectangles_list1)): + self.transform_between_riemann_rects(riemann_rectangles_list1[r-1],riemann_rectangles_list1[r],replace_mobject_with_target_in_scene = True,) + self.transform_between_riemann_rects(riemann_rectangles_list2[r-1],riemann_rectangles_list2[r],replace_mobject_with_target_in_scene = True,) + self.wait(2) + self.play(ReplacementTransform(grp2, text4)) + self.wait(2) + self.play(ReplacementTransform(text4, text5)) + self.wait(4) diff --git a/FSF-2020/calculus/intro-to-calculus/riemannintegrals/mimi.py b/FSF-2020/calculus/intro-to-calculus/riemannintegrals/mimi.py new file mode 100644 index 0000000..2471c87 --- /dev/null +++ b/FSF-2020/calculus/intro-to-calculus/riemannintegrals/mimi.py @@ -0,0 +1,53 @@ +class mimi(GraphScene): + CONFIG = { + "y_max": 5, + "x_max": 6, + "x_min": 0, + "y_min": 0, + "x_axis_width": 5, + "y_axis_height": 5, + "init_dx":0.5, + "graph_origin": ORIGIN+2*DOWN+6*LEFT, + } + def construct(self): + self.setup_axes() + def func(x): + return 0.1*(x)*(x-3)*(x-7)+3 + + graph=self.get_graph(func,x_min=0,x_max=6) + kwargs = { + "x_min" : 1.5, + "x_max" : 5.5, + "fill_opacity" : 0.5, + "stroke_width" : 0.25, + } + flat_rectangles = self.get_riemann_rectangles(self.get_graph(lambda x : 0),dx=self.init_dx,**kwargs) + riemann_rectangles_list = self.get_riemann_rectangles_list(graph,8,max_dx=self.init_dx,power_base=2,start_color=PURPLE,end_color=ORANGE,**kwargs, input_sample_type = "right") + riemann_rectangles_list1 = self.get_riemann_rectangles_list(graph,8,max_dx=self.init_dx,power_base=2,start_color=PURPLE,end_color=ORANGE,**kwargs, input_sample_type = "left") + self.add(graph) + self.play(ReplacementTransform(flat_rectangles,riemann_rectangles_list[0]), ReplacementTransform(flat_rectangles,riemann_rectangles_list1[0])) + #self.play(ReplacementTransform(flat_rectangles,riemann_rectangles_list1[0])) + self.wait(2) + kwargs = { + "x_min" : 3, + "x_max" : 3.5, + "fill_opacity" : 0.5, + "stroke_width" : 0.25, + } + riemann_rectangles_list2 = self.get_riemann_rectangles_list(graph,8,max_dx=self.init_dx,power_base=2,start_color=PURPLE,end_color=ORANGE,**kwargs, input_sample_type = "right") + riemann_rectangles_list3 = self.get_riemann_rectangles_list(graph,8,max_dx=self.init_dx,power_base=2,start_color=PURPLE,end_color=ORANGE,**kwargs, input_sample_type = "left") + #self.play(FadeOut(riemann_rectangles_list[0]), FadeOut(riemann_rectangles_list1[0])) + self.play(ReplacementTransform(flat_rectangles,riemann_rectangles_list2[0]), ReplacementTransform(flat_rectangles,riemann_rectangles_list3[0]), FadeOut(riemann_rectangles_list[0]), FadeOut(riemann_rectangles_list1[0])) + minlim = self.get_vertical_line_to_graph(3,graph,DashedLine) + maxlim = self.get_vertical_line_to_graph(3.5,graph,DashedLine) + line2 = Line(self.graph_origin+2.5*RIGHT, self.graph_origin+2.9*RIGHT) + brace1 = Brace(minlim, LEFT) + brace2 = Brace(line2, DOWN) + brace3 = Brace(maxlim, RIGHT) + br1text = brace1.get_text(r"${M}_{i}$").next_to(brace1, LEFT) + br2text = brace2.get_text(r"$\Delta x$").next_to(brace2, DOWN) + br3text = brace3.get_text(r"${m}_{i}$").next_to(brace3, RIGHT) + text1 = TexMobject(r"\Delta x=(b-a)/n").shift(2*RIGHT) + grp3 = VGroup(br1text, br2text, br3text, brace1, brace2, brace3, text1) + self.play(ShowCreation(grp3)) + self.wait(5) diff --git a/FSF-2020/calculus/intro-to-calculus/riemannintegrals/rierect1.py b/FSF-2020/calculus/intro-to-calculus/riemannintegrals/rierect1.py new file mode 100644 index 0000000..748d766 --- /dev/null +++ b/FSF-2020/calculus/intro-to-calculus/riemannintegrals/rierect1.py @@ -0,0 +1,31 @@ +from manimlib.imports import * +class rierect1(GraphScene): + CONFIG = { + "y_max" : 6, + "y_min" : 0, + "x_max" : 4, + "x_min" : 0, + "y_tick_frequency" : 1, + "x_tick_frequency" : 1, + "axes_color" : WHITE, + "num_graph_anchor_points": 3000, #this is the number of points that graph manim + "graph_origin" : ORIGIN+2*DOWN+4*LEFT, + "x_labeled_nums": None,#list(range(-1,2)), + "y_labeled_nums": None,#list(range(0,2)), + "x_axis_label":"$x$", + "y_axis_label":"$f(x)$", + "x_axis_width": 10, + "y_axis_height": 5, + } + def construct(self): + self.setup_axes() + graph1 = self.get_graph(lambda x : (0.1*(1.5*x+1)**2 +0.5), x_min = 0, x_max = 4) + minlim = self.get_vertical_line_to_graph(1,graph1,DashedLine, color = PINK) + maxlim = self.get_vertical_line_to_graph(3,graph1,DashedLine,color = PINK) + x1 = TexMobject(r"{x}_{1}").next_to(minlim, DOWN) + x2 = TexMobject(r"{x}_{2}").next_to(maxlim, DOWN) + rie1 = self.get_riemann_rectangles(graph1, x_min = 1, x_max = 3, dx = 0.4, input_sample_type = "left", fill_opacity = 1, start_color = YELLOW, end_color = YELLOW) + #rie2 = self.get_riemann_rectangles(graph1, x_min = 1, x_max = 3, dx = 0.01, input_sample_type = "right", fill_opacity = 0.5, start_color = PINK, end_color = LIGHT_PINK) + group = VGroup(graph1, minlim, maxlim, x1, x2, rie1) + self.play(ShowCreation(group)) + self.wait(1.5) diff --git a/FSF-2020/calculus/intro-to-calculus/riemannintegrals/rierect2.py b/FSF-2020/calculus/intro-to-calculus/riemannintegrals/rierect2.py new file mode 100644 index 0000000..e300250 --- /dev/null +++ b/FSF-2020/calculus/intro-to-calculus/riemannintegrals/rierect2.py @@ -0,0 +1,31 @@ +from manimlib.imports import * +class rierect2(GraphScene): + CONFIG = { + "y_max" : 6, + "y_min" : 0, + "x_max" : 4, + "x_min" : 0, + "y_tick_frequency" : 1, + "x_tick_frequency" : 1, + "axes_color" : WHITE, + "num_graph_anchor_points": 3000, #this is the number of points that graph manim + "graph_origin" : ORIGIN+2*DOWN+4*LEFT, + "x_labeled_nums": None,#list(range(-1,2)), + "y_labeled_nums": None,#list(range(0,2)), + "x_axis_label":"$x$", + "y_axis_label":"$f(x)$", + "x_axis_width": 10, + "y_axis_height": 5, + } + def construct(self): + self.setup_axes() + graph1 = self.get_graph(lambda x : (0.1*(1.5*x+1)**2 +0.5), x_min = 0, x_max = 4) + minlim = self.get_vertical_line_to_graph(1,graph1,DashedLine, color = PINK) + maxlim = self.get_vertical_line_to_graph(3,graph1,DashedLine,color = PINK) + x1 = TexMobject(r"{x}_{1}").next_to(minlim, DOWN) + x2 = TexMobject(r"{x}_{2}").next_to(maxlim, DOWN) + rie1 = self.get_riemann_rectangles(graph1, x_min = 1, x_max = 3, dx = 0.1, input_sample_type = "left", fill_opacity = 1, start_color = YELLOW, end_color = YELLOW) + #rie2 = self.get_riemann_rectangles(graph1, x_min = 1, x_max = 3, dx = 0.01, input_sample_type = "right", fill_opacity = 0.5, start_color = PINK, end_color = LIGHT_PINK) + group = VGroup(graph1, minlim, maxlim, x1, x2, rie1) + self.play(ShowCreation(group)) + self.wait(1.5) diff --git a/FSF-2020/calculus/intro-to-calculus/riemannintegrals/rierect3.py b/FSF-2020/calculus/intro-to-calculus/riemannintegrals/rierect3.py new file mode 100644 index 0000000..3542358 --- /dev/null +++ b/FSF-2020/calculus/intro-to-calculus/riemannintegrals/rierect3.py @@ -0,0 +1,31 @@ +from manimlib.imports import * +class rierect3(GraphScene): + CONFIG = { + "y_max" : 6, + "y_min" : 0, + "x_max" : 4, + "x_min" : 0, + "y_tick_frequency" : 1, + "x_tick_frequency" : 1, + "axes_color" : WHITE, + "num_graph_anchor_points": 3000, #this is the number of points that graph manim + "graph_origin" : ORIGIN+2*DOWN+4*LEFT, + "x_labeled_nums": None,#list(range(-1,2)), + "y_labeled_nums": None,#list(range(0,2)), + "x_axis_label":"$x$", + "y_axis_label":"$f(x)$", + "x_axis_width": 10, + "y_axis_height": 5, + } + def construct(self): + self.setup_axes() + graph1 = self.get_graph(lambda x : (0.1*(1.5*x+1)**2 +0.5), x_min = 0, x_max = 4) + minlim = self.get_vertical_line_to_graph(1,graph1,DashedLine, color = PINK) + maxlim = self.get_vertical_line_to_graph(3,graph1,DashedLine,color = PINK) + x1 = TexMobject(r"{x}_{1}").next_to(minlim, DOWN) + x2 = TexMobject(r"{x}_{2}").next_to(maxlim, DOWN) + rie1 = self.get_riemann_rectangles(graph1, x_min = 1, x_max = 3, dx = 0.01, input_sample_type = "left", fill_opacity = 1, start_color = YELLOW, end_color = YELLOW) + #rie2 = self.get_riemann_rectangles(graph1, x_min = 1, x_max = 3, dx = 0.01, input_sample_type = "right", fill_opacity = 0.5, start_color = PINK, end_color = LIGHT_PINK) + group = VGroup(graph1, minlim, maxlim, x1, x2, rie1) + self.play(ShowCreation(group)) + self.wait(1.5) diff --git a/FSF-2020/calculus/series-and-transformations/Fourier Transform/README.md b/FSF-2020/calculus/series-and-transformations/Fourier Transform/README.md index c5d8389..2fa4e04 100644 --- a/FSF-2020/calculus/series-and-transformations/Fourier Transform/README.md +++ b/FSF-2020/calculus/series-and-transformations/Fourier Transform/README.md @@ -7,9 +7,12 @@ ### Applying the same on Graphs  -### Fourier series for non-periodic functions +### Fourier series for non-periodic functions-a  +### Fourier series for non-periodic functions-b + + ### Fourier Series of Square pulse  diff --git a/FSF-2020/calculus/series-and-transformations/Fourier Transform/gifs/file3.gif b/FSF-2020/calculus/series-and-transformations/Fourier Transform/gifs/file3.gif Binary files differindex 533368b..de94810 100644 --- a/FSF-2020/calculus/series-and-transformations/Fourier Transform/gifs/file3.gif +++ b/FSF-2020/calculus/series-and-transformations/Fourier Transform/gifs/file3.gif diff --git a/FSF-2020/calculus/series-and-transformations/Fourier Transform/gifs/file6.gif b/FSF-2020/calculus/series-and-transformations/Fourier Transform/gifs/file6.gif Binary files differnew file mode 100644 index 0000000..de94810 --- /dev/null +++ b/FSF-2020/calculus/series-and-transformations/Fourier Transform/gifs/file6.gif diff --git a/FSF-2020/calculus/series-and-transformations/Fourier Transform/gifs/file7.gif b/FSF-2020/calculus/series-and-transformations/Fourier Transform/gifs/file7.gif Binary files differnew file mode 100644 index 0000000..ab4eed8 --- /dev/null +++ b/FSF-2020/calculus/series-and-transformations/Fourier Transform/gifs/file7.gif diff --git a/FSF-2020/calculus/series-and-transformations/Fourier Transform/video1_DividingAToneIntoItsConstituents.py b/FSF-2020/calculus/series-and-transformations/Fourier Transform/video1_DividingAToneIntoItsConstituents.py index 39db6d8..fdb8719 100644 --- a/FSF-2020/calculus/series-and-transformations/Fourier Transform/video1_DividingAToneIntoItsConstituents.py +++ b/FSF-2020/calculus/series-and-transformations/Fourier Transform/video1_DividingAToneIntoItsConstituents.py @@ -1,13 +1,6 @@ from manimlib.imports import* import numpy as np -# def func(t,n): -# s=0 -# for i in range(1,n+1): -# s+=((-2/(i*np.pi))*((-1)**i)*np.sin(2*np.pi*i*t)) -# return s - - class intro(GraphScene): CONFIG = { "x_min": -3, diff --git a/FSF-2020/calculus/series-and-transformations/Fourier Transform/video2_ColorsAnalogyForFourierSeries.py b/FSF-2020/calculus/series-and-transformations/Fourier Transform/video2_ColorsAnalogyForFourierSeries.py index 8f3706b..c87e58e 100644 --- a/FSF-2020/calculus/series-and-transformations/Fourier Transform/video2_ColorsAnalogyForFourierSeries.py +++ b/FSF-2020/calculus/series-and-transformations/Fourier Transform/video2_ColorsAnalogyForFourierSeries.py @@ -101,27 +101,27 @@ class divideColors(GraphScene): self.get_graph(lambda x:func(x,6,24),x_min=-1,x_max=1).set_color([DARK_BROWN,RED_C]), self.get_graph(lambda x:func(x,7,24),x_min=-1,x_max=1).set_color(DARK_BROWN) ] - #self.y_axis_label="$\\frac { 2 }{ \pi } sin(2\pi t)$" + self.setup_axes(scalee=1) axes.append(self.axes) graph1=self.get_graph(lambda x:func(x,1,1),x_min=-1,x_max=1,color=GREEN_E) - #self.y_axis_label="$\\frac { -1 }{ \pi } sin(4\pi t)$" + self.setup_axes(scalee=1) axes.append(self.axes) graph2=self.get_graph(lambda x:func(x,2,2),x_min=-1,x_max=1,color=GREEN_C) - #self.y_axis_label="$\\frac { 2 }{ 3\pi } sin(6\pi t)$" + self.setup_axes(scalee=1) axes.append(self.axes) graph3=self.get_graph(lambda x:func(x,3,3),x_min=-1,x_max=1,color=GOLD_E) - #self.y_axis_label="$\\frac { -1 }{ 2\pi } sin(8\pi t)$" + self.setup_axes(scalee=1) axes.append(self.axes) graph4=self.get_graph(lambda x:func(x,4,4),x_min=-1,x_max=1,color=GOLD_C) - #self.y_axis_label="$\\frac { 2 }{ 5\pi } sin(10\pi t)$" + self.setup_axes(scalee=1) axes.append(self.axes) graph5=self.get_graph(lambda x:func(x,5,5),x_min=-1,x_max=1,color=ORANGE) - #self.y_axis_label="$\\frac { -1 }{ 3\pi } sin(12\pi t)$" + self.setup_axes(scalee=1) axes.append(self.axes) graph6=self.get_graph(lambda x:func(x,6,6),x_min=-1,x_max=1,color=RED_C) @@ -132,9 +132,7 @@ class divideColors(GraphScene): self.play(ShowCreation(graphs[0])) self.play(Write(coeff[0])) self.wait(1) - # self.play(ApplyMethod(axes[0].scale,0.4),ApplyMethod(graphs[0].scale,0.4),ApplyMethod(axes[1].scale,0.4), - # ApplyMethod(axes[2].scale,0.4),ApplyMethod(axes[3].scale,0.4), - # ApplyMethod(axes[4].scale,0.4),ApplyMethod(axes[5].scale,0.4),ApplyMethod(axes[6].scale,0.4)) + self.play(ReplacementTransform(graphs[0],graphs[1]),ApplyMethod(groups[0].shift,4*LEFT+UP),ReplacementTransform(coeff[0],coeff[2]),FadeIn(coeff[1])) self.play(ReplacementTransform(graphs[1],graphs[2]),ApplyMethod(groups[1].shift,4*RIGHT+UP),ReplacementTransform(coeff[2],coeff[4]),FadeIn(coeff[3])) self.play(ReplacementTransform(graphs[2],graphs[3]),ApplyMethod(groups[2].shift,4*LEFT+2*DOWN),ReplacementTransform(coeff[4],coeff[6]),FadeIn(coeff[5])) @@ -142,24 +140,7 @@ class divideColors(GraphScene): self.play(ReplacementTransform(graphs[4],graphs[5]),ApplyMethod(groups[4].shift,2.5*UP),ReplacementTransform(coeff[8],coeff[10]),FadeIn(coeff[9])) self.play(ReplacementTransform(graphs[5],graphs[6]),ApplyMethod(groups[5].shift,2.5*DOWN),ReplacementTransform(coeff[10],coeff[12]),FadeIn(coeff[11])) - # self.play(ReplacementTransform(graphs[0],graphs[1]),ApplyMethod(groups[0].shift,3*LEFT)) - # self.play(ReplacementTransform(graphs[0],graphs[1]),) - # self.play(ReplacementTransform(graphs[0],graphs[1]),) - # self.play(ReplacementTransform(graphs[0],graphs[1]),) - # self.play(ReplacementTransform(graphs[0],graphs[1]),) - # self.play(ReplacementTransform(graphs[0],graphs[1]),) - - + self.wait(2) - # self.play(ReplacementTransform(function,const)) - # self.play(ShowCreation(sinx),ShowCreation(cosx)) - # self.play(ShowCreation(sin2x),ShowCreation(cos2x)) - # self.play(ShowCreation(sin3x),ShowCreation(cos3x)) - # self.play(ShowCreation(sin4x),ShowCreation(cos4x)) - # sintext=TextMobject("Infinite","sines").shift(5*RIGHT).set_color_by_tex_to_color_map({"Infinite":[YELLOW,RED],"sines":BLUE}) - # costext=TextMobject("Infinite","cosines").shift(5*LEFT).set_color_by_tex_to_color_map({"Infinite":[YELLOW,RED],"cosines":BLUE}) - # sintext.scale(0.6) - # costext.scale(0.6) - # self.play(FadeIn(sintext),FadeIn(costext)) - # self.wait(2)
\ No newline at end of file + diff --git a/FSF-2020/calculus/series-and-transformations/Fourier Transform/video3_seriesVSTransform.py b/FSF-2020/calculus/series-and-transformations/Fourier Transform/video3_seriesVSTransform.py index f23e54f..d35f8bf 100644 --- a/FSF-2020/calculus/series-and-transformations/Fourier Transform/video3_seriesVSTransform.py +++ b/FSF-2020/calculus/series-and-transformations/Fourier Transform/video3_seriesVSTransform.py @@ -1,7 +1,7 @@ from manimlib.imports import * import numpy as np -class compare(GraphScene): +class compare(GraphScene,MovingCameraScene): CONFIG = { "x_min": -3, "x_max": 3, @@ -14,6 +14,9 @@ class compare(GraphScene): "exclude_zero_label": True, "x_labeled_nums": range(-2, 3, 1), } + def setup(self): + GraphScene.setup(self) + MovingCameraScene.setup(self) def returnPairLines(self,left,right,y_each_unit): lineLeft=DashedLine(start=(0,5*y_each_unit,0),end=(0,-5*y_each_unit,0)).shift(left) lineRight=DashedLine(start=(0,5*y_each_unit,0),end=(0,-5*y_each_unit,0)).shift(right) @@ -58,7 +61,7 @@ class compare(GraphScene): self.graph_origin=3.5*RIGHT self.y_axis_label="$\\frac { { l }^{ 2 } }{ 6 } +\sum _{ n=1 }^{ \infty }{ \\frac { 2{ (-1) }^{ n }{ l }^{ 2 }cos(\\frac { n\pi x }{ l } ) }{ { \pi }^{ 2 }{ n }^{ 2 } } }$" self.setup_axes(animate=True,scalee=1) - axes.append(self.axes) + axes.append(self.axes) coeffResult=[ TextMobject("$\\frac { { 1 }^{ 2 } }{ 6 } +\sum _{ n=1 }^{ 1 }{ \\frac { 2{ (-1) }^{ n }{ 1 }^{ 2 }cos(\\frac { n\pi x }{ 1 } ) }{ { \pi }^{ 2 }{ n }^{ 2 } } } $").scale(0.3).shift(4.5*RIGHT+UP).set_color(YELLOW), TextMobject("$\\frac { { 1 }^{ 2 } }{ 6 } +\sum _{ n=1 }^{ 3 }{ \\frac { 2{ (-1) }^{ n }{ 1 }^{ 2 }cos(\\frac { n\pi x }{ 1 } ) }{ { \pi }^{ 2 }{ n }^{ 2 } } } $").scale(0.3).shift(4.5*RIGHT+UP).set_color(YELLOW), @@ -77,7 +80,13 @@ class compare(GraphScene): result1g=self.returnPartResult(1,13) self.play(ApplyMethod(partFunction1.shift,0.2*UP)) self.wait(0.5) + self.play(ReplacementTransform(partFunction1,result1a),Write(coeffResult[0])) + self.play(FadeOut(axes[0]),FadeOut(left),FadeOut(right),FadeOut(function)) + self.camera_frame.save_state() + self.play(self.camera_frame.set_width, 5,self.camera_frame.move_to, 3.5*RIGHT) + + self.play(ReplacementTransform(result1a,result1b),ReplacementTransform(coeffResult[0],coeffResult[1])) self.play(ReplacementTransform(result1b,result1c),ReplacementTransform(coeffResult[1],coeffResult[2])) self.play(ReplacementTransform(result1c,result1d),ReplacementTransform(coeffResult[2],coeffResult[3])) @@ -85,6 +94,9 @@ class compare(GraphScene): self.play(ReplacementTransform(result1e,result1f),ReplacementTransform(coeffResult[4],coeffResult[5])) self.play(ReplacementTransform(result1f,result1g),ReplacementTransform(coeffResult[5],coeffResult[6])) + self.wait(0.5) + self.play(self.camera_frame.set_width, 14,self.camera_frame.move_to, 0) + text4=TextMobject("Here the","obtained function","will always be","periodic","with period equal to the chosen interval").scale(0.4).shift(3.3*DOWN).set_color_by_tex_to_color_map({"obtained function":YELLOW,"periodic":RED}) self.play(Write(text4)) @@ -93,6 +105,7 @@ class compare(GraphScene): self.play(FadeOut(text4)) text5=TextMobject("As we","increase","the","interval of $x$,").scale(0.5).shift(3*DOWN).set_color_by_tex_to_color_map({"increase":RED,"interval of $x$,":YELLOW}) text6=TextMobject("We get","approximation","for","higher intervals!").scale(0.5).shift(3.5*DOWN).set_color_by_tex_to_color_map({"approximation":GREEN,"higher intervals!":YELLOW}) + self.play(FadeIn(axes[0]),FadeIn(left),FadeIn(right),FadeIn(function)) self.play(Write(text5)) self.play(Write(text6)) result2=self.returnPartResult(1.5,20) @@ -101,10 +114,10 @@ class compare(GraphScene): result5=self.returnPartResult(3,20) finalCoeff=coeffResult[6] coeffResult=[ - TextMobject("$\\frac { { 1.5 }^{ 2 } }{ 6 } +\sum _{ n=1 }^{ 20 }{ \\frac { 2{ (-1) }^{ n }{ 1.5 }^{ 2 }cos(\\frac { n\pi x }{ 2 } ) }{ { \pi }^{ 2 }{ n }^{ 2 } } }$").scale(0.3).shift(4.5*RIGHT+1.5*UP).set_color(YELLOW), - TextMobject("$\\frac { { 2 }^{ 2 } }{ 6 } +\sum _{ n=1 }^{ 20 }{ \\frac { 2{ (-1) }^{ n }{ 2 }^{ 2 }cos(\\frac { n\pi x }{ 2 } ) }{ { \pi }^{ 2 }{ n }^{ 2 } } } $").scale(0.3).shift(4.5*RIGHT+1.5*UP).set_color(YELLOW), - TextMobject("$\\frac { { 2.5 }^{ 2 } }{ 6 } +\sum _{ n=1 }^{ 20 }{ \\frac { 2{ (-1) }^{ n }{ 2.5 }^{ 2 }cos(\\frac { n\pi x }{ 2 } ) }{ { \pi }^{ 2 }{ n }^{ 2 } } } $").scale(0.3).shift(4.5*RIGHT+1.5*UP).set_color(YELLOW), - TextMobject("$\\frac { { 3 }^{ 2 } }{ 6 } +\sum _{ n=1 }^{ 20 }{ \\frac { 2{ (-1) }^{ n }{ 3 }^{ 2 }cos(\\frac { n\pi x }{ 2 } ) }{ { \pi }^{ 2 }{ n }^{ 2 } } } $").scale(0.3).shift(4.5*RIGHT+1.5*UP).set_color(YELLOW), + TextMobject("$\\frac { { 1.5 }^{ 2 } }{ 6 } +\sum _{ n=1 }^{ 20 }{ \\frac { 2{ (-1) }^{ n }{ 1.5 }^{ 2 }cos(\\frac { n\pi x }{ 2 } ) }{ { \pi }^{ 2 }{ n }^{ 2 } } }$").scale(0.4).shift(5*RIGHT+1.5*UP).set_color(YELLOW), + TextMobject("$\\frac { { 2 }^{ 2 } }{ 6 } +\sum _{ n=1 }^{ 20 }{ \\frac { 2{ (-1) }^{ n }{ 2 }^{ 2 }cos(\\frac { n\pi x }{ 2 } ) }{ { \pi }^{ 2 }{ n }^{ 2 } } } $").scale(0.4).shift(5*RIGHT+1.5*UP).set_color(YELLOW), + TextMobject("$\\frac { { 2.5 }^{ 2 } }{ 6 } +\sum _{ n=1 }^{ 20 }{ \\frac { 2{ (-1) }^{ n }{ 2.5 }^{ 2 }cos(\\frac { n\pi x }{ 2 } ) }{ { \pi }^{ 2 }{ n }^{ 2 } } } $").scale(0.4).shift(5*RIGHT+2.2*UP).set_color(YELLOW), + TextMobject("$\\frac { { 3 }^{ 2 } }{ 6 } +\sum _{ n=1 }^{ 20 }{ \\frac { 2{ (-1) }^{ n }{ 3 }^{ 2 }cos(\\frac { n\pi x }{ 2 } ) }{ { \pi }^{ 2 }{ n }^{ 2 } } } $").scale(0.4).shift(5*RIGHT+2.2*UP).set_color(YELLOW), ] self.play(ApplyMethod(left.shift,LEFT*x_each_unit*0.5),ApplyMethod(right.shift,RIGHT*x_each_unit*0.5),ReplacementTransform(result1g,result2),ReplacementTransform(finalCoeff,coeffResult[0])) self.play(ApplyMethod(left.shift,LEFT*x_each_unit*0.5),ApplyMethod(right.shift,RIGHT*x_each_unit*0.5),ReplacementTransform(result2,result3),ReplacementTransform(coeffResult[0],coeffResult[1])) @@ -112,22 +125,5 @@ class compare(GraphScene): self.play(ApplyMethod(left.shift,LEFT*x_each_unit*0.5),ApplyMethod(right.shift,RIGHT*x_each_unit*0.5),ReplacementTransform(result4,result5),ReplacementTransform(coeffResult[2],coeffResult[3])) - # coeffResult=[ - # TextMobject("$\\frac { { 2 }^{ 2 } }{ 6 } +\sum _{ n=1 }^{ 1 }{ \\frac { 2{ (-1) }^{ n }{ 2 }^{ 2 }cos(\\frac { n\pi x }{ 2 } ) }{ { \pi }^{ 2 }{ n }^{ 2 } } }$").scale(0.3).shift(4.5*RIGHT+1.5*UP), - # TextMobject("$\\frac { { 2 }^{ 2 } }{ 6 } +\sum _{ n=1 }^{ 4 }{ \\frac { 2{ (-1) }^{ n }{ 2 }^{ 2 }cos(\\frac { n\pi x }{ 2 } ) }{ { \pi }^{ 2 }{ n }^{ 2 } } } $").scale(0.3).shift(4.5*RIGHT+1.5*UP), - # TextMobject("$\\frac { { 2 }^{ 2 } }{ 6 } +\sum _{ n=1 }^{ 10 }{ \\frac { 2{ (-1) }^{ n }{ 2 }^{ 2 }cos(\\frac { n\pi x }{ 2 } ) }{ { \pi }^{ 2 }{ n }^{ 2 } } } $").scale(0.3).shift(4.5*RIGHT+1.5*UP), - # TextMobject("$\\frac { { 2 }^{ 2 } }{ 6 } +\sum _{ n=1 }^{ 20 }{ \\frac { 2{ (-1) }^{ n }{ 2 }^{ 2 }cos(\\frac { n\pi x }{ 2 } ) }{ { \pi }^{ 2 }{ n }^{ 2 } } } $").scale(0.3).shift(4.5*RIGHT+1.5*UP), - # ] - # result2a=self.returnPartResult(2,1) - # result2b=self.returnPartResult(2,4) - # result2c=self.returnPartResult(2,10) - # result2d=self.returnPartResult(2,20) - - # self.play(ReplacementTransform(partFunction2,result2a),ReplacementTransform(coeffResult[0],coeffResult[1])) - # self.play(ReplacementTransform(result2a,result2b),ReplacementTransform(coeffResult[0],coeffResult[1])) - # self.play(ReplacementTransform(result2b,result2c),ReplacementTransform(coeffResult[0],coeffResult[1])) - # self.play(ReplacementTransform(result2c,result2d),ReplacementTransform(coeffResult[0],coeffResult[1])) - # self.wait(0.5) - - self.wait(2)
\ No newline at end of file + self.wait(2) diff --git a/FSF-2020/calculus/series-and-transformations/Fourier Transform/video4_FourierSeriesOfSquarePulse.py b/FSF-2020/calculus/series-and-transformations/Fourier Transform/video4_FourierSeriesOfSquarePulse.py index 5d33fbe..fdf4bb3 100644 --- a/FSF-2020/calculus/series-and-transformations/Fourier Transform/video4_FourierSeriesOfSquarePulse.py +++ b/FSF-2020/calculus/series-and-transformations/Fourier Transform/video4_FourierSeriesOfSquarePulse.py @@ -33,9 +33,9 @@ class fourierSeries(GraphScene,MovingCameraScene): x_each_unit = self.x_axis_width / (self.x_max - self.x_min) y_each_unit = self.y_axis_height / (self.y_max - self.y_min) - equation=TextMobject("$f(x)=\\frac { 4 }{ \pi } \sum _{ k=1,3,5.. }^{ \infty }{ \\frac { 1 }{ k } \sin { 2\pi kx } }$").shift(5*RIGHT+3*UP).set_color(RED).scale(0.4) + equation=TextMobject("$f(x)=\\frac { 4 }{ \pi } \sum _{ k=1,3,5.. }^{ \infty }{ \\frac { 1 }{ k } \sin { 2\pi kx } }$").shift(5*RIGHT+3*UP).set_color(RED).scale(0.5) self.add(equation) - self.setup_axes(animate=True) + self.setup_axes(animate=True,scalee=1) line1=Line(start=(-x_each_unit,y_each_unit,0),end=(-(1/2)*x_each_unit,y_each_unit,0),color=RED) line2=Line(start=(-(1/2)*x_each_unit,y_each_unit,0),end=(-(1/2)*x_each_unit,-y_each_unit,0),color=RED) line3=Line(start=(-(1/2)*x_each_unit,-y_each_unit,0),end=(0,-y_each_unit,0),color=RED) @@ -87,6 +87,11 @@ class fourierSeries(GraphScene,MovingCameraScene): self.wait(1) self.camera_frame.save_state() self.play(self.camera_frame.set_width, 2.25,self.camera_frame.move_to, y_each_unit*UP+RIGHT*x_each_unit*0.3) - self.wait(1) - self.play(self.camera_frame.set_width,14,self.camera_frame.move_to,0) + circleMark=Circle(radius=0.1,color=GREEN).shift(x_each_unit*RIGHT*0.47+UP*y_each_unit*1.1) + text=TextMobject("Gibbs","phenomenon").set_color_by_tex_to_color_map({"Gibbs":BLUE,"phenomenon":YELLOW}).scale(0.1).shift(RIGHT*x_each_unit*0.65+UP*y_each_unit*1.1) + self.wait(0.7) + self.play(ShowCreation(circleMark)) + self.play(Write(text)) + self.wait(0.5) + self.play(self.camera_frame.set_width,14,self.camera_frame.move_to,0,FadeOut(circleMark),FadeOut(text)) self.wait(2) diff --git a/FSF-2020/calculus/series-and-transformations/Power Series/README.md b/FSF-2020/calculus/series-and-transformations/Power Series/README.md index 6885837..2fd400d 100644 --- a/FSF-2020/calculus/series-and-transformations/Power Series/README.md +++ b/FSF-2020/calculus/series-and-transformations/Power Series/README.md @@ -11,4 +11,4 @@  #### Uniform Convergence - + diff --git a/FSF-2020/calculus/series-and-transformations/Power Series/gifs/file4a_UniformConvergence.gif b/FSF-2020/calculus/series-and-transformations/Power Series/gifs/file4a_UniformConvergence.gif Binary files differnew file mode 100644 index 0000000..e284b83 --- /dev/null +++ b/FSF-2020/calculus/series-and-transformations/Power Series/gifs/file4a_UniformConvergence.gif diff --git a/FSF-2020/calculus/series-and-transformations/Power Series/video2_convergence_of_a_function.py b/FSF-2020/calculus/series-and-transformations/Power Series/video2_convergence_of_a_function.py index 19b8b8b..8680792 100644 --- a/FSF-2020/calculus/series-and-transformations/Power Series/video2_convergence_of_a_function.py +++ b/FSF-2020/calculus/series-and-transformations/Power Series/video2_convergence_of_a_function.py @@ -69,10 +69,7 @@ class graphScene(GraphScene): eqText[i].scale(0.6) eqText[i].set_color(BLUE) eqText[i].shift(ORIGIN+UP*2*y_each_unit+RIGHT*3.3*x_each_unit) - # eqTextTerm=TextMobject("And so on..!") - # eqTextTerm.set_color(BLUE) - # eqTextTerm.scale(0.6) - # eqTextTerm.shift(ORIGIN+UP*2*y_each_unit+3*RIGHT*x_each_unit) + equation1 = self.get_graph(lambda x : 1,color = RED,x_min = -8,x_max=8) equation2 = self.get_graph(lambda x : 1-math.pow(x,2),color = RED,x_min = -1.7,x_max=1.7) equation3 = self.get_graph(lambda x : 1-math.pow(x,2)+math.pow(x,4),color = RED,x_min = -1.6,x_max=1.6) diff --git a/FSF-2020/calculus/series-and-transformations/Power Series/video3_radius_and_intervalOfConvergence.py b/FSF-2020/calculus/series-and-transformations/Power Series/video3_radius_and_intervalOfConvergence.py index f35fea8..af4bdea 100644 --- a/FSF-2020/calculus/series-and-transformations/Power Series/video3_radius_and_intervalOfConvergence.py +++ b/FSF-2020/calculus/series-and-transformations/Power Series/video3_radius_and_intervalOfConvergence.py @@ -105,9 +105,4 @@ class graphScene(GraphScene,MovingCameraScene): self.wait(1) self.play(self.camera_frame.set_width,14) self.wait(1.3) - # self.camera_frame.save_state() - # self.camera_frame.set_width(5.5) - # self.play(self.camera_frame.move_to, ORIGIN) - # self.wait(1) - # self.camera_frame.set_width(14) - # self.wait(1.5) + diff --git a/FSF-2020/calculus/series-and-transformations/Power Series/video4_UniformConvergence.py b/FSF-2020/calculus/series-and-transformations/Power Series/video4_UniformConvergence.py index 1f3e26c..b75da59 100644 --- a/FSF-2020/calculus/series-and-transformations/Power Series/video4_UniformConvergence.py +++ b/FSF-2020/calculus/series-and-transformations/Power Series/video4_UniformConvergence.py @@ -3,19 +3,15 @@ import math class uniformlyConvergent(Scene): def construct(self): - #introText1=TextMobject("Again consider the","above","example") introText2=TextMobject("Let","$g(x)=\\frac { 1 }{ 1+{ x }^{ 2 } }$","and","x=0.5 $\in$(-1,1)") introText3=TextMobject("Lets analyse..","!") - #introText1.scale(0.8) + introText2.scale(0.7) introText3.scale(0.9) introText3.shift(DOWN) - #introText1.set_color_by_tex_to_color_map({"above":YELLOW}) + introText2.set_color_by_tex_to_color_map({"$g(x)=\\frac { 1 }{ 1+{ x }^{ 2 } }$":BLUE,"x=0.5 $\in$(-1,1)":YELLOW}) introText3.set_color_by_tex_to_color_map({"!":GREEN}) - #self.play(Write(introText1)) - #self.wait(0.5) - #self.play(FadeOut(introText1)) self.play(Write(introText2)) self.play(FadeIn(introText3)) self.wait(2) @@ -65,7 +61,7 @@ class graphScene(GraphScene,ZoomedScene): def setup(self): GraphScene.setup(self) - #MovingCameraScene.setup(self) + ZoomedScene.setup(self) @@ -110,19 +106,7 @@ class graphScene(GraphScene,ZoomedScene): self.activate_zooming(animate=True) for p in range(0,5): self.play(Write(lines[p])) - # self.wait(0.5) - # self.camera_frame.save_state() - # self.camera_frame.set_width(0.6) - # self.play(self.camera_frame.move_to, points[0]) - # self.wait(0.4) - # self.play(self.camera_frame.move_to, points[1]) - # self.wait(0.4) - # self.play(self.camera_frame.move_to, points[2]) - # self.wait(0.3) - # self.play(self.camera_frame.move_to, points[3]) - # self.wait(1) - # self.play(self.camera_frame.move_to,ORIGIN) - # self.camera_frame.set_width(14) + self.wait(1) self.get_zoomed_display_pop_out_animation() diff --git a/FSF-2020/calculus/series-and-transformations/README.md b/FSF-2020/calculus/series-and-transformations/README.md index 4747205..0ca6397 100644 --- a/FSF-2020/calculus/series-and-transformations/README.md +++ b/FSF-2020/calculus/series-and-transformations/README.md @@ -4,10 +4,9 @@ GitHub Handle: <a href="https://github.com/GSri30/">GSri30</a> Sub-Topics Covered:
<ul>
- <li>Power Series
- <li>Taylor Series
- <li>Laplace Transformation
- <li>Fourier Transformation
- <li>z-Transform
- <li>Constant-Q transform
+ <li><a href="https://math.animations.fossee.in/contents/series-and-transformations/series/taylor-series">Taylor Series</a>
+ <li><a href="https://math.animations.fossee.in/contents/series-and-transformations/series/power-series">Power Series</a>
+ <li><a href="https://math.animations.fossee.in/contents/series-and-transformations/transformations/fourier-transform">Fourier Transformation</a>
+ <li><a href="https://math.animations.fossee.in/contents/series-and-transformations/transformations/laplace-transform">Laplace Transformation</a>
+ <li><a href="https://math.animations.fossee.in/contents/series-and-transformations/transformations/z-transform">Z-Transform</a>
</ul>
diff --git a/FSF-2020/calculus/series-and-transformations/Taylor Series/README.md b/FSF-2020/calculus/series-and-transformations/Taylor Series/README.md index ce3b088..88eb772 100644 --- a/FSF-2020/calculus/series-and-transformations/Taylor Series/README.md +++ b/FSF-2020/calculus/series-and-transformations/Taylor Series/README.md @@ -2,7 +2,7 @@  #### Taylor Series GeneralForm - + #### Radius Of Convergence  diff --git a/FSF-2020/calculus/series-and-transformations/Taylor Series/gifs/file2_TaylorExpansionGeneralForm.gif b/FSF-2020/calculus/series-and-transformations/Taylor Series/gifs/file2_TaylorExpansionGeneralForm.gif Binary files differindex e6d9171..33dfa81 100644 --- a/FSF-2020/calculus/series-and-transformations/Taylor Series/gifs/file2_TaylorExpansionGeneralForm.gif +++ b/FSF-2020/calculus/series-and-transformations/Taylor Series/gifs/file2_TaylorExpansionGeneralForm.gif diff --git a/FSF-2020/calculus/series-and-transformations/Taylor Series/gifs/file2a_TaylorExpansionGeneralForm.gif b/FSF-2020/calculus/series-and-transformations/Taylor Series/gifs/file2a_TaylorExpansionGeneralForm.gif Binary files differnew file mode 100644 index 0000000..33dfa81 --- /dev/null +++ b/FSF-2020/calculus/series-and-transformations/Taylor Series/gifs/file2a_TaylorExpansionGeneralForm.gif diff --git a/FSF-2020/calculus/series-and-transformations/Taylor Series/video1_Example_TaylorExpansion.py b/FSF-2020/calculus/series-and-transformations/Taylor Series/video1_Example_TaylorExpansion.py index b132811..a0c7176 100644 --- a/FSF-2020/calculus/series-and-transformations/Taylor Series/video1_Example_TaylorExpansion.py +++ b/FSF-2020/calculus/series-and-transformations/Taylor Series/video1_Example_TaylorExpansion.py @@ -95,7 +95,6 @@ class graphScene(GraphScene,MovingCameraScene): obj.set_color(GOLD_A) group=VGroup(coeff[0],coeff[1],coeff[2]) - #group.shift(2*LEFT+2*DOWN) firstApprox=[self.get_graph(lambda x:1,color=BLUE)] secondApprox=[self.get_graph(lambda x:1,color=BLUE), @@ -142,13 +141,6 @@ class graphScene(GraphScene,MovingCameraScene): bottomText8.scale(0.5) bottomText1.shift(4.5*RIGHT+2.5*DOWN) - # bottomText2.shift(4.5*RIGHT+2.5*DOWN) - # bottomText3.shift(4.5*RIGHT+2.5*DOWN) - # bottomText4.shift(4.5*RIGHT+2.5*DOWN) - # bottomText5.shift(4.5*RIGHT+2.5*DOWN) - # bottomText6.shift(4.5*RIGHT+2.5*DOWN) - # bottomText7.shift(4.5*RIGHT+2.5*DOWN) - # bottomText8.shift(4.5*RIGHT+2.5*DOWN) bottomText2.shift(3*RIGHT*x_each_unit+2.5*DOWN*y_each_unit) bottomText3.shift(3*RIGHT*x_each_unit+2.5*DOWN*y_each_unit) bottomText4.shift(3*RIGHT*x_each_unit+2.5*DOWN*y_each_unit) @@ -230,16 +222,7 @@ class graphScene(GraphScene,MovingCameraScene): self.play(FadeOut(self.axes),FadeOut(textFinal),FadeOut(secondGraph),FadeOut(trTextGrup),FadeOut(mainfunction),FadeOut(fx),FadeOut(coeff[0]),FadeOut(coeff[1]),FadeOut(coeff[2])) self.play(Write(finalFormula)) self.wait(2) - # self.play(ReplacementTransform(secondApprox[2],secondApprox[3])) - # self.wait(0.5) - # self.play(ReplacementTransform(secondApprox[3],secondApprox[4])) - # self.wait(0.5) - # self.play(ReplacementTransform(secondApprox[4],secondApprox[5])) - # self.wait(0.5) - # self.play(ReplacementTransform(secondApprox[0],secondApprox[0])) - # self.wait(0.5) - # self.play(ReplacementTransform(secondApprox[0],secondApprox[0])) - # self.wait(0.5) + diff --git a/FSF-2020/calculus/series-and-transformations/Taylor Series/video2_TaylorExpansionGeneralForm.py b/FSF-2020/calculus/series-and-transformations/Taylor Series/video2_TaylorExpansionGeneralForm.py index c177ab4..5be336b 100644 --- a/FSF-2020/calculus/series-and-transformations/Taylor Series/video2_TaylorExpansionGeneralForm.py +++ b/FSF-2020/calculus/series-and-transformations/Taylor Series/video2_TaylorExpansionGeneralForm.py @@ -7,7 +7,7 @@ class intro(Scene): equation=TextMobject("$f(x)=$","${ e }^{ -x^{ 2 } }$") equation.scale(2) equation.set_color_by_tex_to_color_map({"${ e }^{ -x^{ 2 } }$":RED}) - text=TextMobject("at $a=1$") + text=TextMobject("about $x=1$") text.scale(0.7) text.shift(DOWN) @@ -41,7 +41,7 @@ def formFormula(coeff_list,variable_list): return expansion,coeff_list -class graphScene(GraphScene): +class graphScene(GraphScene,MovingCameraScene): CONFIG = { "x_min": -8, "x_max": 8, @@ -55,6 +55,9 @@ class graphScene(GraphScene): "exclude_zero_label": True, "x_labeled_nums": range(-8, 8, 1), } + def setup(self): + GraphScene.setup(self) + MovingCameraScene.setup(self) def construct(self): x_each_unit = self.x_axis_width / (self.x_max - self.x_min) y_each_unit = self.y_axis_height / (self.y_max - self.y_min) @@ -62,7 +65,7 @@ class graphScene(GraphScene): equation=TextMobject("$f(x)=$","${ e }^{ -x^{ 2 } }$") equation.scale(0.55) equation.set_color_by_tex_to_color_map({"${ e }^{ -x^{ 2 } }$":RED}) - text=TextMobject("$a=1$") + text=TextMobject("about $x=1$") text.scale(0.55) equation.shift(3.39*UP+5*LEFT) text.shift(3*UP+5*LEFT) @@ -80,7 +83,7 @@ class graphScene(GraphScene): trTextGrup.scale(0.5) trTextGrup.to_corner(UP+RIGHT) self.play(Write(trTextGrup)) - self.setup_axes(animate=True) + self.setup_axes(animate=True,scalee=1) fx=TextMobject("${ e }^{ -x^{ 2 } }$") fx.scale(0.5) @@ -91,29 +94,29 @@ class graphScene(GraphScene): self.wait(1.4) coeff=[TextMobject("$e^{-1}$"),TextMobject("$f'(x)$"),TextMobject("$\\frac { f''(x) }{ 2! } $")] - coeff[0].shift(3.33*UP+3.65*RIGHT) - coeff[0].scale(0.45) - coeff[1].shift(3.33*UP+4.13*RIGHT) - coeff[1].scale(0.275) - coeff[2].shift(3.33*UP+5.36*RIGHT) - coeff[2].scale(0.28) + coeff[0].shift(4.1*y_each_unit*UP+5.15*RIGHT*x_each_unit) + coeff[0].scale(0.3) + coeff[1].shift(4*y_each_unit*UP+5.7*RIGHT*x_each_unit) + coeff[1].scale(0.2) + coeff[2].shift(4*y_each_unit*UP+7.3*RIGHT*x_each_unit) + coeff[2].scale(0.18) for obj in coeff: obj.set_color(GOLD_A) - firstApprox=[self.get_graph(lambda x:math.exp(-1),color=BLUE,x_min=-5.5,x_max=5.5)] - secondApprox=[self.get_graph(lambda x:math.exp(-1)-2*(x-1)*math.exp(-1),color=BLUE,x_min=-5.5,x_max=5.5), - self.get_graph(lambda x:math.exp(-1)+3*(x-1)*math.exp(-1),color=BLUE,x_min=-5.5,x_max=5.5), - self.get_graph(lambda x:math.exp(-1)-4*(x-1)*math.exp(-1),color=BLUE,x_min=-5.5,x_max=5.5)] - thirdApprox=[self.get_graph(lambda x:math.exp(-1)-2*(x-1)*math.exp(-1)-2*math.exp(-1)*(x-1)**2,color=BLUE,x_max=5.5,x_min=-5.5), - self.get_graph(lambda x:math.exp(-1)-2*(x-1)*math.exp(-1)-0.1*math.exp(-1)*(x-1)**2,color=BLUE,x_max=5.5,x_min=-5.5), - self.get_graph(lambda x:math.exp(-1)-2*(x-1)*math.exp(-1),color=BLUE,x_max=5.5,x_min=-5.5), - self.get_graph(lambda x:math.exp(-1)-2*(x-1)*math.exp(-1)+0.5*math.exp(-1)*(x-1)**2,color=BLUE,x_max=5.5,x_min=-5.5), - self.get_graph(lambda x:math.exp(-1)-2*(x-1)*math.exp(-1)+2*math.exp(-1)*(x-1)**2,color=BLUE,x_max=5.5,x_min=-5.5)] + firstApprox=[self.get_graph(lambda x:math.exp(-1),color=BLUE,x_min=-3,x_max=4)] + secondApprox=[self.get_graph(lambda x:math.exp(-1)-2*(x-1)*math.exp(-1),color=BLUE,x_min=-3,x_max=4), + self.get_graph(lambda x:math.exp(-1)+3*(x-1)*math.exp(-1),color=BLUE,x_min=-3,x_max=4), + self.get_graph(lambda x:math.exp(-1)-4*(x-1)*math.exp(-1),color=BLUE,x_min=-3,x_max=4)] + thirdApprox=[self.get_graph(lambda x:math.exp(-1)-2*(x-1)*math.exp(-1)-2*math.exp(-1)*(x-1)**2,color=BLUE,x_max=4,x_min=-3), + self.get_graph(lambda x:math.exp(-1)-2*(x-1)*math.exp(-1)-0.1*math.exp(-1)*(x-1)**2,color=BLUE,x_max=4,x_min=-3), + self.get_graph(lambda x:math.exp(-1)-2*(x-1)*math.exp(-1),color=BLUE,x_max=4,x_min=-3), + self.get_graph(lambda x:math.exp(-1)-2*(x-1)*math.exp(-1)+0.5*math.exp(-1)*(x-1)**2,color=BLUE,x_max=4,x_min=-3), + self.get_graph(lambda x:math.exp(-1)-2*(x-1)*math.exp(-1)+2*math.exp(-1)*(x-1)**2,color=BLUE,x_max=4,x_min=-3)] - firstGraph=self.get_graph(lambda x:math.exp(-1),color=BLUE,x_min=-5.5,x_max=5.5) - secondGraph=self.get_graph(lambda x:math.exp(-1)-2*(x-1)*math.exp(-1),color=BLUE,x_min=-5.5,x_max=5.5) - thirdGraph=self.get_graph(lambda x:math.exp(-1)-2*(x-1)*math.exp(-1)+math.exp(-1)*(x-1)**2,color=BLUE,x_max=5.5,x_min=-5.5) + firstGraph=self.get_graph(lambda x:math.exp(-1),color=BLUE,x_min=-3,x_max=4) + secondGraph=self.get_graph(lambda x:math.exp(-1)-2*(x-1)*math.exp(-1),color=BLUE,x_min=-3,x_max=4) + thirdGraph=self.get_graph(lambda x:math.exp(-1)-2*(x-1)*math.exp(-1)+math.exp(-1)*(x-1)**2,color=BLUE,x_max=4,x_min=-3) bottomText1=TextMobject("Apply","$f(1)=T_{n}(1)$") bottomText2=TextMobject("This gives","$a_{ 0 }=e^{-1}$") @@ -147,16 +150,35 @@ class graphScene(GraphScene): bottomText8.scale(0.5) bottomText1.shift(4.5*RIGHT+2.5*DOWN) - bottomText2.shift(4.5*RIGHT+2.5*DOWN) - bottomText3.shift(4.5*RIGHT+2.5*DOWN) - bottomText4.shift(4.5*RIGHT+2.5*DOWN) - bottomText5.shift(4.5*RIGHT+2.5*DOWN) - bottomText6.shift(4.5*RIGHT+2.5*DOWN) - bottomText7.shift(4.5*RIGHT+2.5*DOWN) - bottomText8.shift(4.5*RIGHT+2.5*DOWN) + bottomText2.shift(5*RIGHT*x_each_unit+2.5*DOWN*y_each_unit) + bottomText3.shift(5*RIGHT*x_each_unit+2.5*DOWN*y_each_unit) + bottomText4.shift(5*RIGHT*x_each_unit+2.5*DOWN*y_each_unit) + bottomText5.shift(5*RIGHT*x_each_unit+2.5*DOWN*y_each_unit) + bottomText6.shift(5.7*RIGHT*x_each_unit+2.5*DOWN*y_each_unit) + bottomText7.shift(5.7*RIGHT*x_each_unit+2.5*DOWN*y_each_unit) + bottomText8.shift(5.7*RIGHT*x_each_unit+2.5*DOWN*y_each_unit) + + bottomText2.scale(0.7) + bottomText3.scale(0.7) + bottomText4.scale(0.7) + bottomText5.scale(0.7) + bottomText6.scale(0.7) + bottomText7.scale(0.7) + bottomText8.scale(0.7) self.play(Write(bottomText1)) - self.wait(1) + self.wait(0.8) + self.camera_frame.save_state() + self.play(self.camera_frame.set_width, 8, + self.camera_frame.move_to, x_each_unit*UP+x_each_unit*2*RIGHT, + ApplyMethod(trTextGrup.move_to,4*y_each_unit*UP+6.1*RIGHT*x_each_unit), + ApplyMethod(bottomText1.move_to,5.4*RIGHT*x_each_unit+2.5*DOWN*y_each_unit), + ApplyMethod(equation.shift,1.39*DOWN+2*RIGHT+RIGHT*x_each_unit*2), + ApplyMethod(text.shift,1.39*DOWN+2*RIGHT+RIGHT*x_each_unit*2),) + self.play(ApplyMethod(text.scale,0.5),ApplyMethod(equation.scale,0.5),ApplyMethod(bottomText1.scale,0.6),ApplyMethod(trTextGrup.scale,0.7)) + self.play(ApplyMethod(text.shift,0.25*UP)) + self.wait(0.6) + self.play(ShowCreation(firstApprox[0]),ReplacementTransform(bottomText1,bottomText2)) #change coeff in tn(x) self.play(ReplacementTransform(generalized_eq_coeff[0],coeff[0])) @@ -166,8 +188,6 @@ class graphScene(GraphScene): self.play(ReplacementTransform(firstApprox[0],secondApprox[1])) self.wait(0.5) self.play(ReplacementTransform(secondApprox[1],secondApprox[2])) - # self.wait(0.5) - # self.play(ReplacementTransform(secondApprox[2],secondApprox[0])) self.wait(1) self.play(ReplacementTransform(bottomText3,bottomText4),FadeOut(secondApprox[2])) self.wait(1) @@ -179,8 +199,6 @@ class graphScene(GraphScene): self.play(ReplacementTransform(secondGraph,thirdApprox[0])) self.wait(0.6) self.play(ReplacementTransform(thirdApprox[0],thirdApprox[1])) - # self.wait(0.6) - # self.play(ReplacementTransform(thirdApprox[1],thirdApprox[2])) self.wait(0.6) self.play(ReplacementTransform(thirdApprox[1],thirdApprox[3])) self.wait(0.6) @@ -193,10 +211,13 @@ class graphScene(GraphScene): self.wait(2) textFinal=TextMobject("And so on..!") - textFinal.scale(0.7) - textFinal.shift(4.5*RIGHT+2.5*DOWN) + textFinal.scale(0.35) + textFinal.shift(5.7*RIGHT*x_each_unit+2.5*DOWN*y_each_unit) self.play(ReplacementTransform(bottomText8,textFinal)) - self.wait(2.5) + self.wait(1) + self.play(FadeOut(equation),FadeOut(text)) + self.play(self.camera_frame.set_width, 15, + self.camera_frame.move_to, 0) finalFormula=TextMobject("Hence","$T_{ n }(x)$","=","$f(1)+f'(1)(x-1)+\\frac { f''(1) }{ 2! }(x-1)^2+..+\\frac { { f }^{ n }(1) }{ n! } { (x-1) }^{ n }$") finalFormula.scale(0.8) @@ -204,4 +225,4 @@ class graphScene(GraphScene): self.play(FadeOut(self.axes),FadeOut(textFinal),FadeOut(thirdGraph),FadeOut(trTextGrup),FadeOut(mainfunction),FadeOut(fx),FadeOut(coeff[0]),FadeOut(coeff[1]),FadeOut(coeff[2])) self.play(Write(finalFormula)) - self.wait(2)
\ No newline at end of file + self.wait(2) diff --git a/FSF-2020/calculus/series-and-transformations/Taylor Series/video4_DivergentRemainder.py b/FSF-2020/calculus/series-and-transformations/Taylor Series/video4_DivergentRemainder.py index 1f41c97..6b368da 100644 --- a/FSF-2020/calculus/series-and-transformations/Taylor Series/video4_DivergentRemainder.py +++ b/FSF-2020/calculus/series-and-transformations/Taylor Series/video4_DivergentRemainder.py @@ -43,7 +43,6 @@ class graphScene(GraphScene): bottomText1=TextMobject("$R_{n}(x)=\\frac { d }{ dx } ($","area bounded","$)$") bottomText1.set_color_by_tex_to_color_map({"area bounded":ORANGE}) - #bottomText2.set_color_by_tex_to_color_map({"area bounded":BLUE}) arrow=TextMobject("$\downarrow$") arrow.scale(2.5) arrow.shift(ORIGIN+x_each_unit*RIGHT*9.5+UP*y_each_unit) @@ -56,12 +55,8 @@ class graphScene(GraphScene): increasingText.scale(0.4) bottomText1.scale(0.5) - #bottomText2.scale(0.5) - #bottomText3.scale(0.5) bottomText1.shift(3.5*LEFT+2*DOWN) - #bottomText2.shift(3.5*LEFT+2.4*DOWN) - #bottomText3.shift(3.5*LEFT+2.8*DOWN) dline=DashedLine(start=ORIGIN+8*y_each_unit*UP,end=ORIGIN+8*y_each_unit*DOWN) dline.shift(ORIGIN+x_each_unit*4*RIGHT) @@ -72,11 +67,9 @@ class graphScene(GraphScene): self.play(Write(dline)) self.wait(0.5) self.play(ShowCreation(area1),ShowCreation(area2),Write(bottomText1)) - # self.play(Write(bottomText2)) - # self.play(FadeIn(bottomText3)) self.play(Write(arrow)) self.wait(0.7) self.play(Write(increasingText)) self.play(FadeIn(followupText)) self.wait(2) -
\ No newline at end of file + diff --git a/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file3_Non_Standard_Basis.py b/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file3_Non_Standard_Basis.py deleted file mode 100644 index 6410a2c..0000000 --- a/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file3_Non_Standard_Basis.py +++ /dev/null @@ -1,51 +0,0 @@ -from manimlib.imports import * - -class NSB(ThreeDScene): - def construct(self): - - axes = ThreeDAxes(x_min = -4,x_max=4,y_min=-4,y_max=4,z_min=-4,z_max=4) - self.play(ShowCreation(axes)) - self.move_camera(phi=60*DEGREES,theta=45*DEGREES,run_time=3) - self.begin_ambient_camera_rotation(rate=0.5) - - matrix = [[0.577,0.577,0.577],[-0.577,0.577,0.577],[0.577,-0.577,0.577]] - - line1 = Line(start = ORIGIN,end = 1*RIGHT) - line1.set_color(DARK_BLUE) - tip1 = Polygon(RIGHT,0.9*RIGHT-0.1*DOWN,0.9*RIGHT-0.1*UP) - tip1.set_opacity(1) - tip1.set_fill(DARK_BLUE) - tip1.set_color(DARK_BLUE) - - arrow2 = Line(start = ORIGIN,end = 1*UP) - arrow2.set_color(DARK_BLUE) - tip2 = Polygon(UP,0.9*UP-0.1*RIGHT,0.9*UP-0.1*LEFT) - tip2.set_opacity(1) - tip2.set_fill(DARK_BLUE) - tip2.set_color(DARK_BLUE) - arrow2.set_color(DARK_BLUE) - - arrow3 = Line(start = ORIGIN,end = [0,0,1]) - arrow3.set_color(DARK_BLUE) - tip3 = Polygon([0,0,1],[0,0,0.9]-0.1*RIGHT,[0,0,0.9]-0.1*LEFT) - tip3.set_opacity(1) - tip3.set_fill(DARK_BLUE) - tip3.set_color(DARK_BLUE) - - line1.apply_matrix(matrix) - tip1.apply_matrix(matrix) - arrow2.apply_matrix(matrix) - tip2.apply_matrix(matrix) - arrow3.apply_matrix(matrix) - tip3.apply_matrix(matrix) - - self.play(ShowCreation(line1), ShowCreation(tip1), ShowCreation(arrow2), ShowCreation(tip2), ShowCreation(arrow3), ShowCreation(tip3)) - - text = TextMobject(r"This is also a set of Orthonormal Vectors") - text.set_color(DARK_BLUE) - self.add_fixed_in_frame_mobjects(text) - text.scale(0.6) - text.move_to(3*DOWN+3.5*RIGHT) - self.play(Write(text)) - - self.wait(7)
\ No newline at end of file diff --git a/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/README.md b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/README.md new file mode 100644 index 0000000..832aa5d --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/README.md @@ -0,0 +1,18 @@ +# Contributer: Archit Sangal +My Github Account : <a href="https://github.com/architsangal">architsangal</a> (https://github.com/architsangal) +<br/></br> + +## Sub-Topics Covered: ++ Gramm-Schmidt Orthogonalization Process + +#### Video 1: Introduction to Gram-Schmidt Orthogonalization Process + + +#### Video 2: Obtaining orthogonal vectors using projections + + +#### Video 3: Visual Explanation of how Gram-Schmidt Orthogonalization Process give mutually orthonormal vectors + + +#### Video 4: Example of Orthonormal Vectors which are different from standard basis +
\ No newline at end of file diff --git a/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file_introduction.py b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file1_introduction.py index ccd23c9..ccd23c9 100644 --- a/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file_introduction.py +++ b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file1_introduction.py diff --git a/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file1_projections.py b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file2_projections.py index dd4b8d4..dd4b8d4 100755 --- a/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file1_projections.py +++ b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file2_projections.py diff --git a/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file2_orthonormal.py b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file3_orthonormal.py index af51fc6..a74b641 100644 --- a/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file2_orthonormal.py +++ b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file3_orthonormal.py @@ -6,7 +6,7 @@ class Algo(ThreeDScene): axes = ThreeDAxes(x_min = -5,x_max=5,y_min=-3,y_max=3,z_min=-4,z_max=4) self.play(ShowCreation(axes)) - text = TextMobject(r"This is the vector $\beta_1(=\left[\begin{array}{c} 4\\0\\0 \end{array}\right])$") + text = TextMobject(r"This is the vector $\beta_1 =\left[\begin{array}{c} 4\\0\\0 \end{array}\right]$") text.set_color(GREEN) text.scale(0.6) text.move_to(3*UP+5*LEFT) @@ -42,7 +42,7 @@ class Algo(ThreeDScene): self.wait() self.play(FadeOut(text)) - text = TextMobject(r"Consider another vector $\beta_2(=\left[\begin{array}{c} 2\\2\\0 \end{array}\right])$") + text = TextMobject(r"Consider another vector $\beta_2=\left[\begin{array}{c} 2\\2\\0 \end{array}\right]$") text1 = TextMobject(r"which is linearly independent to $\beta_1$") text.set_color(GREEN) text1.set_color(GREEN) @@ -141,15 +141,15 @@ class Algo(ThreeDScene): self.add_fixed_orientation_mobjects(axis[1]) ############################################################################# - text = TextMobject(r"These are the same two orthonormal vectors $\alpha_{1}$ and $\alpha_{2}$") - text.scale(0.6) - text.set_color(DARK_BLUE) - self.add_fixed_in_frame_mobjects(text) - text.move_to(3*(DOWN+RIGHT)) - self.play(Write(text)) + self.move_camera(phi=70*DEGREES,theta=30*DEGREES,run_time=3) + xy_plane = Polygon(5*RIGHT+3*UP,-5*RIGHT+3*UP,-5*RIGHT-3*UP,5*RIGHT-3*UP) + xy_plane.set_color("#333333") + xy_plane.set_fill("#333333") + xy_plane.set_opacity(1) + xy_plane.fade(0.7) + self.play(ShowCreation(xy_plane)) - self.move_camera(phi=60*DEGREES,theta=45*DEGREES,run_time=3) - self.begin_ambient_camera_rotation(rate=0.3) + #self.begin_ambient_camera_rotation(rate=0.1) line1 = Line(start = ORIGIN,end = 1*RIGHT) line1.set_color(DARK_BLUE) @@ -183,9 +183,9 @@ class Algo(ThreeDScene): a_tip_c1.set_fill(GOLD_E) a_tip_c1.set_color(GOLD_E) - self.play(FadeOut(text), ShowCreation(a_line), ShowCreation(a_tip), ShowCreation(a_line_c1), ShowCreation(a_tip_c1)) + self.play(ShowCreation(a_line), ShowCreation(a_tip), ShowCreation(a_line_c1), ShowCreation(a_tip_c1)) - text = TextMobject(r"Now, we have a vector $\beta_3(=\left[\begin{array}{c} 2\\2\\2 \end{array}\right])$") + text = TextMobject(r"Now, we have a vector $\beta_3=\left[\begin{array}{c} 2\\2\\2 \end{array}\right]$") text.set_color(GOLD_E) text.scale(0.7) self.add_fixed_in_frame_mobjects(text) @@ -197,8 +197,8 @@ class Algo(ThreeDScene): p_line1 = Line(start = ORIGIN,end = 2*RIGHT) p_line1.set_color(GOLD_E) - p_tip1 = Polygon(RIGHT,0.8*RIGHT+0.2*DOWN,0.8*RIGHT+0.2*UP) - p_tip1.move_to(2*RIGHT) + p_tip1 = Polygon(2*RIGHT,1.8*RIGHT+0.2*DOWN,1.8*RIGHT+0.2*UP) + p_tip1.set_opacity(1) p_tip1.set_fill(GOLD_E) p_tip1.set_color(GOLD_E) @@ -211,6 +211,7 @@ class Algo(ThreeDScene): self.add_fixed_in_frame_mobjects(text) text.move_to(3*(DOWN+RIGHT)) self.play(Write(text)) + self.begin_ambient_camera_rotation(rate=0.05) self.wait() self.play(FadeOut(text)) @@ -241,6 +242,7 @@ class Algo(ThreeDScene): self.add_fixed_in_frame_mobjects(text) text.move_to(3*(DOWN+RIGHT)) self.play(Write(text)) + self.play(ShowCreation(o_line1), ShowCreation(o_tip1)) self.wait(2) self.play(FadeOut(a_line_c1), FadeOut(a_tip_c1), @@ -266,7 +268,7 @@ class Algo(ThreeDScene): last_a_tip.set_fill(PURPLE_E) last_a_tip.set_color(PURPLE_E) - self.wait() + self.wait(5) text = TextMobject(r"Take projection on $\alpha_2$") text.scale(0.6) text.set_color(GOLD_E) @@ -283,7 +285,7 @@ class Algo(ThreeDScene): self.add_fixed_in_frame_mobjects(text) text.move_to(3*DOWN+3.5*RIGHT) self.play(Write(text)) - self.play(ShowCreation(o_line1), ShowCreation(o_tip1)) + #self.play(ShowCreation(o_line1), ShowCreation(o_tip1)) self.wait(2) self.play(ShowCreation(last_a_tip), ShowCreation(last_a)) self.wait() @@ -299,16 +301,16 @@ class Algo(ThreeDScene): self.play(FadeOut(o_line1), FadeOut(o_tip1), FadeOut(a_line1_c1), FadeOut(a_tip1_c1), Transform(last_a,larrow3), Transform(last_a_tip,ltip3)) text = TextMobject(r"Normalize, the vector") - text1 = TextMobject(r"$\beta_3$-(projection of $\beta_3$ on $\alpha_1$ + projection of $\beta_3$ on $\alpha_2$") + text1 = TextMobject(r"$\beta_3$-(projection of $\beta_3$ on $\alpha_1$ + projection of $\beta_3$ on $\alpha_2)$") text.set_color(PURPLE_E) text1.set_color(PURPLE_E) - text.scale(0.6) - text1.scale(0.6) + text.scale(0.55) + text1.scale(0.55) self.add_fixed_in_frame_mobjects(text) - self.add_fixed_in_frame_mobjects(text1) text.move_to(3*DOWN+3*RIGHT) - text1.move_to(3.5*DOWN+3*RIGHT) + text1.move_to(3.5*DOWN+3.25*RIGHT) self.play(Write(text)) + self.add_fixed_in_frame_mobjects(text1) self.play(Write(text1)) arrow3 = Line(start = ORIGIN,end = [0,0,1]) @@ -330,4 +332,4 @@ class Algo(ThreeDScene): text.move_to(3*DOWN+3.5*RIGHT) self.play(Write(text)) - self.wait(3)
\ No newline at end of file + self.wait(8) diff --git a/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file4_Non_Standard_Basis.py b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file4_Non_Standard_Basis.py new file mode 100644 index 0000000..1d23aa2 --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file4_Non_Standard_Basis.py @@ -0,0 +1,69 @@ +from manimlib.imports import * + +class NSB(ThreeDScene): + def construct(self): + + line1 = Line(start = ORIGIN,end = 1*RIGHT) + line1.set_color(DARK_BLUE) + tip1 = Polygon(RIGHT,0.9*RIGHT-0.1*DOWN,0.9*RIGHT-0.1*UP) + tip1.set_opacity(1) + tip1.set_fill(DARK_BLUE) + tip1.set_color(DARK_BLUE) + + arrow2 = Line(start = ORIGIN,end = 1*UP) + arrow2.set_color(DARK_BLUE) + tip2 = Polygon(UP,0.9*UP-0.1*RIGHT,0.9*UP-0.1*LEFT) + tip2.set_opacity(1) + tip2.set_fill(DARK_BLUE) + tip2.set_color(DARK_BLUE) + arrow2.set_color(DARK_BLUE) + + arrow3 = Line(start = ORIGIN,end = [0,0,1]) + arrow3.set_color(DARK_BLUE) + tip3 = Polygon([0,0,1],[0,0,0.9]-0.1*RIGHT,[0,0,0.9]-0.1*LEFT) + tip3.set_opacity(1) + tip3.set_fill(DARK_BLUE) + tip3.set_color(DARK_BLUE) + + axes = ThreeDAxes(x_min = -3,x_max=3,y_min=-3,y_max=3,z_min=-3,z_max=3) + self.play(ShowCreation(axes)) + self.move_camera(phi=70*DEGREES,theta=0*DEGREES,run_time=3) + self.begin_ambient_camera_rotation(rate=0.2) + + #matrix = [[1,0,0],[0,1,0],[0,0,1]] + matrix = [[0.70710678118,-0.57735026919,-0.57735026919],[0.70710678118,0.57735026919,0.57735026919],[0,-0.57735026919,0.57735026919]] + matrix1 = [[0.70710678118,0,0],[0.70710678118,1,0],[0,0,1]] + + matrix1 = [[0.70710678118,-0.70710678118,0],[0.70710678118,0.70710678118,0],[0,0,1]] + matrix2 = [[1,0,0],[0,0.70710678118,0.70710678118],[0,-0.70710678118,0.70710678118]] + + + line1.apply_matrix(matrix1) + tip1.apply_matrix(matrix1) + arrow2.apply_matrix(matrix1) + tip2.apply_matrix(matrix1) + arrow3.apply_matrix(matrix1) + tip3.apply_matrix(matrix1) + + line1.apply_matrix(matrix2) + tip1.apply_matrix(matrix2) + arrow2.apply_matrix(matrix2) + tip2.apply_matrix(matrix2) + arrow3.apply_matrix(matrix2) + tip3.apply_matrix(matrix2) + + self.play(ShowCreation(line1), + ShowCreation(tip1), + ShowCreation(arrow2), + ShowCreation(tip2), + ShowCreation(arrow3), + ShowCreation(tip3)) + + text = TextMobject(r"This is also a set of Orthonormal Vectors") + text.set_color(DARK_BLUE) + self.add_fixed_in_frame_mobjects(text) + text.scale(0.6) + text.move_to(3*DOWN+3.5*RIGHT) + self.play(Write(text)) + + self.wait(22) diff --git a/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file5.gif b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file5.gif Binary files differnew file mode 100644 index 0000000..cdc0f2d --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file5.gif diff --git a/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file6.gif b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file6.gif Binary files differnew file mode 100644 index 0000000..e03f265 --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file6.gif diff --git a/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file7.gif b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file7.gif Binary files differnew file mode 100644 index 0000000..19a13dd --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file7.gif diff --git a/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file8.gif b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file8.gif Binary files differnew file mode 100644 index 0000000..0ef4551 --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file8.gif diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/README.md b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/README.md new file mode 100644 index 0000000..2a46424 --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/README.md @@ -0,0 +1,30 @@ +# Contributer: Archit Sangal +My Github Account : <a href="https://github.com/architsangal">architsangal</a> (https://github.com/architsangal) +<br/></br> + +## Sub-Topics Covered: ++ Linear Transformations (Linear Maps) + +#### Video 1: Visually understanding linear transformation(using grid) + + +#### Video 2: Linear Transformation when form 1 is given + + +#### Video 3: Matrix Representation Of Linear Transformation + + +#### Video 4: Understand Linear Transformations visually + + +#### Video 5: Uniform Scaling + + +#### Fig.1 Horizontal Shear + + +#### Fig.2 Vertical Shear + + +#### Video 6: Rotation by an angle of in anticlockwise direction +
\ No newline at end of file diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file.txt b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file.txt deleted file mode 100644 index cae98ce..0000000 --- a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file.txt +++ /dev/null @@ -1,3 +0,0 @@ -file 'text.mp4' -file 'LinearTransformation.mp4' -file 'NonLinearTransformation.mp4' diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file10.gif b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file10.gif Binary files differnew file mode 100644 index 0000000..d996130 --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file10.gif diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file11.gif b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file11.gif Binary files differnew file mode 100644 index 0000000..d8c64b7 --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file11.gif diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file12.gif b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file12.gif Binary files differnew file mode 100644 index 0000000..92bdff6 --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file12.gif diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file13.gif b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file13.gif Binary files differnew file mode 100644 index 0000000..ba6c156 --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file13.gif diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file14.gif b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file14.gif Binary files differnew file mode 100644 index 0000000..fd9bc7b --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file14.gif diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file1_transformations.py b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file1_transformations.py index 677f890..0182bd9 100644 --- a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file1_transformations.py +++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file1_transformations.py @@ -2,16 +2,20 @@ from manimlib.imports import * class text(Scene): def construct(self): - text1 = TextMobject("For a grid, undergoing a linear transformation, all it's straight lines") + text1 = TextMobject("For a grid, undergoing a linear transformation, all its straight lines") text1.scale(0.9) text2 = TextMobject("must either remain straight lines or sends to a point in the grid formed") text2.scale(0.9) + text3 = TextMobject("Origin must remain where it was before transformation.") + text3.scale(0.9) text1.move_to(ORIGIN+UP) text2.move_to(ORIGIN) + text3.move_to(ORIGIN+DOWN) self.play(Write(text1)) self.play(Write(text2)) + self.play(Write(text3)) self.wait() - self.play(FadeOut(text1),FadeOut(text2)) + self.play(FadeOut(text1),FadeOut(text2),FadeOut(text3)) class LinearTransformation(LinearTransformationScene): CONFIG = { @@ -34,6 +38,7 @@ class NonLinearTransformation(Scene): def construct(self): grid = NumberPlane() self.play(ShowCreation(grid),run_time =2) + # I have taken reference from purusharth's code NonLinearTrans = lambda coordinates : coordinates + np.array([np.sin(coordinates[1]),np.sin(coordinates[0]),0,]) grid.prepare_for_nonlinear_transform() self.play(grid.apply_function,NonLinearTrans) @@ -42,4 +47,27 @@ class NonLinearTransformation(Scene): text[1].move_to(1.5*DOWN+4*LEFT) text.add_background_rectangle() self.play(Write(text)) - self.wait()
\ No newline at end of file + self.wait() + +class MoveOrigin(LinearTransformationScene): + + CONFIG = { + "show_basis_vectors": False, + } + def construct(self): + self.wait() + + dot = Dot(ORIGIN, color = YELLOW) + self.add_transformable_mobject(dot) + self.apply_nonlinear_transformation(self.func) + text = TextMobject("This is also not a linear transformation as the origin moves from its original position") + text.move_to(2*DOWN) + text.scale(0.5) + text.set_color(YELLOW) + text.add_background_rectangle() + self.play(Write(text)) + self.wait() + + def func(self, point): + matrix_transform = self.get_matrix_transformation([[1, -1], [1, 1]]) + return matrix_transform(point) + UP+ RIGHT diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file_before_matrix.py b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file2_before_matrix.py index 96e456d..1f6badd 100755 --- a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file_before_matrix.py +++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file2_before_matrix.py @@ -69,7 +69,7 @@ class Linear(GraphScene): class withgrid(LinearTransformationScene): def construct(self): - heading = TextMobject(r"Now, Imagine this happening for all the vectors") + heading = TextMobject(r"Now, imagine this happening for all the points") heading.scale(0.5) heading.move_to(UP*2.5+LEFT*4) self.play(Write(heading)) @@ -141,6 +141,7 @@ class ThreeDExplanation(ThreeDScene): text = TextMobject(r"$T(x,y) = (x+y,x-y,x+2y)$") text.scale(0.75) text.move_to(UP*2.5+LEFT*4) + text.move_to(-UP*3+LEFT*4) self.add_fixed_in_frame_mobjects(text) self.play(Write(text)) self.wait() @@ -218,15 +219,15 @@ class ThreeDExplanation(ThreeDScene): self.wait(3) self.stop_ambient_camera_rotation() - ending = TextMobject(r"$T(\left[\begin{array}{c}x \\ y\end{array}\right]) = \left[\begin{array}{c} x+y \\ x-y \\ x+2y \end{array}\right]$") + ending = TextMobject(r"$T(\left[\begin{array}{c}x \\ y\end{array}\right])$ = ",r"$\left[\begin{array}{c} x+y \\ x-y\\ x+2y \end{array}\right]$") #\begin{array}{c} x+y \\ x-y -- \\ x+2y -- \end{array}\right]$") ending.scale(0.75) - ending.move_to(-UP*2+LEFT*4) - self.play(Transform(text,ending)) + ending.move_to(-UP*3+LEFT*4) self.add_fixed_in_frame_mobjects(ending) + self.play(FadeOut(text),Write(ending)) self.play(FadeOut(plane)) - self.wait(3) + self.wait(2) - self.begin_ambient_camera_rotation(rate=0.5) - self.wait(5) + self.begin_ambient_camera_rotation(rate=0.3) + self.wait(8) self.stop_ambient_camera_rotation() diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/square.py b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file3_square.py index e828de4..e828de4 100644 --- a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/square.py +++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file3_square.py diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file2_Understand_Linear_Transformations_visually.py b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file4_Understand_Linear_Transformations_visually.py index 577032d..577032d 100644 --- a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file2_Understand_Linear_Transformations_visually.py +++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file4_Understand_Linear_Transformations_visually.py diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file3_Uniform_Scaling.py b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file5_Uniform_Scaling.py index a7856a5..a7856a5 100644 --- a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file3_Uniform_Scaling.py +++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file5_Uniform_Scaling.py diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file4_Horizontal_Shear.py b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file6_Horizontal_Shear.py index 91f098e..91f098e 100644 --- a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file4_Horizontal_Shear.py +++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file6_Horizontal_Shear.py diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file4_Horizontal_Shear_gif.gif b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file6_Horizontal_Shear_gif.gif Binary files differindex 9bef1b6..9bef1b6 100644 --- a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file4_Horizontal_Shear_gif.gif +++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file6_Horizontal_Shear_gif.gif diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file5_Vertical_Shear.py b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file7_Vertical_Shear.py index 718e4e0..718e4e0 100644 --- a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file5_Vertical_Shear.py +++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file7_Vertical_Shear.py diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file5_Vertical_Shear_gif.gif b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file7_Vertical_Shear_gif.gif Binary files differindex 7ca323f..7ca323f 100644 --- a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file5_Vertical_Shear_gif.gif +++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file7_Vertical_Shear_gif.gif diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file6_linear_transformation.py b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file8_linear_transformation.py index 01a0cef..01a0cef 100755 --- a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file6_linear_transformation.py +++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file8_linear_transformation.py diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file9.gif b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file9.gif Binary files differnew file mode 100644 index 0000000..017e0c7 --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file9.gif diff --git a/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/README.md b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/README.md new file mode 100644 index 0000000..e287fa1 --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/README.md @@ -0,0 +1,15 @@ +# Contributer: Archit Sangal +My Github Account : <a href="https://github.com/architsangal">architsangal</a> (https://github.com/architsangal) +<br/></br> + +## Sub-Topics Covered: ++ Orthonormal Bases + +#### Video 1: Example of Orthonormal bases + + +#### Video 2: Adding the projections of a vector on orthonormal basis will produce the same vector + + +#### Video 3: Relating the example and the property +
\ No newline at end of file diff --git a/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file1_orthogonal.py b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file1_orthogonal.py index a5d96f5..a5d96f5 100755 --- a/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file1_orthogonal.py +++ b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file1_orthogonal.py diff --git a/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file2_sum_of_projections_part1.py b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file2_sum_of_projections_part1.py index 81a0888..141e99b 100755 --- a/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file2_sum_of_projections_part1.py +++ b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file2_sum_of_projections_part1.py @@ -43,7 +43,7 @@ class LinearTrans(LinearTransformationScene): text3.add_background_rectangle()
self.play(ShowCreation(arrow),Write(text3))
self.wait()
- v_cor = TextMobject("(1,3)")
+ v_cor = TextMobject("(1 , 3)")
v_cor.move_to(3.2*UP+1.3*RIGHT)
v_cor.set_color(BLUE)
v_cor.scale(0.75)
@@ -71,7 +71,7 @@ class LinearTrans(LinearTransformationScene): v1_cor.add_background_rectangle()
self.play(Write(v1_cor))
self.wait(0.5)
- text1 = TextMobject(r"(1.8,2.4)")
+ text1 = TextMobject("(1.8 , 2.4)")
text1.move_to(2.1*UP+2.5*RIGHT)
text1.scale(0.75)
text1.set_color("#6B8E23")
@@ -95,7 +95,7 @@ class LinearTrans(LinearTransformationScene): v2_cor.add_background_rectangle()
self.play(Write(v2_cor))
self.wait(0.5)
- text2 = TextMobject(r"(-0.8,0.6)")
+ text2 = TextMobject("(-0.8 , 0.6)")
text2.move_to(0.75*UP+1.75*LEFT)
text2.scale(0.75)
text2.set_color("#8b0000")
diff --git a/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file3_sum_of_projections_part2.py b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file3_sum_of_projections_part2.py index 9d25192..2899286 100644 --- a/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file3_sum_of_projections_part2.py +++ b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file3_sum_of_projections_part2.py @@ -3,12 +3,6 @@ class ThreeDExplanation(ThreeDScene): def construct(self): - text = TextMobject("Let us consider the example discussed above again. These are the things we know:-") - text.scale(0.75) - self.add_fixed_in_frame_mobjects(text) - text.move_to(3*UP) - self.play(Write(text)) - self.wait(2) basis = TextMobject(r"Set of Orthonormal Basis - $\left(\begin{array}{c}\frac{1}{\sqrt{2}}\\\frac{1}{\sqrt{2}}\\0\end{array}\right),\left(\begin{array}{c}\frac{-1}{\sqrt{2}}\\\frac{1}{\sqrt{2}}\\0\end{array}\right),\left(\begin{array}{c}0\\0\\1\end{array}\right)$") basis.scale(0.75) basis.move_to(UP*1.5) @@ -31,7 +25,7 @@ class ThreeDExplanation(ThreeDScene): self.play(Write(eq2)) self.play(Write(eq3)) self.wait() - self.play(FadeOut(text), FadeOut(basis), FadeOut(eq), FadeOut(v), FadeOut(eq1), FadeOut(eq2), FadeOut(eq3)) + self.play(FadeOut(basis), FadeOut(eq), FadeOut(v), FadeOut(eq1), FadeOut(eq2), FadeOut(eq3)) self.wait() text = TextMobject("These are the 3 mutually orthonormal basis of the set(", r"$v_1$, ", r"$v_2$, ", r"$v_3$",")") @@ -44,13 +38,20 @@ class ThreeDExplanation(ThreeDScene): self.play(Write(text)) self.wait() - axes = ThreeDAxes(x_min = -9,x_max=9,y_min=-9,y_max=9,z_min=-9,z_max=9) + axes = ThreeDAxes(x_min = -6,x_max=6,y_min=-6,y_max=6,z_min=-6,z_max=6) self.play(ShowCreation(axes)) - self.move_camera(distance = 100, phi=30*DEGREES,theta=45*DEGREES,run_time=3) - self.begin_ambient_camera_rotation(rate=0.3) - - dashedline1 = DashedLine(start = -12*(UP+RIGHT), end = 12*(UP+RIGHT)) - dashedline2 = DashedLine(start = -12*(UP+LEFT), end = 12*(UP+LEFT)) + self.move_camera(distance = 100, phi=45*DEGREES,theta=45*DEGREES,run_time=5) + self.begin_ambient_camera_rotation(rate=0.1) + + xy_plane = Polygon(6*RIGHT+6*UP,-6*RIGHT+6*UP,-6*RIGHT-6*UP,6*RIGHT-6*UP) + xy_plane.set_color("#333333") + xy_plane.set_fill("#333333") + xy_plane.set_opacity(1) + xy_plane.fade(0.7) + self.play(ShowCreation(xy_plane)) + + dashedline1 = DashedLine(start = -6*(UP+RIGHT), end = 6*(UP+RIGHT)) + dashedline2 = DashedLine(start = -6*(UP+LEFT), end = 6*(UP+LEFT)) dashedline3 = DashedLine(start = 4*UP+3*RIGHT+[0,0,5], end = 3.5*UP+3.5*RIGHT) dashedline4 = DashedLine(start = 4*UP+3*RIGHT+[0,0,5], end = 0.5*UP+0.5*LEFT) dashedline5 = DashedLine(start = 4*UP+3*RIGHT+[0,0,5], end = [0,0,5]) @@ -95,15 +96,17 @@ class ThreeDExplanation(ThreeDScene): a_line = Line(start = ORIGIN,end = 4*UP+3*RIGHT+[0,0,5]) a_line.set_color(GOLD_E) - a_tip = Polygon(4*UP+3*RIGHT+[0,0,5],3.6*UP+2.7*RIGHT+[0,0,4.5]+0.1*UP+0.1*LEFT,3.6*UP+2.7*RIGHT+[0,0,4.5]+0.1*DOWN+0.1*RIGHT) + a_tip = Polygon(3.92*UP+2.94*RIGHT+[0,0,4.9],3.6*UP+2.7*RIGHT+[0,0,4.5]+0.1*UP+0.1*LEFT,3.6*UP+2.7*RIGHT+[0,0,4.5]+0.1*DOWN+0.1*RIGHT) a_tip.set_opacity(1) a_tip.set_fill(GOLD_E) a_tip.set_color(GOLD_E) self.play(ShowCreation(a_line), ShowCreation(a_tip)) - self.wait(9) + self.stop_ambient_camera_rotation() + self.move_camera(distance = 100, phi=45*DEGREES,theta=135*DEGREES,run_time=5) + self.play(ShowCreation(dashedline3),ShowCreation(dashedline4),ShowCreation(dashedline5)) - self.wait(6) + self.wait() pv1 = Line(start = ORIGIN,end = 4*UP+3*RIGHT+[0,0,5]) pv1.set_color(GOLD_E) @@ -142,13 +145,18 @@ class ThreeDExplanation(ThreeDScene): v3_p = Line(start = ORIGIN,end = [0,0,5]) v3_p.set_color(YELLOW_E) - v3_p_tip = Polygon([0,0,5],[0,0,4.8]+0.2*RIGHT,[0,0,4.8]+0.2*LEFT) + v3_p_tip = Polygon([0,0,5.15],[0,0,4.8]+0.2*RIGHT,[0,0,4.8]+0.2*LEFT) v3_p_tip.set_opacity(1) v3_p_tip.set_fill(YELLOW_E) v3_p_tip.set_color(YELLOW_E) - self.stop_ambient_camera_rotation() - self.play(Transform(pv1,v1_p), Transform(pv1tip,v1_p_tip), Transform(pv2,v2_p), Transform(pv2tip,v2_p_tip), Transform(pv3,v3_p), Transform(pv3tip,v3_p_tip)) + #self.stop_ambient_camera_rotation() + self.play(Transform(pv1,v1_p), + Transform(pv1tip,v1_p_tip), + Transform(pv2,v2_p), + Transform(pv2tip,v2_p_tip), + Transform(pv3,v3_p), + Transform(pv3tip,v3_p_tip)) self.play(FadeOut(dashedline1), FadeOut(dashedline2), FadeOut(dashedline3), diff --git a/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file4.gif b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file4.gif Binary files differnew file mode 100644 index 0000000..4891350 --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file4.gif diff --git a/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file5.gif b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file5.gif Binary files differnew file mode 100644 index 0000000..d7eb0bc --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file5.gif diff --git a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file2_mobius_strip.gif b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file6.gif Binary files differindex 9623046..1df6413 100644 --- a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file2_mobius_strip.gif +++ b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file6.gif diff --git a/FSF-2020/linear-algebra/linear-transformations/README.md b/FSF-2020/linear-algebra/linear-transformations/README.md index 692201e..067755e 100644 --- a/FSF-2020/linear-algebra/linear-transformations/README.md +++ b/FSF-2020/linear-algebra/linear-transformations/README.md @@ -1,9 +1,10 @@ # Contributer: Archit Sangal
-My Github Account : <a href="https://github.com/architsangal">architsangal</a>
+My Github Account : <a href="https://github.com/architsangal">architsangal</a> (https://github.com/architsangal). These code were written during the course of FOSSEE Summer Fellowship 2020 under the FLOSS: Mathematics using Python.
<br/></br>
+
## Sub-Topics Covered:
-+ Vector Space Homomorphisms (Linear Maps)
++ Linear Transformations (Linear Maps)
+ The Four Fundamental Subspaces
+ Rank-Nullity Theorem
+ Orthonormal basis
-+ Gramm-Schmidt Orthogonalization Process
++ Gramm-Schmidt Orthogonalization Process
\ No newline at end of file diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/README.md b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/README.md new file mode 100644 index 0000000..6c90bf4 --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/README.md @@ -0,0 +1,30 @@ +# Contributer: Archit Sangal +My Github Account : <a href="https://github.com/architsangal">architsangal</a> (https://github.com/architsangal) +<br/></br> + +## Sub-Topics Covered: ++ The Four Fundamental Subspaces + +#### Video 1: Writing System of linear equations in form of Ax=b + + +#### Video 2: Column Space is same as the image of Linear Transformation + + +#### Video 3: Existance of Solution w.r.t. vector b + + +#### Video 4: Null Space (Visually) + + +#### Video 5: Definition 1 is equivalent to Definition 2 + + +#### Video 6: Relation between Row Space and Null Space + + +#### Fig. 1 Naming of the left null space + + +#### Video 7: Left Null Space(Visually) +
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A = TextMobject(r"$A = $",r"$\left( \begin{array}{c c c} 1 & 2 & 1 \\ 1 & 3 & 1 \\ 2 & 1 & 4 \\ 3 & 2 & 3 \end{array} \right)$") + A = TextMobject(r"$A = $",r"$\left( \begin{array}{c c} 1 & 2 \\ 3 & 4 \end{array} \right)$") A.move_to(2*UP) A[1].set_color(color = DARK_BLUE) A.scale(0.75) - self.play(Write(A),run_time = 1) + self.play(Write(A),run_time = 1) - CS_A = TextMobject(r"Column Space of $A = x_{1}$",r"$\left( \begin{array}{c} 1 \\ 1 \\ 2 \\ 3 \end{array} \right)$",r"$+x_{2}$",r"$ \left( \begin{array}{c} 2 \\ 3 \\ 1 \\ 2 \end{array} \right)$",r"$ + x_{3}$",r"$\left( \begin{array}{c} 1 \\ 1 \\ 4 \\ 3 \end{array} \right)$") + CS_A = TextMobject(r"Column Space of $A = x_{1}$",r"$\left( \begin{array}{c} 1 \\ 3 \end{array} \right)$",r"$+x_{2}$",r"$ \left( \begin{array}{c} 2 \\ 4\end{array} \right)$") CS_A.move_to(1.5*LEFT+1*DOWN) CS_A[1].set_color(color = DARK_BLUE) CS_A[3].set_color(color = DARK_BLUE) - CS_A[5].set_color(color = DARK_BLUE) CS_A.scale(0.75) self.play(Write(CS_A),run_time = 2) - arrow1 = Arrow(start = 1.25*UP,end = 0.25*DOWN+1.75*LEFT) - arrow2 = Arrow(start = 1.35*UP+0.5*RIGHT,end = 0.25*DOWN+0.5*RIGHT) - arrow3 = Arrow(start = 1.25*UP+0.75*RIGHT,end = 0.25*DOWN+2.9*RIGHT) + arrow1 = Arrow(start = 1.25*UP,end = (0.25*DOWN+1.75*LEFT+0.25*DOWN+1.2*RIGHT)/2) + arrow3 = Arrow(start = 1.25*UP+0.75*RIGHT,end = (0.25*DOWN+2.9*RIGHT+0.25*DOWN)/2) + + arrow1.scale(1.5) + arrow3.scale(1.5) Defn = TextMobject("Linear Combination of Columns of Matrix") Defn.move_to(3*DOWN) - self.play(Write(Defn), ShowCreation(arrow1), ShowCreation(arrow2), ShowCreation(arrow3),run_time = 1) + self.play(Write(Defn), ShowCreation(arrow1), ShowCreation(arrow3),run_time = 1) self.wait(1) class solution(LinearTransformationScene): @@ -43,7 +44,7 @@ class solution(LinearTransformationScene): self.wait() self.play(FadeOut(o)) - A = TextMobject(r"Let $A$(= ",r"$\left[\begin{array}{c c} 1 & -1 \\ 1 & -1 \end{array}\right]$",r")denote the matrix the of this linear transformation.") + A = TextMobject(r"Let $A$ be ",r"$\left[\begin{array}{c c} 1 & -1 \\ 1 & -1 \end{array}\right]$",r". $A$ denotes the matrix the of this linear transformation.") A.move_to(2*DOWN) A.scale(0.75) A.add_background_rectangle() @@ -116,8 +117,8 @@ class solution2nd(LinearTransformationScene): arrow2 = Arrow(start = ORIGIN,end = UP+LEFT) arrow3 = Arrow(start = ORIGIN,end = 3*UP+4*RIGHT) arrow1.set_color(YELLOW) - arrow2.set_color(YELLOW) - arrow3.set_color(YELLOW) + arrow2.set_color(ORANGE) + arrow3.set_color(PURPLE) arrow1.scale(1.3) arrow2.scale(1.5) arrow3.scale(1.1) @@ -135,7 +136,7 @@ class solution2nd(LinearTransformationScene): self.wait() self.play(FadeOut(o)) - A = TextMobject(r"Matrix the of this linear transformation is $A$(= ",r"$\left[\begin{array}{c c} 1 & -1 \\ 1 & -1 \end{array}\right]$",r") again.") + A = TextMobject(r"Let the matrix the of this linear transformation be $A$ =",r"$\left[\begin{array}{c c} 1 & -1 \\ 1 & -1 \end{array}\right]$",r" again.") A.move_to(2*DOWN) A.scale(0.75) A.add_background_rectangle() diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/solution.py b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file3_solution.py index fb31881..eb310f3 100644 --- a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/solution.py +++ b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file3_solution.py @@ -5,16 +5,16 @@ class solution(LinearTransformationScene): self.setup() self.wait() - o = TextMobject(r"This is the original $2D$ vector space(before Linear Transformation)") - o.move_to(DOWN) + o = TextMobject(r"This is the original vector space $R^2$ (before Linear Transformation)") + o.move_to(3*DOWN) o.scale(0.75) o.add_background_rectangle() self.play(Write(o)) self.wait() self.play(FadeOut(o)) - A = TextMobject("Let $A$ denote the matrix the of this linear transformation.") - A.move_to(DOWN) + A = TextMobject(r"Consider the matrix the of this linear transformation $A$ = $\left[\begin{array}{c c} 1 & -1 \\ 1 & -1 \end{array}\right]$") + A.move_to(3*DOWN) A.scale(0.75) A.add_background_rectangle() self.play(Write(A)) @@ -23,8 +23,8 @@ class solution(LinearTransformationScene): self.wait() self.play(FadeOut(A)) - o = TextMobject(r"This is the transformed vector space i.e. a line ($1D$)") - o.move_to(DOWN) + o = TextMobject(r"This is the transformed vector space") + o.move_to(3*DOWN) o.scale(0.75) o.add_background_rectangle() self.play(Write(o)) @@ -32,15 +32,16 @@ class solution(LinearTransformationScene): self.play(FadeOut(o)) arrow2 = Arrow(start = ORIGIN, end = 2*DOWN+2*LEFT) - arrow2.set_color(DARK_BLUE) + arrow2.set_color(PURPLE) arrow2.scale(1.2) self.play(ShowCreation(arrow2)) self.wait() - o1 = TextMobject("If the vector lies in the transformed vector space") + o1 = TextMobject("If the ","vector b"," lies in the transformed vector space") o2 = TextMobject("(the line) then the solution exist") - o1.move_to(2*DOWN+2*RIGHT) - o2.move_to(2.5*DOWN+2*RIGHT) + o1.move_to(2.5*DOWN+2*RIGHT) + o1[1].set_color(PURPLE) + o2.move_to(3*DOWN+2.5*RIGHT) o1.scale(0.75) o2.scale(0.75) o1.add_background_rectangle() @@ -53,15 +54,16 @@ class solution(LinearTransformationScene): self.play(FadeOut(arrow2)) arrow1 = Arrow(start = ORIGIN, end = 2*UP+RIGHT) - arrow1.set_color(DARK_BLUE) + arrow1.set_color(ORANGE) arrow1.scale(1.3) self.play(ShowCreation(arrow1)) self.wait() - o1 = TextMobject("If the vector does lies in the transformed") + o1 = TextMobject("If the ","vector b"," does lies in the transformed") o2 = TextMobject("vector space then the does not solution exist") - o1.move_to(2*DOWN+2*RIGHT) - o2.move_to(2.5*DOWN+2*RIGHT) + o1.move_to(2.5*DOWN+2*RIGHT) + o1[1].set_color(ORANGE) + o2.move_to(3*DOWN+2.5*RIGHT) o1.scale(0.75) o2.scale(0.75) o1.add_background_rectangle() diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/null_space.py b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file4_null_space.py index dfc3cb4..3c52677 100644 --- a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/null_space.py +++ b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file4_null_space.py @@ -5,8 +5,8 @@ class null_space(LinearTransformationScene): self.setup() self.wait() - o = TextMobject(r"This is the original $2D$ vector space(before Linear Transformation)") - o.move_to(DOWN) + o = TextMobject(r"This is the original vector space $R^2$(before Linear Transformation)") + o.move_to(3*DOWN) o.scale(0.75) o.add_background_rectangle() self.play(Write(o)) @@ -64,7 +64,7 @@ class null_space(LinearTransformationScene): self.add_transformable_mobject(arrow6) self.add_transformable_mobject(arrow7) - o1 = TextMobject("Notice, entire set of vectors which belong to the vector") + o1 = TextMobject("Notice, entire set of vectors which belongs to the vector") o2 = TextMobject(r"subspace(Linear Span of $\left(\begin{array}{c} 1 \\ 1 \end{array}\right)$) transforms to zero") o1.move_to(2*DOWN+2.5*RIGHT) o2.move_to(2.75*DOWN+2.5*RIGHT) @@ -83,7 +83,7 @@ class null_space(LinearTransformationScene): self.play(FadeOut(o1), FadeOut(o2)) o = TextMobject(r"Hence, the vector space formed by linear span of $\left(\begin{array}{c} 1 \\ 1 \end{array}\right)$ is the null space of $A$") - o.move_to(DOWN) + o.move_to(3*DOWN) o.scale(0.75) o.add_background_rectangle() self.play(Write(o)) diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file5_Row_Space_part_1.py b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file5_Row_Space_part_1.py new file mode 100644 index 0000000..5259eb4 --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file5_Row_Space_part_1.py @@ -0,0 +1,68 @@ +from manimlib.imports import * +class LS(Scene): + def construct(self): + text1 = TextMobject(r"Consider a matrix $A =$") + text2 = TextMobject(r"[") + text3 = TextMobject(r"$\begin{array}{c c} 1 & -2\end{array}$") + text4 = TextMobject(r"$\begin{array}{c c} 1 & -1\end{array}$") + text5 = TextMobject(r"]") + + text2.scale(2) + text5.scale(2) + + text1.set_color(DARK_BLUE) + text2.set_color(DARK_BLUE) + text3.set_color(PURPLE) + text4.set_color(YELLOW) + text5.set_color(DARK_BLUE) + + text1.move_to(3.5*LEFT+3*UP+2*RIGHT) + text2.move_to(0.75*LEFT+3*UP+2*RIGHT) + text3.move_to(3.25*UP+2*RIGHT) + text4.move_to(2.75*UP+2*RIGHT) + text5.move_to(0.75*RIGHT+3*UP+2*RIGHT) + + self.play(FadeIn(text1), FadeIn(text2), FadeIn(text3), FadeIn(text4), FadeIn(text5)) + self.wait() + + ttext1 = TextMobject(r"$A^T =$") + ttext2 = TextMobject(r"[") + ttext3 = TextMobject(r"$\begin{array}{c} 1 \\ -2\end{array}$") + ttext4 = TextMobject(r"$\begin{array}{c} 1 \\ -1\end{array}$") + ttext5 = TextMobject(r"]") + + ttext2.scale(2) + ttext5.scale(2) + + ttext1.set_color(DARK_BLUE) + ttext2.set_color(DARK_BLUE) + ttext3.set_color(PURPLE) + ttext4.set_color(YELLOW) + ttext5.set_color(DARK_BLUE) + + ttext1.move_to(2*LEFT+1.5*UP+2*RIGHT) + ttext2.move_to(1*LEFT+1.5*UP+2*RIGHT) + ttext3.move_to(0.5*LEFT+1.5*UP+2*RIGHT) + ttext4.move_to(0.5*RIGHT+1.5*UP+2*RIGHT) + ttext5.move_to(1*RIGHT+1.5*UP+2*RIGHT) + + self.play(FadeIn(ttext1), FadeIn(ttext2), FadeIn(ttext3), FadeIn(ttext4), FadeIn(ttext5)) + + rtext = TextMobject(r"Row Space of $A$ = Column Space of $A^T = a_1$",r"$\left[\begin{array}{c} 1 \\ -2\end{array}\right]$",r"$+a_2$",r"$\left[\begin{array}{c} 1 \\ -1\end{array}\right]$") + rtext[1].set_color(PURPLE) + rtext[3].set_color(YELLOW) + rtext.move_to(2*DOWN+1.5*LEFT) + rtext.scale(0.75) + + self.play(Write(rtext)) + self.wait() + + arrow1 = Arrow(start = 1.5*RIGHT+UP, end = 1.25*(DOWN+RIGHT)) + arrow2 = Arrow(start = 2.5*RIGHT+UP, end = 1.25*DOWN+3.25*RIGHT) + arrow1.scale(1.25) + arrow2.scale(1.25) + arrow1.set_color(PURPLE) + arrow2.set_color(YELLOW) + + self.play(ShowCreation(arrow1), ShowCreation(arrow2)) + self.wait(2) diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file2_Row_Space.py b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file6_Row_Space_part_2.py index b16a32a..b16a32a 100644 --- a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file2_Row_Space.py +++ b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file6_Row_Space_part_2.py diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file7_Row_space_Orthogonal_Complements.py b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file7_Row_space_Orthogonal_Complements.py new file mode 100644 index 0000000..c81d370 --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file7_Row_space_Orthogonal_Complements.py @@ -0,0 +1,150 @@ +from manimlib.imports import * +class row_space(LinearTransformationScene): + def construct(self): + + self.setup() + self.wait() + + o = TextMobject(r"This is the original vector space $R^2$(before Linear Transformation)") + o.move_to(DOWN) + o.scale(0.75) + o.add_background_rectangle() + self.play(Write(o)) + self.wait() + self.play(FadeOut(o)) + + o1 = TextMobject("Consider a set of vectors which are linear") + o2 = TextMobject(r"span of a $\left(\begin{array}{c} 1 \\ 1 \end{array}\right)$i.e. the null space.") + o1.move_to(2*DOWN+3*RIGHT) + o2.move_to(2.75*DOWN+3*RIGHT) + o1.scale(0.7) + o2.scale(0.7) + o1.add_background_rectangle() + o2.add_background_rectangle() + self.play(Write(o1)) + self.play(Write(o2)) + + arrow = Arrow(start = ORIGIN, end = UP+RIGHT) + arrow.set_color(YELLOW) + arrow1 = Arrow(start = ORIGIN, end = 2*(UP+RIGHT)) + arrow1.set_color(YELLOW) + arrow2 = Arrow(start = ORIGIN, end = 3*(UP+RIGHT)) + arrow2.set_color(YELLOW) + arrow3 = Arrow(start = ORIGIN, end = 4*(UP+RIGHT)) + arrow3.set_color(YELLOW) + arrow4 = Arrow(start = ORIGIN, end = DOWN+LEFT) + arrow4.set_color(YELLOW) + arrow5 = Arrow(start = ORIGIN, end = 2*(DOWN+LEFT)) + arrow5.set_color(YELLOW) + arrow6 = Arrow(start = ORIGIN, end = 3*(DOWN+LEFT)) + arrow6.set_color(YELLOW) + arrow7 = Arrow(start = ORIGIN, end = 4*(DOWN+LEFT)) + arrow7.set_color(YELLOW) + + arrow.scale(1.5) + arrow1.scale(1.2) + arrow2.scale(1.15) + arrow3.scale(1.1) + arrow4.scale(1.5) + arrow5.scale(1.2) + arrow6.scale(1.15) + arrow7.scale(1.1) + + self.play(ShowCreation(arrow), + ShowCreation(arrow1), + ShowCreation(arrow2), + ShowCreation(arrow3), + ShowCreation(arrow4), + ShowCreation(arrow5), + ShowCreation(arrow6), + ShowCreation(arrow7), + ) + + self.wait(2) + self.play(FadeOut(o1), FadeOut(o2)) + + o1 = TextMobject("Consider a set of vectors which are linear") + o2 = TextMobject(r"span of a $\left(\begin{array}{c} 1 \\ -1 \end{array}\right)$i.e. the row space.") + o1.move_to(2*DOWN+3*RIGHT) + o2.move_to(2.75*DOWN+3*RIGHT) + o1.scale(0.7) + o2.scale(0.7) + o1.add_background_rectangle() + o2.add_background_rectangle() + self.play(Write(o1)) + self.play(Write(o2)) + + rarrow = Arrow(start = ORIGIN, end = -UP+RIGHT) + rarrow.set_color(PURPLE) + rarrow1 = Arrow(start = ORIGIN, end = 2*(-UP+RIGHT)) + rarrow1.set_color(PURPLE) + rarrow2 = Arrow(start = ORIGIN, end = 3*(-UP+RIGHT)) + rarrow2.set_color(PURPLE) + rarrow3 = Arrow(start = ORIGIN, end = 4*(-UP+RIGHT)) + rarrow3.set_color(PURPLE) + rarrow4 = Arrow(start = ORIGIN, end = -DOWN+LEFT) + rarrow4.set_color(PURPLE) + rarrow5 = Arrow(start = ORIGIN, end = 2*(-DOWN+LEFT)) + rarrow5.set_color(PURPLE) + rarrow6 = Arrow(start = ORIGIN, end = 3*(-DOWN+LEFT)) + rarrow6.set_color(PURPLE) + rarrow7 = Arrow(start = ORIGIN, end = 4*(-DOWN+LEFT)) + rarrow7.set_color(PURPLE) + + rarrow.scale(1.5) + rarrow1.scale(1.2) + rarrow2.scale(1.15) + rarrow3.scale(1.1) + rarrow4.scale(1.5) + rarrow5.scale(1.2) + rarrow6.scale(1.15) + rarrow7.scale(1.1) + + self.play(ShowCreation(rarrow), + ShowCreation(rarrow1), + ShowCreation(rarrow2), + ShowCreation(rarrow3), + ShowCreation(rarrow4), + ShowCreation(rarrow5), + ShowCreation(rarrow6), + ShowCreation(rarrow7), + ) + + self.wait(2) + self.play(FadeOut(o1), FadeOut(o2)) + + self.add_transformable_mobject(arrow) + self.add_transformable_mobject(arrow1) + self.add_transformable_mobject(arrow2) + self.add_transformable_mobject(arrow3) + self.add_transformable_mobject(arrow4) + self.add_transformable_mobject(arrow5) + self.add_transformable_mobject(arrow6) + self.add_transformable_mobject(arrow7) + + self.add_transformable_mobject(rarrow) + self.add_transformable_mobject(rarrow1) + self.add_transformable_mobject(rarrow2) + self.add_transformable_mobject(rarrow3) + self.add_transformable_mobject(rarrow4) + self.add_transformable_mobject(rarrow5) + self.add_transformable_mobject(rarrow6) + self.add_transformable_mobject(rarrow7) + + o1 = TextMobject("Notice, entire set of vectors which belong to the null space of $A$ transforms to zero") + o2 = TextMobject(r"and entire set of vectors which belong to the row space of $A$ transforms to column space of $A$.") + o1.move_to(2.5*DOWN) + o2.move_to(3.5*DOWN) + o1.scale(0.7) + o2.scale(0.7) + o1.add_background_rectangle() + o2.add_background_rectangle() + self.play(Write(o1)) + self.play(Write(o2)) + self.wait() + + matrix = [[1,-1],[1,-1]] + self.apply_matrix(matrix) + self.wait(3) + + self.play(FadeOut(o1), FadeOut(o2))
\ No newline at end of file diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file8_Left_Null_Space.py b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file8_Left_Null_Space.py new file mode 100755 index 0000000..fd05e75 --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file8_Left_Null_Space.py @@ -0,0 +1,26 @@ +from manimlib.imports import * + +class Left_Null_Space(Scene): + def construct(self): + + A = TextMobject(r"Left Null Space of A") + A.move_to(3*UP) + defn = TextMobject(r"It is a vector space that consists of all the solution $x$ to the equation $A^{T}x=0$") + defn.move_to(2*UP) + defn.scale(0.75) + eqn1 = TextMobject(r"$A^{T}x=0 \cdots (i)$") + eqn1.move_to(UP) + self.play(Write(A), Write(defn), Write(eqn1),run_time=1) + statement = TextMobject(r"Taking transpose of eqn $(i)$") + eqn = TextMobject(r"$(A^{T}x)^{T}=0$") + eqn.move_to(DOWN) + eqn2 = TextMobject(r"$x^{T}(A^{T})^{T}=0$") + eqn2.move_to(DOWN) + eqn3 = TextMobject(r"$x^{T}A=0$") + eqn3.move_to(DOWN) + self.play(Write(statement),Write(eqn),run_time=1) + self.wait(0.5) + self.play(Transform(eqn,eqn2),run_time=1) + self.wait(0.5) + self.play(Transform(eqn,eqn3),run_time=1) + self.wait(0.5)
\ No newline at end of file diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file9_left_null_space.py b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file9_left_null_space.py new file mode 100644 index 0000000..61285be --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file9_left_null_space.py @@ -0,0 +1,186 @@ +from manimlib.imports import * +class row_space(LinearTransformationScene): + def construct(self): + + self.setup() + self.wait() + + o = TextMobject(r"This is the original vector space $R^2$(before Linear Transformation)") + o.move_to(DOWN) + o.scale(0.75) + o.add_background_rectangle() + self.play(Write(o)) + self.wait() + self.play(FadeOut(o)) + + o1 = TextMobject("Consider a set of vectors which are linear") + o2 = TextMobject(r"span of a $\left(\begin{array}{c} 1 \\ 1 \end{array}\right)$i.e. the null space.") + o1.move_to(2*DOWN+3*RIGHT) + o2.move_to(2.75*DOWN+3*RIGHT) + o1.scale(0.7) + o2.scale(0.7) + o1.add_background_rectangle() + o2.add_background_rectangle() + self.play(Write(o1)) + self.play(Write(o2)) + + arrow = Arrow(start = ORIGIN, end = UP+RIGHT) + arrow.set_color(YELLOW) + arrow1 = Arrow(start = ORIGIN, end = 2*(UP+RIGHT)) + arrow1.set_color(YELLOW) + arrow2 = Arrow(start = ORIGIN, end = 3*(UP+RIGHT)) + arrow2.set_color(YELLOW) + arrow3 = Arrow(start = ORIGIN, end = 4*(UP+RIGHT)) + arrow3.set_color(YELLOW) + arrow4 = Arrow(start = ORIGIN, end = DOWN+LEFT) + arrow4.set_color(YELLOW) + arrow5 = Arrow(start = ORIGIN, end = 2*(DOWN+LEFT)) + arrow5.set_color(YELLOW) + arrow6 = Arrow(start = ORIGIN, end = 3*(DOWN+LEFT)) + arrow6.set_color(YELLOW) + arrow7 = Arrow(start = ORIGIN, end = 4*(DOWN+LEFT)) + arrow7.set_color(YELLOW) + + arrow.scale(1.5) + arrow1.scale(1.2) + arrow2.scale(1.15) + arrow3.scale(1.1) + arrow4.scale(1.5) + arrow5.scale(1.2) + arrow6.scale(1.15) + arrow7.scale(1.1) + + self.play(ShowCreation(arrow), + ShowCreation(arrow1), + ShowCreation(arrow2), + ShowCreation(arrow3), + ShowCreation(arrow4), + ShowCreation(arrow5), + ShowCreation(arrow6), + ShowCreation(arrow7), + ) + + self.wait(2) + self.play(FadeOut(o1), FadeOut(o2)) + + o1 = TextMobject("Consider a set of vectors which are linear") + o2 = TextMobject(r"span of a vector $\left(\begin{array}{c} 1 \\ -1 \end{array}\right)$i.e. the row space.") + o1.move_to(2*DOWN+3*RIGHT) + o2.move_to(2.75*DOWN+3*RIGHT) + o1.scale(0.7) + o2.scale(0.7) + o1.add_background_rectangle() + o2.add_background_rectangle() + self.play(Write(o1)) + self.play(Write(o2)) + + rarrow = Arrow(start = ORIGIN, end = -UP+RIGHT) + rarrow.set_color(PURPLE) + rarrow1 = Arrow(start = ORIGIN, end = 2*(-UP+RIGHT)) + rarrow1.set_color(PURPLE) + rarrow2 = Arrow(start = ORIGIN, end = 3*(-UP+RIGHT)) + rarrow2.set_color(PURPLE) + rarrow3 = Arrow(start = ORIGIN, end = 4*(-UP+RIGHT)) + rarrow3.set_color(PURPLE) + rarrow4 = Arrow(start = ORIGIN, end = -DOWN+LEFT) + rarrow4.set_color(PURPLE) + rarrow5 = Arrow(start = ORIGIN, end = 2*(-DOWN+LEFT)) + rarrow5.set_color(PURPLE) + rarrow6 = Arrow(start = ORIGIN, end = 3*(-DOWN+LEFT)) + rarrow6.set_color(PURPLE) + rarrow7 = Arrow(start = ORIGIN, end = 4*(-DOWN+LEFT)) + rarrow7.set_color(PURPLE) + + rarrow.scale(1.5) + rarrow1.scale(1.2) + rarrow2.scale(1.15) + rarrow3.scale(1.1) + rarrow4.scale(1.5) + rarrow5.scale(1.2) + rarrow6.scale(1.15) + rarrow7.scale(1.1) + + self.play(ShowCreation(rarrow), + ShowCreation(rarrow1), + ShowCreation(rarrow2), + ShowCreation(rarrow3), + ShowCreation(rarrow4), + ShowCreation(rarrow5), + ShowCreation(rarrow6), + ShowCreation(rarrow7), + ) + + self.wait(2) + self.play(FadeOut(o1), FadeOut(o2)) + + self.add_transformable_mobject(arrow) + self.add_transformable_mobject(arrow1) + self.add_transformable_mobject(arrow2) + self.add_transformable_mobject(arrow3) + self.add_transformable_mobject(arrow4) + self.add_transformable_mobject(arrow5) + self.add_transformable_mobject(arrow6) + self.add_transformable_mobject(arrow7) + + self.add_transformable_mobject(rarrow) + self.add_transformable_mobject(rarrow1) + self.add_transformable_mobject(rarrow2) + self.add_transformable_mobject(rarrow3) + self.add_transformable_mobject(rarrow4) + self.add_transformable_mobject(rarrow5) + self.add_transformable_mobject(rarrow6) + self.add_transformable_mobject(rarrow7) + + matrix = [[1,-1],[1,-1]] + self.apply_matrix(matrix) + self.wait(3) + + o1 = TextMobject("Consider a set of vectors which are linear span of a vector") + o2 = TextMobject(r"$\left(\begin{array}{c} 1 \\ -1 \end{array}\right)$ which is orthogonal to column space i.e. Left Null Space") + o1.move_to(2*DOWN) + o2.move_to(2.75*DOWN) + o1.scale(0.7) + o2.scale(0.7) + o1.add_background_rectangle() + o2.add_background_rectangle() + self.play(Write(o1)) + self.play(Write(o2)) + + rarrow = Arrow(start = ORIGIN, end = -UP+RIGHT) + rarrow.set_color(YELLOW) + rarrow1 = Arrow(start = ORIGIN, end = 2*(-UP+RIGHT)) + rarrow1.set_color(YELLOW) + rarrow2 = Arrow(start = ORIGIN, end = 3*(-UP+RIGHT)) + rarrow2.set_color(YELLOW) + rarrow3 = Arrow(start = ORIGIN, end = 4*(-UP+RIGHT)) + rarrow3.set_color(YELLOW) + rarrow4 = Arrow(start = ORIGIN, end = -DOWN+LEFT) + rarrow4.set_color(YELLOW) + rarrow5 = Arrow(start = ORIGIN, end = 2*(-DOWN+LEFT)) + rarrow5.set_color(YELLOW) + rarrow6 = Arrow(start = ORIGIN, end = 3*(-DOWN+LEFT)) + rarrow6.set_color(YELLOW) + rarrow7 = Arrow(start = ORIGIN, end = 4*(-DOWN+LEFT)) + rarrow7.set_color(YELLOW) + + rarrow.scale(1.5) + rarrow1.scale(1.2) + rarrow2.scale(1.15) + rarrow3.scale(1.1) + rarrow4.scale(1.5) + rarrow5.scale(1.2) + rarrow6.scale(1.15) + rarrow7.scale(1.1) + + self.play(ShowCreation(rarrow), + ShowCreation(rarrow1), + ShowCreation(rarrow2), + ShowCreation(rarrow3), + ShowCreation(rarrow4), + ShowCreation(rarrow5), + ShowCreation(rarrow6), + ShowCreation(rarrow7), + ) + + self.wait(2) + self.play(FadeOut(o1), FadeOut(o2)) diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/README.md b/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/README.md new file mode 100644 index 0000000..9d49b4f --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/README.md @@ -0,0 +1,9 @@ +# Contributer: Archit Sangal +My Github Account : <a href="https://github.com/architsangal">architsangal</a> (https://github.com/architsangal) +<br/></br> + +## Sub-Topics Covered: ++ The Rank-Nullity Theorem + +#### Video 1: Visually understanding linear transformation(using grid) +
\ No newline at end of file diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file2.gif b/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file2.gif Binary files differnew file mode 100644 index 0000000..46efc66 --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file2.gif diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/Basis_of_a_dual_vector_space.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/Basis_of_a_dual_vector_space.py new file mode 100644 index 0000000..630670e --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/Basis_of_a_dual_vector_space.py @@ -0,0 +1,126 @@ +from manimlib.imports import *
+class DualVectorSpace(ZoomedScene):
+
+ def construct(self):
+ c1 = Ellipse(radius = 2,color=BLUE)
+ c2 = Ellipse(radius = 2,color=YELLOW)
+ c1.rotate(np.pi/2)
+ c2.rotate(np.pi/2)
+ c1.shift(2*LEFT+0.6*UP)
+ c2.shift(2*RIGHT+0.6*UP)
+ c1.scale(2)
+ c2.scale(2)
+ self.play(ShowCreation(c1))
+ self.play(ShowCreation(c2))
+ dot1 = SmallDot(color=BLUE).shift(2*LEFT+2*UP)
+ dot2 = SmallDot(color=BLUE).shift(2*LEFT+1.5*UP)
+ dot3 = SmallDot(color=BLUE).shift(2*LEFT+1*UP)
+ dot4 = SmallDot(color=BLUE).shift(2*LEFT+0.5*UP)
+ dot5 = SmallDot(color=BLUE).shift(2*LEFT)
+ dot6 = SmallDot(color=BLUE).shift(2*LEFT+0.5*DOWN)
+ dot7 = SmallDot(color=BLUE).shift(2*LEFT+1*DOWN)
+ text1 = TextMobject(r"$V$").scale(0.6).shift(3*UP+2*LEFT)
+ text2 = TextMobject(r"$V^* = \{T:V\rightarrow F\}$").scale(0.6).shift(3*UP+2.5*RIGHT)
+ self.play(ShowCreation(dot1),ShowCreation(dot2),ShowCreation(dot3),ShowCreation(dot4),ShowCreation(dot5),ShowCreation(dot6),ShowCreation(dot7))
+ v1 = TextMobject(r"$v_1$").scale(0.5).shift(2.2*LEFT+2*UP)
+ v2 = TextMobject(r"$v_2$").scale(0.5).shift(2.2*LEFT+1.5*UP)
+ v3 = TextMobject(r"$v_3$").scale(0.5).shift(2.2*LEFT+1*UP)
+ v4 = TextMobject(r"$v_4$").scale(0.5).shift(2.2*LEFT+0.5*UP)
+ v5 = TextMobject(r"$v_5$").scale(0.5).shift(2.2*LEFT)
+ v6 = TextMobject(r"$v_6$").scale(0.5).shift(2.2*LEFT+0.5*DOWN)
+ v7 = TextMobject(r"$v_7$").scale(0.5).shift(2.2*LEFT+1*DOWN)
+ self.play(ShowCreation(v1),ShowCreation(v2),ShowCreation(v3),ShowCreation(v4),ShowCreation(v5),ShowCreation(v6),ShowCreation(v7))
+ self.play(ShowCreation(text1))
+ dot9 = SmallDot(color=YELLOW).shift(2*RIGHT+2*UP)
+ dot10 = SmallDot(color=YELLOW).shift(2*RIGHT+1.5*UP)
+ dot11 = SmallDot(color=YELLOW).shift(2*RIGHT+1*UP)
+ dot12 = SmallDot(color=YELLOW).shift(2*RIGHT+0.5*UP)
+ dot13 = SmallDot(color=YELLOW).shift(2*RIGHT)
+ dot14 = SmallDot(color=YELLOW).shift(2*RIGHT+0.5*DOWN)
+ dot15 = SmallDot(color=YELLOW).shift(2*RIGHT+1*DOWN)
+ self.play(ShowCreation(dot9),ShowCreation(dot10),ShowCreation(dot11),ShowCreation(dot12),ShowCreation(dot13),ShowCreation(dot14),ShowCreation(dot15))
+ v9 = TextMobject(r"${T_1}$").scale(0.5).shift(2.2*RIGHT+2*UP)
+ v10 = TextMobject(r"${T_2}$").scale(0.5).shift(2.2*RIGHT+1.5*UP)
+ v11 = TextMobject(r"${T_3}$").scale(0.5).shift(2.2*RIGHT+1*UP)
+ v12 = TextMobject(r"${T_4}$").scale(0.5).shift(2.2*RIGHT+0.5*UP)
+ v13 = TextMobject(r"${T_5}$").scale(0.5).shift(2.2*RIGHT)
+ v14 = TextMobject(r"${T_6}$").scale(0.5).shift(2.2*RIGHT+0.5*DOWN)
+ v15 = TextMobject(r"${T_7}$").scale(0.5).shift(2.2*RIGHT+1*DOWN)
+ self.play(ShowCreation(v9),ShowCreation(v10),ShowCreation(v11),ShowCreation(v12),ShowCreation(v13),ShowCreation(v14),ShowCreation(v15))
+ self.play(ShowCreation(text2))
+ line1 = Line(start=dot1,end=dot9,stroke_width=0.95)
+ line2 = Line(start=dot2,end=dot10,stroke_width=0.95)
+ line3 = Line(start=dot3,end=dot11,stroke_width=0.95)
+ line4 = Line(start=dot4,end=dot12,stroke_width=0.95)
+ line5 = Line(start=dot5,end=dot13,stroke_width=0.95)
+ line6 = Line(start=dot6,end=dot14,stroke_width=0.95)
+ line7 = Line(start=dot7,end=dot15,stroke_width=0.95)
+ self.play(ShowCreation(line1),ShowCreation(line2),ShowCreation(line3),ShowCreation(line4),ShowCreation(line5),ShowCreation(line6),ShowCreation(line7))
+ self.wait(1.5)
+ rect1 = Rectangle(stroke_width=0.5,width=1,height=1.9).set_fill(color=BLUE,opacity=0.3)
+ vgroup1 = VGroup(dot3,dot4,v3,v4)
+ rect1.surround(vgroup1)
+ self.play(ShowCreation(rect1))
+ text3 = TextMobject(r"Basis of $V$ = $\{v_3, v_4\}$").shift(4.6*LEFT+1*UP).scale(0.5)
+ self.play(ShowCreation(text3))
+ self.wait(1.5)
+ rect2 = Rectangle(stroke_width=0.5,width=1,height=1.7).set_fill(color=YELLOW,opacity=0.3)
+ vgroup2 = VGroup(dot11,dot12,v11,v12)
+ rect2.surround(vgroup2)
+ self.play(ShowCreation(rect2))
+ text4 = TextMobject(r"Basis of $V^*$ = $\{{T_3},{T_4} \}$").shift(4.6*RIGHT+1*UP).scale(0.5)
+ self.play(ShowCreation(text4))
+ self.wait(2.5)
+ v9.move_to(3*LEFT+3*UP).scale(1.2).set_color(YELLOW)
+ colon = TextMobject(":").shift(3*UP+2.6*LEFT)
+ vgroup3 = VGroup(line1,line2,line3,line4,line5,line6,line7)
+ vgroup4 = VGroup(v10,v11,v12,v13,v14,v15,rect1,rect2,text3,text4,c2)
+ vgroup5 = VGroup(dot9,dot10,dot11,dot12,dot13,dot14,dot15)
+ text5 = TextMobject(r"$F$").scale(0.6).shift(3*UP+2*RIGHT)
+ dot9 = SmallDot(color=GREEN).shift(2*RIGHT+2*UP)
+ dot10 = SmallDot(color=GREEN).shift(2*RIGHT+1.5*UP)
+ dot11 = SmallDot(color=GREEN).shift(2*RIGHT+1*UP)
+ dot12 = SmallDot(color=GREEN).shift(2*RIGHT+0.5*UP)
+ dot13 = SmallDot(color=GREEN).shift(2*RIGHT)
+ dot14 = SmallDot(color=GREEN).shift(2*RIGHT+0.5*DOWN)
+ dot15 = SmallDot(color=GREEN).shift(2*RIGHT+1*DOWN)
+ f1 = TextMobject(r"${f_1}$").scale(0.5).shift(2.2*RIGHT+2*UP)
+ f2 = TextMobject(r"${f_2}$").scale(0.5).shift(2.2*RIGHT+1.5*UP)
+ f3 = TextMobject(r"${f_3}$").scale(0.5).shift(2.2*RIGHT+1*UP)
+ f4 = TextMobject(r"${f_4}$").scale(0.5).shift(2.2*RIGHT+0.5*UP)
+ f5 = TextMobject(r"${f_5}$").scale(0.5).shift(2.2*RIGHT)
+ f6 = TextMobject(r"${f_6}$").scale(0.5).shift(2.2*RIGHT+0.5*DOWN)
+ f7 = TextMobject(r"${f_7}$").scale(0.5).shift(2.2*RIGHT+1*DOWN)
+ vgroup6 = VGroup(f1,f2,f3,f4,f5,f6,f7)
+ arrow = Arrow(stroke_width=1.6).scale(1.5).shift(3*UP)
+ c3 = Ellipse(radius = 2,color=GREEN)
+ c3.rotate(np.pi/2)
+ c3.shift(2*RIGHT+0.6*UP)
+ c3.scale(2)
+ self.play(ShowCreation(v9))
+ self.wait(1.5)
+ self.play(ShowCreation(arrow),ShowCreation(colon),Transform(text2,text5),FadeOut(vgroup3),FadeOut(vgroup4),FadeOut(vgroup5))
+ self.play(ShowCreation(vgroup5),ShowCreation(vgroup6),ShowCreation(c3))
+ self.wait(0.7)
+ self.play(ShowCreation(vgroup3))
+ self.wait(3)
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/Dual_Basis_Example.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/Dual_Basis_Example.py new file mode 100644 index 0000000..d79ec3e --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/Dual_Basis_Example.py @@ -0,0 +1,97 @@ +from manimlib.imports import *
+import numpy as np
+
+class Dual_Basis(GraphScene):
+ CONFIG={
+ "x_min": -7,
+ "x_max": 7,
+ "y_min": -7,
+ "y_max": 7,
+ "graph_origin": ORIGIN,
+ "x_axis_label":"$X$",
+ "y_axis_label":"$Y$",
+ "x_labeled_nums": list(np.arange(-7, 8,1)),
+ "y_labeled_nums": list(np.arange(-7, 8,1)),
+ "x_axis_width": 10,
+ "y_axis_height": 10,
+ "x_tick_frequency":1,
+ "axes_color": GREY,
+ "area_opacity": 3,
+ "num_rects": 10,
+ }
+ def construct(self):
+ self.setup_axes(animate = True)
+ XD = self.x_axis_width/(self.x_max- self.x_min)
+ YD = self.y_axis_height/(self.y_max- self.y_min)
+ a1=2*XD*RIGHT+1*YD*UP
+ a2=3*XD*RIGHT+1*YD*UP
+ vec1=Vector(direction=a1,stroke_width=2).set_color(RED_E)
+ vec1.shift(self.graph_origin)
+ v1_label=TextMobject(r"$v_1$")
+ v1_label=(v1_label.shift(self.graph_origin+a1+0.1)).scale(.6)
+ self.play(ShowCreation(vec1),ShowCreation(v1_label))
+ text1=TextMobject(r"\text{$v_1$}",r"\text{$= (2,1)$}").scale(.6)
+ text1[0].set_color(RED_E)
+ text1.shift(5*LEFT+3.5*UP)
+ self.play(ShowCreation(text1))
+ self.wait(1.5)
+ vec2=Vector(direction=a2,stroke_width=2).set_color(YELLOW_E)
+ vec2.shift(self.graph_origin)
+ v2_label=TextMobject(r"$v_2$")
+ v2_label=(v2_label.shift(self.graph_origin+a2+0.1)).scale(.6)
+ self.play(ShowCreation(vec2),ShowCreation(v2_label))
+ text2=TextMobject(r"\text{$v_2$}",r"\text{$= (3,1)$}").scale(.6)
+ text2[0].set_color(YELLOW_E)
+ text2.shift(5*LEFT+3*UP)
+ self.play(ShowCreation(text2))
+ self.wait(1.5)
+ text3=TextMobject(r"\text{${T_2}$}",r"\text{$(v_1)$}",r"\text{$= 0$}").scale(.6)
+ text3[0].set_color(BLUE)
+ text3[1].set_color(RED_E)
+ text3.shift(4.94*LEFT+2.5*UP)
+ self.play(ShowCreation(text3))
+ self.wait(1.5)
+ text4=TextMobject(r"\text{${T_2}$}",r"\text{$= x - 2y$}").scale(.6)
+ text4[0].set_color(BLUE)
+ text4.shift(4.9*LEFT+2*UP)
+ self.play(ShowCreation(text4))
+ self.wait(1.5)
+ line1 = self.get_graph(lambda x : x/2, x_min = -5,x_max=5,color=BLUE)
+ v1_dual_label = TextMobject(r"${T_2}$").scale(.6).shift(3.9*RIGHT+1.85*UP)
+ self.play(ShowCreation(line1),ShowCreation(v1_dual_label))
+ self.wait(1.5)
+ text5=TextMobject(r"\text{${T_1}$}",r"\text{$(v_2)$}",r"\text{$= 0$}").scale(.6)
+ text5[1].set_color(YELLOW_E)
+ text5[0].set_color(PINK)
+ text5.shift(4.94*LEFT+1.5*UP)
+ self.play(ShowCreation(text5))
+ self.wait(1.5)
+ line2 = self.get_graph(lambda x : x/3, x_min = -5,x_max=5,color=PINK)
+ v2_dual_label = TextMobject(r"${T_1}$").scale(.6).shift(3.9*RIGHT+1.3*UP)
+ self.play(ShowCreation(line2),ShowCreation(v2_dual_label))
+ self.wait(1.5)
+ text6=TextMobject(r"\text{${T_1}$}",r"\text{$= - x + 3y$}").scale(.6)
+ text6[0].set_color(PINK)
+ text6.shift(4.76*LEFT+1*UP)
+ self.play(ShowCreation(text6))
+ self.wait(3)
+ text7 = TextMobject(r"\text{B =}",r"\text{$[$}",r"\text{$v_1,$}",r"\text{$v_2$}",r"\text{$]$}",r"\text{=}",r"\text{$[(2,1), (3,1)]$}").scale(0.6).shift(3*UP+4.5*LEFT)
+ text7[2].set_color(RED_E)
+ text7[3].set_color(YELLOW_E)
+ self.play(FadeOut(text1),FadeOut(text2),FadeOut(text3),FadeOut(text4),FadeOut(text5),FadeOut(text6))
+ self.play(ShowCreation(text7))
+ self.wait(0.7)
+ text8 = TextMobject(r"\text{B$^* =$}",r"\text{$[$}",r"\text{${T_1}$,}",r"\text{${T_2} $}",r"\text{$]$}",r"\text{=}",r"\text{$[-x + 3y, x - 2y]$}").scale(0.6).shift(2.3*UP+4.1*LEFT)
+ text8[3].set_color(BLUE)
+ text8[2].set_color(PINK)
+ self.play(ShowCreation(text8))
+ self.wait(3)
+
+
+
+
+
+
+
+
+
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/Dual_of_a_Cube.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/Dual_of_a_Cube.py new file mode 100644 index 0000000..a6f501e --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/Dual_of_a_Cube.py @@ -0,0 +1,38 @@ +from manimlib.imports import *
+class Duality(ThreeDScene):
+
+
+ def construct(self):
+ axes = ThreeDAxes()
+ self.set_camera_orientation(phi = 65*DEGREES,theta =80*DEGREES)
+ self.begin_ambient_camera_rotation(rate=0.09)
+ cube = Cube(stroke_width=5,color=WHITE).scale(2)
+ cube.set_opacity(0.2)
+ self.play(ShowCreation(cube))
+ dot1= Dot(color=RED).scale(0.85).shift([2,0,0])
+ self.play(ShowCreation(dot1))
+ dot2= Dot(color=YELLOW).scale(0.85).shift([-2,0,0])
+ self.play(ShowCreation(dot2))
+ dot3= Dot(color=BLUE).scale(0.85).shift([0,-2,0])
+ self.play(ShowCreation(dot3))
+ dot4= Dot(color=GREEN).scale(0.85).shift([0,2,0])
+ self.play(ShowCreation(dot4))
+ dot5= Dot(color=ORANGE).scale(0.85).shift([0,0,2])
+ self.play(ShowCreation(dot5))
+ dot6= Dot(color=PINK).scale(0.85).shift([0,0,-2])
+ self.play(ShowCreation(dot6))
+ line1 = Line(start=[0,0,2],end=[2,0,0],stroke_width=2.5,color=BLACK)
+ line2 = Line(start=[0,0,2],end=[-2,0,0],stroke_width=2.5,color=BLACK)
+ line3 = Line(start=[0,0,2],end=[0,-2,0],stroke_width=2.5,color=BLACK)
+ line4 = Line(start=[0,0,2],end=[0,2,0],stroke_width=2.5,color=BLACK)
+ line5 = Line(start=[2,0,0],end=[0,0,-2],stroke_width=2.5,color=BLACK)
+ line6 = Line(start=[-2,0,0],end=[0,0,-2],stroke_width=2.5,color=BLACK)
+ line7 = Line(start=[0,-2,0],end=[0,0,-2],stroke_width=2.5,color=BLACK)
+ line8 = Line(start=[0,2,0],end=[0,0,-2],stroke_width=2.5,color=BLACK)
+ line9 = Line(start=[0,2,0],end=[-2,0,0],stroke_width=2.5,color=BLACK)
+ line10 = Line(start=[-2,0,0],end=[0,-2,0],stroke_width=2.5,color=BLACK)
+ line11 = Line(start=[0,-2,0],end=[2,0,0],stroke_width=2.5,color=BLACK)
+ line12 = Line(start=[2,0,0],end=[0,2,0],stroke_width=2.5,color=BLACK)
+ self.play(ShowCreation(line1),ShowCreation(line2),ShowCreation(line3),ShowCreation(line4),ShowCreation(line5),ShowCreation(line6),ShowCreation(line7),ShowCreation(line8),ShowCreation(line9),ShowCreation(line10),ShowCreation(line11),ShowCreation(line12))
+ self.wait(10)
+
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/Duality_in_Sets.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/Duality_in_Sets.py new file mode 100644 index 0000000..693017e --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/Duality_in_Sets.py @@ -0,0 +1,25 @@ +from manimlib.imports import *
+import numpy as np
+class Duality_in_sets(Scene):
+ def construct(self):
+ circle1 = Circle(radius=0.4,color=BLACK).shift(2.3*LEFT)
+ circle1.set_fill(color=RED,opacity=200)
+ rect1=Rectangle(height=2,width=2,color=GREY).shift(2*LEFT)
+ rect1.set_fill(color=DARK_BLUE,opacity=1)
+ text1 = TextMobject("S").scale(0.7).shift(0.9*UP+0.7*LEFT)
+ text2 = TextMobject("X",color=BLACK,stroke_width=0.5).scale(0.5).shift(2.3*LEFT)
+ self.play(ShowCreation(rect1),ShowCreation(text1),ShowCreation(circle1),ShowCreation(text2))
+ circle2 = Circle(radius=0.4,color=BLACK).shift(1.7*RIGHT)
+ circle2.set_fill(color=BLACK,opacity=200)
+ rect2=Rectangle(height=2,width=2,color=GREY).shift(2*RIGHT)
+ rect2.set_fill(color=DARK_BLUE,opacity=1)
+ text3 = TextMobject("S").scale(0.7).shift(0.9*UP+3.3*RIGHT)
+ text4 = TextMobject(r"X$^c$",color=BLACK,stroke_width=0.2).scale(0.5).shift(2.55*RIGHT+0.6*UP)
+ text5 = TextMobject(r"\text{The subset}",r"\text{X$^c$}",r"\text{is the dual of subset}",r"\text{X}").scale(0.6).shift(2.7*UP+0.5*LEFT)
+ text5[1].set_color(GREY)
+ text5[3].set_color(GREY)
+ self.play(ShowCreation(rect2),ShowCreation(circle2),ShowCreation(text3),ShowCreation(text4))
+ self.wait(2)
+ self.play(ShowCreation(text5))
+ self.wait(3)
+
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/Linear_Functional.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/Linear_Functional.py new file mode 100644 index 0000000..6edc918 --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/Linear_Functional.py @@ -0,0 +1,29 @@ +from manimlib.imports import *
+import numpy as np
+class LinearFunctional(Scene):
+ def construct(self):
+ big_box=Rectangle().scale(2.7)
+ box = Rectangle(height=2,width=2,color=DARK_GREY).set_fill(color=PURPLE,opacity=350)
+ arrow1 = Arrow(color=RED).shift(1.8*LEFT+0.5*UP)
+ arrow2 = Arrow(color=RED).shift(1.8*LEFT+0.5*DOWN)
+ arrow3 = Arrow(color=GREEN).shift(0.5*UP+1.8*RIGHT)
+ arrow4 = Arrow(color=GREEN).shift(0.5*DOWN+1.8*RIGHT)
+ Linear = TextMobject("LINEAR",color=BLACK).scale(0.5).shift(0.2*UP)
+ Functional = TextMobject("FUNCTIONAL",color=BLACK).scale(0.5).shift(0.2*DOWN)
+ u = TextMobject(r"$\vec{u}$",color=YELLOW).scale(0.7).shift(2.8*LEFT+0.5*UP)
+ v = TextMobject(r"$\vec{v}$",color=YELLOW).scale(0.7).shift(2.8*LEFT+0.5*DOWN)
+ f1 = TextMobject(r"$f_1$",color=YELLOW).scale(0.7).shift(2.8*RIGHT+0.5*UP)
+ f2 = TextMobject(r"$f_2$",color=YELLOW).scale(0.7).shift(2.8*RIGHT+0.5*DOWN)
+ text = TextMobject(r"The Linear Functional is a function that takes $\vec{u}, \vec{v} \in$ V as inputs and gives the output $f_1, f_2\in$ F.").scale(0.55).shift(2*DOWN)
+ self.play(ShowCreation(big_box))
+ self.play(ShowCreation(box))
+ self.play(ShowCreation(Linear),ShowCreation(Functional))
+ self.wait(2)
+ self.play(ShowCreation(arrow1),ShowCreation(u))
+ self.play(ShowCreation(arrow3),ShowCreation(f1))
+ self.wait(0.7)
+ self.play(ShowCreation(arrow2),ShowCreation(v))
+ self.play(ShowCreation(arrow4),ShowCreation(f2))
+ self.wait(1)
+ self.play(ShowCreation(text))
+ self.wait(4)
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/gifs4/Basis_of_a_dual_vector_space.mp4 b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/gifs4/Basis_of_a_dual_vector_space.mp4 Binary files differnew file mode 100644 index 0000000..b96f541 --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/gifs4/Basis_of_a_dual_vector_space.mp4 diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/gifs4/Dual_Basis_Example.mp4 b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/gifs4/Dual_Basis_Example.mp4 Binary files differnew file mode 100644 index 0000000..c93be25 --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/gifs4/Dual_Basis_Example.mp4 diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/gifs4/Dual_of_a_Cube.mp4 b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/gifs4/Dual_of_a_Cube.mp4 Binary files differnew file mode 100644 index 0000000..ebfb564 --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/gifs4/Dual_of_a_Cube.mp4 diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/gifs4/Duality_in_Sets.mp4 b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/gifs4/Duality_in_Sets.mp4 Binary files differnew file mode 100644 index 0000000..86cc693 --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/gifs4/Duality_in_Sets.mp4 diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/gifs4/Linear_functional.mp4 b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/gifs4/Linear_functional.mp4 Binary files differnew file mode 100644 index 0000000..d41fada --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/gifs4/Linear_functional.mp4 diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/Function_Scalar_Multiplication.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/Function_Scalar_Multiplication.py new file mode 100644 index 0000000..ac74792 --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/Function_Scalar_Multiplication.py @@ -0,0 +1,62 @@ +from manimlib.imports import *
+from scipy import exp
+class FunctionScalarMultiplication(GraphScene):
+ CONFIG = {
+ "x_min" : -5,
+ "x_max" : 5,
+ "y_min" : -5,
+ "y_max" : 5,
+ "y_tick_frequency" : 1,
+ "x_tick_frequency" : 1,
+ "axes_color":LIGHT_GRAY,
+ "graph_origin": ORIGIN,
+ }
+ def construct(self):
+ self.setup_axes(animate = True)
+ curve1 = self.get_graph(lambda x : 1/3*(x**2)+1, x_min=-2,x_max=2.5,color=ORANGE)
+ curve2 = self.get_graph(lambda x : 2*(1/3*(x**2)+1), x_min=-2,x_max=2.5,color=GOLD)
+ fx= TextMobject("$f(x)$").scale(0.6).shift(1.25*UP + 2.2*LEFT)
+ gx= TextMobject("$2 \cdot f(x)$").scale(0.6).shift(0.5*UP + 2.1*LEFT)
+ f1 = self.get_vertical_line_to_graph(-2,curve1,color=YELLOW)
+ f2 = self.get_vertical_line_to_graph(-1.5,curve1,color=YELLOW)
+ f3 = self.get_vertical_line_to_graph(-1,curve1,color=YELLOW)
+ f4 = self.get_vertical_line_to_graph(-0.5,curve1,color=YELLOW)
+ f5 = self.get_vertical_line_to_graph(0,curve1,color=YELLOW)
+ f6 = self.get_vertical_line_to_graph(0.5,curve1,color=YELLOW)
+ f7 = self.get_vertical_line_to_graph(1,curve1,color=YELLOW)
+ f8 = self.get_vertical_line_to_graph(1.5,curve1,color=YELLOW)
+ f9 = self.get_vertical_line_to_graph(2,curve1,color=YELLOW)
+ f10 = self.get_vertical_line_to_graph(2.5,curve1,color=YELLOW)
+ self.play(ShowCreation(curve1),ShowCreation(fx))
+ self.wait(1.5)
+ self.play(ShowCreation(f1),ShowCreation(f2),ShowCreation(f3),ShowCreation(f4),ShowCreation(f5),ShowCreation(f6),ShowCreation(f7),ShowCreation(f8),ShowCreation(f9),ShowCreation(f10))
+ self.wait(1.7)
+ line1=Line(color=YELLOW).shift(5*LEFT+1.8*UP).scale(0.5)
+ line1.rotate(np.pi/2)
+ scalar = TextMobject("2 x").scale(0.65).shift(5.5*LEFT+1.9*UP)
+ equal = TextMobject("=").scale(0.65).shift(4.5*LEFT+1.9*UP)
+ line2=Line(color=BLUE).shift(4*LEFT+2.3*UP)
+ line2.rotate(np.pi/2)
+ self.play(ShowCreation(line1),ShowCreation(scalar),ShowCreation(equal),ShowCreation(line2))
+ g1 = self.get_vertical_line_to_graph(-2,curve2,color=BLUE)
+ g2 = self.get_vertical_line_to_graph(-1.5,curve2,color=BLUE)
+ g3 = self.get_vertical_line_to_graph(-1,curve2,color=BLUE)
+ g4 = self.get_vertical_line_to_graph(-0.5,curve2,color=BLUE)
+ g5 = self.get_vertical_line_to_graph(0,curve2,color=BLUE)
+ g6 = self.get_vertical_line_to_graph(0.5,curve2,color=BLUE)
+ g7 = self.get_vertical_line_to_graph(1,curve2,color=BLUE)
+ g8 = self.get_vertical_line_to_graph(1.5,curve2,color=BLUE)
+ g9 = self.get_vertical_line_to_graph(2,curve2,color=BLUE)
+ g10 = self.get_vertical_line_to_graph(2.5,curve2,color=BLUE)
+ self.play(ShowCreation(g1),ShowCreation(g2),ShowCreation(g3),ShowCreation(g4),ShowCreation(g5),ShowCreation(g6),ShowCreation(g7),ShowCreation(g8),ShowCreation(g9),ShowCreation(g10))
+ self.wait(2)
+ fx2=TextMobject("2$\cdot f(x)$").scale(0.6).shift(2.6*UP+2.3*LEFT)
+ self.play(ShowCreation(curve2),ShowCreation(fx2))
+ self.wait(1.5)
+ self.play(FadeOut(curve1),FadeOut(fx))
+ sc_mult=TextMobject("$(2 f(x)) = 2f(x)$",color=GOLD).scale(0.65).shift(0.65*UP + 5*LEFT)
+ rect = Rectangle(height=0.5,width=2)
+ rect.surround(sc_mult)
+ self.play(ShowCreation(sc_mult),ShowCreation(rect))
+ self.wait(3)
+
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/Function_Space_Addition.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/Function_Space_Addition.py new file mode 100644 index 0000000..5ce0e11 --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/Function_Space_Addition.py @@ -0,0 +1,89 @@ +from manimlib.imports import *
+from scipy import sin,exp
+class FunctionalVectorSpace(GraphScene):
+ CONFIG = {
+ "x_min" : -5,
+ "x_max" : 5,
+ "y_min" : -5,
+ "y_max" : 5,
+ "y_tick_frequency" : 1,
+ "x_tick_frequency" : 1,
+ "axes_color":LIGHT_GRAY,
+ "graph_origin": ORIGIN,
+
+
+ }
+ def construct(self):
+ self.setup_axes(animate = True)
+ curve1 = self.get_graph(lambda x : exp(x) + 0.5, x_min=-2,x_max=2.5,color=ORANGE)
+ curve2 = self.get_graph(lambda x : 1/3*(x**2)+1, x_min=-2,x_max=2.5,color=DARK_BLUE)
+ curve3 = self.get_graph(lambda x : 1/3*(x**2)+1 + exp(x) + 0.5, x_min=-2,x_max=2.5,color=BLACK)
+ fx= TextMobject("$f(x)$").scale(0.6).shift(1.25*UP + 2.1*LEFT)
+ gx= TextMobject("$g(x)$").scale(0.6).shift(0.5*UP + 2.1*LEFT)
+ f1 = self.get_vertical_line_to_graph(-2,curve1,color=YELLOW)
+ f2 = self.get_vertical_line_to_graph(-1.5,curve1,color=YELLOW)
+ f3 = self.get_vertical_line_to_graph(-1,curve1,color=YELLOW)
+ f4 = self.get_vertical_line_to_graph(-0.5,curve1,color=YELLOW)
+ f5 = self.get_vertical_line_to_graph(0,curve1,color=YELLOW)
+ f6 = self.get_vertical_line_to_graph(0.5,curve1,color=YELLOW)
+ f7 = self.get_vertical_line_to_graph(1,curve1,color=YELLOW)
+ f8 = self.get_vertical_line_to_graph(1.5,curve1,color=YELLOW)
+ f9 = self.get_vertical_line_to_graph(2,curve1,color=YELLOW)
+ f10 = self.get_vertical_line_to_graph(2.5,curve1,color=YELLOW)
+
+ self.play(ShowCreation(curve1),ShowCreation(gx))
+ self.wait(1.2)
+ self.play(ShowCreation(curve2),ShowCreation(fx))
+ self.wait(1.2)
+ self.play(ShowCreation(f1),ShowCreation(f2),ShowCreation(f3),ShowCreation(f4),ShowCreation(f5),ShowCreation(f6),ShowCreation(f7),ShowCreation(f8),ShowCreation(f9),ShowCreation(f10))
+ self.wait(1.7)
+ g1 = self.get_vertical_line_to_graph(-2,curve2,color=BLUE)
+ g2 = self.get_vertical_line_to_graph(-1.5,curve2,color=BLUE)
+ g3 = self.get_vertical_line_to_graph(-1,curve2,color=BLUE)
+ g4 = self.get_vertical_line_to_graph(-0.5,curve2,color=BLUE)
+ g5 = self.get_vertical_line_to_graph(0,curve2,color=BLUE)
+ g6 = self.get_vertical_line_to_graph(0.5,curve2,color=BLUE)
+ g7 = self.get_vertical_line_to_graph(1,curve2,color=BLUE)
+ g8 = self.get_vertical_line_to_graph(1.5,curve2,color=BLUE)
+ g9 = self.get_vertical_line_to_graph(2,curve2,color=BLUE)
+ g10 = self.get_vertical_line_to_graph(2.5,curve2,color=BLUE)
+ self.play(ShowCreation(g1),ShowCreation(g2),ShowCreation(g3),ShowCreation(g4),ShowCreation(g5),ShowCreation(g6),ShowCreation(g7),ShowCreation(g8),ShowCreation(g9),ShowCreation(g10))
+ line1=Line(color=BLUE).shift(5*LEFT+2.3*UP).scale(0.25)
+ line1.rotate(np.pi/2)
+ line2=Line(color=YELLOW).shift(6*LEFT+2.5*UP).scale(0.5)
+ line2.rotate(np.pi/2)
+ line3=Line(color=PURPLE_B).shift(4*LEFT+2.7*UP).scale(0.75)
+ line3.rotate(np.pi/2)
+ add=TextMobject("+").shift(2.4*UP+5.5*LEFT).scale(0.7)
+ equal=TextMobject("=").shift(2.4*UP+4.5*LEFT).scale(0.7)
+ self.play(ShowCreation(line2),ShowCreation(line1),ShowCreation(add),ShowCreation(equal),ShowCreation(line3))
+ self.wait(2)
+ self.play(FadeOut(curve1),FadeOut(curve2))
+ self.wait(3)
+ h1 = self.get_vertical_line_to_graph(-2,curve3,color=PURPLE_B)
+ h2 = self.get_vertical_line_to_graph(-1.5,curve3,color=PURPLE_B)
+ h3 = self.get_vertical_line_to_graph(-1,curve3,color=PURPLE_B)
+ h4 = self.get_vertical_line_to_graph(-0.5,curve3,color=PURPLE_B)
+ h5 = self.get_vertical_line_to_graph(0,curve3,color=PURPLE_B)
+ h6 = self.get_vertical_line_to_graph(0.5,curve3,color=PURPLE_B)
+ h7 = self.get_vertical_line_to_graph(1,curve3,color=PURPLE_B)
+ h8 = self.get_vertical_line_to_graph(1.5,curve3,color=PURPLE_B)
+ h9 = self.get_vertical_line_to_graph(2,curve3,color=PURPLE_B)
+ h10 = self.get_vertical_line_to_graph(2.5,curve3,color=PURPLE_B)
+
+ line1.shift(1*LEFT+0.9*UP)
+ equal.shift(0.3*LEFT+0.2*UP)
+ f=TextMobject("$f(x)$").scale(0.5).shift(5.6*LEFT+3.2*UP)
+ g=TextMobject("$g(x)$").scale(0.5).shift(5.6*LEFT+2.4*UP)
+ fg=TextMobject("$(f + g)(x)$").scale(0.5).shift(2.85*UP+3.3*LEFT)
+ self.play(FadeOut(add),ShowCreation(equal),ShowCreation(line1),ShowCreation(f),ShowCreation(g),ShowCreation(fg),FadeOut(fx),FadeOut(gx))
+ self.wait(1.7)
+ self.play(ShowCreation(h1),ShowCreation(h2),ShowCreation(h3),ShowCreation(h4),ShowCreation(h5),ShowCreation(h6),ShowCreation(h7),ShowCreation(h8),ShowCreation(h9),ShowCreation(h10))
+ curve3 = self.get_graph(lambda x : 1/3*(x**2)+1 + exp(x) + 0.5, x_min=-2,x_max=2.5,color=RED_A)
+ fgx=TextMobject("$(f + g)(x)$").scale(0.5).shift(1.65*UP+2.4*LEFT)
+ self.play(ShowCreation(curve3),ShowCreation(fgx))
+ sum=TextMobject("$(f + g)(x) = f(x) + g(x)$",color=GOLD).scale(0.65).shift(0.8*UP + 5*LEFT)
+ rect = Rectangle(height=0.5,width=2)
+ rect.surround(sum)
+ self.play(ShowCreation(sum),ShowCreation(rect))
+ self.wait(3)
\ No newline at end of file diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/Integral_Properties.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/Integral_Properties.py new file mode 100644 index 0000000..97c0e09 --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/Integral_Properties.py @@ -0,0 +1,77 @@ +from manimlib.imports import *
+from scipy import sin
+class Integral_Properties(GraphScene):
+ CONFIG = {
+ "x_min" : 0,
+ "x_max" : 5,
+ "y_min" : 0,
+ "y_max" : 6,
+ "y_tick_frequency" : 1,
+ "x_tick_frequency" : 1,
+ "axes_color":LIGHT_GRAY,
+ "x_labeled_nums" : list(range(6)),
+ "y_labeled_nums" : list(range(6))
+ }
+ def construct(self):
+ self.setup_axes(animate=False)
+ curve1 = self.get_graph(lambda x : sin(x), x_min=0,x_max=2.5,color=RED)
+ curve2 = self.get_graph(lambda x : x, x_min=0,x_max=2.5,color=DARK_BLUE)
+ curve3 = self.get_graph(lambda x : sin(x) + x, x_min=0,x_max=2.5,color=GREEN)
+ fx = TextMobject(r"$f(x)$").scale(0.5).shift(1*RIGHT+1.8*DOWN)
+ gx = TextMobject(r"$g(x)$").scale(0.5).shift(1*RIGHT)
+ sum = TextMobject(r"$f(x) + g(x)$").scale(0.5).shift(1.3*RIGHT+0.6*UP)
+ area1 = self.get_area(curve1,0,2.5)
+ area2 = self.get_area(curve2,0,2.5)
+ area3 = self.get_area(curve3,0,2.5)
+ area2.set_fill(color=PURPLE)
+ area3.set_fill(color=ORANGE)
+ text1=TextMobject(r"$\int_{0}^{2.5}$ f(x) dx = Area under the curve f(x)",color=BLUE_C).scale(0.7).shift(2.7*RIGHT+3*UP)
+ text2=TextMobject(r"$\int_{0}^{2.5}$ g(x) dx = Area under the curve g(x)",color=PURPLE_B).scale(0.7).shift(2.7*RIGHT+2.4*UP)
+ text3=TextMobject(r"Area under the curve f(x) + g(x) = $\int_{0}^{2.5} (f(x) + g(x)) dx$",color=ORANGE).scale(0.7).shift(2.7*RIGHT+1.8*UP)
+ text4=TextMobject(r"\text{$\int_{0}^{2.5}$ (f(x) + g(x)) dx}",r"\text{ = }",r"\text{ $\int_{0}^{2.5}$ f(x) dx }",r"\text{+}",r"\text{$\int_{0}^{2.5}$ g(x) dx}").scale(0.62).shift(2.7*RIGHT+2.7*UP)
+ text4[0].set_color(ORANGE)
+ text4[2].set_color(BLUE_C)
+ text4[4].set_color(PURPLE_B)
+ self.play(ShowCreation(curve1), ShowCreation(fx))
+ self.wait(1.2)
+ self.play(ShowCreation(curve2),ShowCreation(gx))
+ self.wait(1.2)
+ self.play(ShowCreation(area1))
+ self.play(ShowCreation(text1))
+ self.wait(1.5)
+ self.play(ShowCreation(area2))
+ self.play(ShowCreation(text2))
+ self.wait(1.5)
+ self.play(ShowCreation(curve3),ShowCreation(sum))
+ self.play(ShowCreation(area3))
+ self.play(ShowCreation(text3))
+ self.wait(2)
+ self.play(FadeOut(text1),FadeOut(text2),FadeOut(text3))
+ self.wait(1)
+ self.play(ShowCreation(text4))
+ self.wait(3)
+ self.play(FadeOut(curve1),FadeOut(curve2),FadeOut(area1),FadeOut(area2))
+ self.wait(1.5)
+ self.play(FadeOut(text4),FadeOut(area2),FadeOut(curve2),FadeOut(gx),FadeOut(curve3),FadeOut(sum),FadeOut(area3),ShowCreation(curve1),ShowCreation(fx))
+ self.wait(1.5)
+ self.play(ShowCreation(area1),ShowCreation(text1))
+ self.wait(1.5)
+ curve4 = self.get_graph(lambda x : 2*sin(x), x_min=0,x_max=2.5,color=RED)
+ area4 = self.get_area(curve4,0,2.5)
+ area4.set_fill(color=YELLOW)
+ fx2 = TextMobject(r"$2f(x)$").scale(0.7).shift(1*RIGHT+1.2*DOWN)
+ scalar_mul=TextMobject(r"$\int_{0}^{2.5} ( 2f(x) ) dx$ = 2 $\times$ Area under the curve f(x)",color=YELLOW).scale(0.7).shift(2.7*RIGHT+2.4*UP)
+ self.play(ShowCreation(curve4),ShowCreation(fx2))
+ self.wait(1)
+ self.play(ShowCreation(area4))
+ self.wait(2)
+ self.play(ShowCreation(scalar_mul))
+ self.wait(2)
+ text5=TextMobject(r"\text{$\int_{0}^{2.5}$ (2 f(x)) dx}",r"\text{ = }",r"\text{2 $\int_{0}^{2.5}$ f(x) dx }").scale(0.67).shift(2.7*RIGHT+2.7*UP)
+ text5[0].set_color(YELLOW)
+ text5[2].set_color(BLUE_C)
+ self.play(FadeOut(text1),FadeOut(scalar_mul))
+ self.wait(1)
+ self.play(ShowCreation(text5))
+ self.wait(3)
+
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/gifs3/Addition_of_Functions.gif b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/gifs3/Addition_of_Functions.gif Binary files differnew file mode 100644 index 0000000..6c42b74 --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/gifs3/Addition_of_Functions.gif diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/gifs3/Function_Space_Example.gif b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/gifs3/Function_Space_Example.gif Binary files differnew file mode 100644 index 0000000..996a9de --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/gifs3/Function_Space_Example.gif diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/gifs3/Scalar_Multiplicaton_of_Functions.gif b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/gifs3/Scalar_Multiplicaton_of_Functions.gif Binary files differnew file mode 100644 index 0000000..8fff2c8 --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/gifs3/Scalar_Multiplicaton_of_Functions.gif diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Conjugate_Symmetry_and_Positivity_of_Inner_Product.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Conjugate_Symmetry_and_Positivity_of_Inner_Product.py new file mode 100644 index 0000000..1d84842 --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Conjugate_Symmetry_and_Positivity_of_Inner_Product.py @@ -0,0 +1,141 @@ +from manimlib.imports import *
+VECTORS = [[0, 2],
+ [1, 1],
+ [0, -2],
+ [1, -1],
+ [2, -2],
+ [2, 2],
+ [2, 2],
+ [-2, -1],
+ [3, 4]]
+class Scene1(LinearTransformationScene):
+ CONFIG = {
+ "include_background_plane": True,
+ "include_foreground_plane": False,
+ "show_coordinates": True,
+ "show_basis_vectors": False,
+ "basis_vector_stroke_width": 3,
+ }
+ def construct(self):
+ text1 = TextMobject(r"\text{$u$}",r"\text{ = $0 + 2i$, }",r"\text{$v$}",r"\text{ = $1 + i$}").scale(0.6).shift(3.5*UP+4*LEFT)
+ text1[0].set_color(YELLOW)
+ text1[2].set_color(RED)
+ text1.add_background_rectangle()
+ self.play(ShowCreation(text1))
+ text2 = TextMobject(r"\text{$\overline{u}$}",r"\text{ = $0 - 2i$, }",r"\text{$\overline{v}$}",r"\text{ = $1 - i$}").scale(0.6).shift(3*UP+4*LEFT)
+ text2[0].set_color(YELLOW)
+ text2[2].set_color(RED)
+ text2.add_background_rectangle()
+ self.play(ShowCreation(text2))
+ self.wait(2)
+ v1 = self.add_vector(VECTORS[0],color = YELLOW, stroke_width = 3.5)
+ u = TextMobject(r"$u$",color=YELLOW).shift(0.3*LEFT+2*UP).scale(0.6)
+ self.play(ShowCreation(u))
+ v1b = self.add_vector(VECTORS[2],color = YELLOW, stroke_width = 3.5)
+ ub = TextMobject(r"$\overline{u}$",color=YELLOW).shift(2*DOWN+0.3*LEFT).scale(0.6)
+ self.play(ShowCreation(ub))
+ self.wait(2)
+ v2 = self.add_vector(VECTORS[1],color = RED, stroke_width = 3.5)
+ v = TextMobject(r"$v$",color=RED).shift(1.2*RIGHT+1*UP).scale(0.6)
+ self.play(ShowCreation(v))
+ v2b = self.add_vector(VECTORS[3],color = RED, stroke_width = 3.5)
+ vb = TextMobject(r"$\overline{v}$",color=RED).shift(1.2*RIGHT+1*DOWN).scale(0.6)
+ self.play(ShowCreation(vb))
+ text3 = TextMobject(r"\text{$<u, v>$}",r"\text{ = }",r"\text{$\overline{u}$",r"\text{$\cdot$}",r"\text{$v$}",r"\text{ = }",r"\text{$2 - 2i$}").shift(2.5*UP+3.7*LEFT).scale(0.6)
+ text3[0].set_color(BLUE)
+ text3[2].set_color(YELLOW)
+ text3[4].set_color(RED)
+ text3.add_background_rectangle()
+ self.play(ShowCreation(text3))
+ self.wait(2)
+ text4 = TextMobject(r"\text{$<\overline{u, v}>$",r"\text{ = }",r"\text{$\overline{u}$",r"\text{$\cdot$}",r"\text{$v$}",r"\text{ = }",r"\text{$2 + 2i$}").shift(2*UP+3.7*LEFT).scale(0.6)
+ text4[0].set_color(BLUE)
+ text4[2].set_color(YELLOW)
+ text4[4].set_color(RED)
+ text4.add_background_rectangle()
+ line = Line(stroke_width = 1.5).scale(0.33).shift(2.2*UP+3.54*LEFT)
+ self.play(ShowCreation(text4),ShowCreation(line))
+ self.wait(2)
+ self.play(FadeOut(v1),FadeOut(v1b),FadeOut(v2),FadeOut(v2b),FadeOut(u),FadeOut(ub),FadeOut(v),FadeOut(vb))
+ v3 = self.add_vector(VECTORS[4],color = BLUE, stroke_width = 3.5)
+ uv = TextMobject(r"$\overline{u}\cdot v$",color=BLUE).shift(2.4*RIGHT+2.1*DOWN).scale(0.6)
+ self.play(ShowCreation(uv))
+ v3b = self.add_vector(VECTORS[5],color = BLUE, stroke_width = 3.5)
+ uvb = TextMobject(r"$\overline{\overline{u}\cdot v}$",color=BLUE).shift(2.4*RIGHT+2.1*UP).scale(0.6)
+ self.play(ShowCreation(uvb))
+ self.wait(2)
+ text5 = TextMobject(r"\text{$<v, u>$}",r"\text{ = }",r"\text{$\overline{v}$",r"\text{$\cdot$}",r"\text{$u$}",r"\text{ = }",r"\text{$2 + 2i$}").shift(1.5*UP+3.7*LEFT).scale(0.6)
+ text5[0].set_color(MAROON_B)
+ text5[2].set_color(RED)
+ text5[4].set_color(YELLOW)
+ text5.add_background_rectangle()
+ self.play(ShowCreation(text5))
+ self.wait(2)
+ v4 = self.add_vector(VECTORS[5],color = MAROON_B, stroke_width = 3.5)
+ vu = TextMobject(r"$\overline{v}\cdot u$",color=MAROON_B).shift(1.3*RIGHT+2.1*UP).scale(0.6)
+ self.play(ShowCreation(vu))
+ self.play(FadeOut(uvb))
+ self.wait(2)
+ text6 = TextMobject(r"\text{$<\overline{u, v}>$",r"\text{ = }",r"\text{$<v, u>$").scale(0.6).shift(0.8*UP+4.2*LEFT)
+ text6[0].set_color(BLUE)
+ text6[2].set_color(MAROON_B)
+ text6.add_background_rectangle()
+ self.play(ShowCreation(text6))
+ rect = Rectangle(height = 0.7,width = 3.5)
+ rect.surround(text6)
+ self.play(ShowCreation(rect))
+ self.wait(3)
+ self.play(FadeOut(line),FadeOut(text1),FadeOut(text2),FadeOut(text3),FadeOut(text4),FadeOut(text5),FadeOut(text6),FadeOut(v4),FadeOut(vu),FadeOut(v3),FadeOut(uv),FadeOut(rect),FadeOut(v3b))
+
+ text7 = TextMobject(r"\text{$u$}",r"\text{ = $(1 + i) > 0$}").scale(0.6).shift(3.5*UP+4.5*LEFT)
+ text7[0].set_color(YELLOW)
+ text7.add_background_rectangle()
+ self.play(ShowCreation(text7))
+ v5 = self.add_vector(VECTORS[1],color = YELLOW, stroke_width = 3.5)
+ u = TextMobject(r"$u$",color=YELLOW).shift(1.2*RIGHT+1*UP).scale(0.6)
+ self.play(ShowCreation(u))
+ self.wait(1.5)
+ text8 = TextMobject(r"\text{$<u, u>$}",r"\text{ = $(0 + 2i) > 0$ }").scale(0.6).shift(2.7*UP+4*LEFT)
+ text8[0].set_color(GREEN)
+ text8.add_background_rectangle()
+ rect1 = Rectangle(height = 0.55, width = 3.3)
+ rect1.surround(text8)
+ self.play(ShowCreation(text8),ShowCreation(rect1))
+ self.wait(2)
+ v6 = self.add_vector(VECTORS[0],color = GREEN, stroke_width = 3.5)
+ uu = TextMobject(r"$<u, u>$",color=GREEN).shift(0.8*LEFT+1.9*UP).scale(0.6)
+ self.play(ShowCreation(uu))
+ text9 = TextMobject(r"\text{$v$}",r"\text{ = $(-2 - i) < 0$}").scale(0.6).shift(1.5*UP+4.4*LEFT)
+ text9[0].set_color(RED)
+ text9.add_background_rectangle()
+ self.play(ShowCreation(text9))
+ self.wait(1.5)
+ v7 = self.add_vector(VECTORS[7],color = RED, stroke_width = 3.5)
+ v = TextMobject(r"$v$",color=RED).shift(2.2*LEFT+1*DOWN).scale(0.6)
+ self.play(ShowCreation(v))
+ self.wait(1.5)
+ text10 = TextMobject(r"\text{$<v, v>$}",r"\text{ = $(3 + 4i) > 0$ }").scale(0.6).shift(0.7*UP+4*LEFT)
+ text10[0].set_color(BLUE)
+ text10.add_background_rectangle()
+ rect2 = Rectangle(height=0.55,width=3.3)
+ rect2.surround(text10)
+ self.play(ShowCreation(text10),ShowCreation(rect2))
+ self.wait(2)
+ v8 = self.add_vector(VECTORS[8],color = BLUE, stroke_width = 3.5)
+ vv = TextMobject(r"$<v, v>$",color=BLUE).shift(2.1*RIGHT+3.8*UP).scale(0.6)
+ self.play(ShowCreation(vv))
+ self.wait(4)
+
+
+
+
+
+
+
+
+
+
+
+
+
+
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Inner_Product_Example.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Inner_Product_Example.py new file mode 100644 index 0000000..97b9696 --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Inner_Product_Example.py @@ -0,0 +1,182 @@ +from manimlib.imports import *
+from scipy import sin,cos
+class Inner_Product_Space_Example(GraphScene):
+ CONFIG = {
+ "x_min" : 0,
+ "x_max" : 5,
+ "y_min" : 0,
+ "y_max" : 6,
+ "y_tick_frequency" : 1,
+ "x_tick_frequency" : 1,
+ "axes_color":LIGHT_GRAY,
+ "x_labeled_nums" : list(range(6)),
+ "y_labeled_nums" : list(range(6))
+ }
+ def construct(self):
+ self.setup_axes(animate=True)
+ text = TextMobject(r"$f(x), g(x), h(x) \in C[0, 2]$",color=GOLD).scale(0.5).shift(3.5*UP+5.5*LEFT)
+ fx = TextMobject(r"$f(x)$ = sin(x)",color=GOLD).scale(0.5).shift(3*UP+6*LEFT)
+ gx = TextMobject(r"$g(x)$ = x",color=GOLD).scale(0.5).shift(2.5*UP+6.25*LEFT)
+ hx = TextMobject(r"$h(x)$ = 1.4",color=GOLD).scale(0.5).shift(2*UP+6.2*LEFT)
+
+ curve1 = self.get_graph(lambda x : sin(x), x_min=0,x_max=2,color=RED)
+ curve2 = self.get_graph(lambda x : x, x_min=0,x_max=2,color=DARK_BLUE)
+ curve3 = self.get_graph(lambda x : 1.4, x_min=0,x_max=2,color=GREEN)
+ text1 = TextMobject(r"$f(x)$").scale(0.5).shift(1.7*DOWN)
+
+ text2 = TextMobject(r"$g(x)$").scale(0.5).shift(0.34*DOWN)
+ text3 = TextMobject(r"$h(x)$").scale(0.5).shift(1.1*DOWN)
+
+
+ self.play(ShowCreation(text))
+ self.play(ShowCreation(curve1),ShowCreation(text1),ShowCreation(fx))
+ self.wait(1)
+ self.play(ShowCreation(curve2),ShowCreation(text2),ShowCreation(gx))
+ self.wait(1)
+ self.play(ShowCreation(curve3),ShowCreation(text3),ShowCreation(hx))
+ self.wait(2)
+ curve4 = self.get_graph(lambda x : sin(x) + x, x_min=0,x_max=2,color=YELLOW)
+ text4 = TextMobject(r"$f(x) + g(x)$").scale(0.5).shift(0.5*UP+0.5*RIGHT)
+ self.wait(1.5)
+
+ self.play(ShowCreation(curve4),ShowCreation(text4),FadeOut(curve2),FadeOut(text2),FadeOut(curve1),FadeOut(text1))
+ self.wait(1.5)
+ text5 = TextMobject(r"\text{$<f(x) + g(x), h(x)>$ = ",r"\text{$\int_{0}^{2} (f(x) + g(x))h(x)$ $dx$}",r"\text{= 4.78}").scale(0.57).shift(3.3*RIGHT+3.5*UP)
+ text5[1].set_color(ORANGE)
+ self.play(ShowCreation(text5))
+
+ curve5 = self.get_graph(lambda x : (sin(x) + x)*1.6, x_min=0,x_max=2,color=ORANGE)
+ text6 = TextMobject(r"$(f(x) + g(x))\cdot h(x)$").scale(0.5).shift(2.2*UP+0.72*RIGHT)
+ area1 = self.get_area(curve5,0,2)
+ area1.set_color(ORANGE)
+ self.wait(1)
+ self.play(FadeOut(curve4),FadeOut(text4),FadeOut(curve3),FadeOut(text3),ShowCreation(curve5),ShowCreation(text6),ShowCreation(area1))
+ self.wait(2)
+ text7 = TextMobject(r"\text{$<f(x), h(x)>$ = ",r"\text{$\int_{0}^{2} (f(x)h(x)$ $dx$}",r"\text{= 1.98}").scale(0.57).shift(4.5*RIGHT+3*UP)
+ text7[1].set_color(BLUE)
+ self.play(ShowCreation(text7))
+ self.wait(1.5)
+ curve6 = self.get_graph(lambda x : (sin(x))*1.6, x_min=0,x_max=2,color=BLUE)
+ text8 = TextMobject(r"$f(x)\cdot h(x)$").scale(0.5).shift(0.9*DOWN+0.3*RIGHT)
+ area2 = self.get_area(curve6,0,2)
+ self.play(ShowCreation(curve6),ShowCreation(text8),ShowCreation(area2))
+ self.wait(1.5)
+ text9 = TextMobject(r"\text{$<g(x), h(x)>$ = ",r"\text{$\int_{0}^{2} (g(x)h(x)$ $dx$}",r"\text{= 2.8}").scale(0.57).shift(4.5*RIGHT+2.5*UP)
+ text9[1].set_color(MAROON_B)
+ self.play(ShowCreation(text9))
+ self.wait(1.5)
+ curve7 = self.get_graph(lambda x : x*1.6, x_min=0,x_max=2,color=MAROON_B)
+ text10 = TextMobject(r"$g(x)\cdot h(x)$").scale(0.5).shift(0.3*RIGHT+0.78*UP)
+ area3 = self.get_area(curve7,0,2)
+ area3.set_color(MAROON_B)
+ self.play(ShowCreation(curve7),ShowCreation(text10),ShowCreation(area3))
+ self.wait(2.6)
+ curve8 = self.get_graph(lambda x : (sin(x))*1.6 + x*1.6, x_min=0,x_max=2,color=RED_C)
+ area4 = self.get_area(curve8,0,2)
+ area4.set_color(RED_C)
+ text11 = TextMobject(r"$f(x)h(x) + g(x)h(x)$").scale(0.5).shift(2.2*UP + 0.76*RIGHT)
+ self.play(FadeOut(curve6),FadeOut(text8),FadeOut(curve7),FadeOut(text10),FadeOut(area2),FadeOut(area3),ShowCreation(curve8),ShowCreation(area4))
+ self.wait(1)
+ self.play(Transform(text6,text11))
+ self.wait(1.7)
+ text12 = TextMobject(r"$<f(x) + g(x), h(x)>$ = $<f(x), h(x)>$ + $<g(x), h(x)>$").scale(0.465).shift(0.7*UP+4*RIGHT)
+ rect1 = Rectangle(height=0.5)
+ rect1.surround(text12)
+ self.play(ShowCreation(text12),ShowCreation(rect1))
+ self.wait(3)
+ self.play(FadeOut(text6),FadeOut(text5),FadeOut(text7),FadeOut(text9),FadeOut(text12),FadeOut(rect1),FadeOut(curve8),FadeOut(area4),FadeOut(text11),FadeOut(curve5),FadeOut(area1))
+
+ curve2.set_color(ORANGE)
+ self.play(ShowCreation(curve1),ShowCreation(text1))
+ self.wait(1)
+ self.play(ShowCreation(curve2),ShowCreation(text2))
+ self.wait(2)
+ curve9 = self.get_graph(lambda x : 2*sin(x), x_min=0,x_max=2,color=GREEN)
+ text13 = TextMobject(r"$2f(x)$").scale(0.5).shift(0.75*DOWN)
+ self.play(Transform(curve1,curve9),Transform(text1,text13))
+ self.wait(1.5)
+
+ text14 = TextMobject(r"\text{$<2f(x), g(x)>$ = ",r"\text{$\int_{0}^{2} (2f(x))g(x)$ $dx$}",r"\text{= 3.48}").scale(0.57).shift(4*RIGHT+3.5*UP)
+ text14[1].set_color(YELLOW)
+ self.play(ShowCreation(text14))
+ self.wait(2.2)
+ curve10 = self.get_graph(lambda x : 2*sin(x)*x, x_min=0,x_max=2,color=YELLOW)
+ text15 = TextMobject(r"$2f(x)\cdot g(x)$").scale(0.5).shift(0.35*RIGHT+1.03*UP)
+ area5 = self.get_area(curve10,0,2)
+ area5.set_color(YELLOW)
+ self.play(ShowCreation(area5),ShowCreation(curve10),ShowCreation(text15),FadeOut(curve1),FadeOut(text1),FadeOut(curve2),FadeOut(text2))
+ self.wait(2)
+ text16 = TextMobject(r"\text{$<f(x), g(x)>$ = ",r"\text{$\int_{0}^{2} f(x)g(x)$ $dx$}",r"\text{= 1.74}").scale(0.57).shift(3.8*RIGHT+2.9*UP)
+ text16[1].set_color(TEAL)
+ self.play(ShowCreation(text16))
+ self.wait(1.7)
+ curve11 = self.get_graph(lambda x : sin(x)*x, x_min=0,x_max=2,color=TEAL)
+ area6 = self.get_area(curve11,0,2)
+ area6.set_color(TEAL)
+ text17 = TextMobject(r"$f(x)\cdot g(x)$").scale(0.5).shift(0.4*RIGHT+0.7*DOWN)
+ self.play(ShowCreation(curve11),ShowCreation(text17),ShowCreation(area6))
+ self.wait(2)
+
+ text18 = TextMobject(r"\text{$2 <f(x), g(x)>$ = ",r"\text{$2 \int_{0}^{2} f(x)g(x)$ $dx$}",r"\text{= 3.48}").scale(0.57).shift(4*RIGHT+2.3*UP)
+ text18[1].set_color(DARK_BLUE)
+ self.play(ShowCreation(text18))
+ self.wait(2)
+ curve12 = self.get_graph(lambda x : 2*sin(x)*x, x_min=0,x_max=2,color=DARK_BLUE)
+ area7 = self.get_area(curve12,0,2)
+ area7.set_color(DARK_BLUE)
+ text19 = TextMobject(r"= $2( f(x)\cdot g(x) )$").scale(0.5).shift(1.89*RIGHT+1.03*UP)
+ self.play(ShowCreation(curve12),ShowCreation(area7),ShowCreation(text19),FadeOut(text17),FadeOut(area6),FadeOut(curve11))
+
+ self.wait(2.5)
+ text20 = TextMobject(r"$<2f(x), g(x)>$ = $2<f(x), g(x)>$").scale(0.57).shift(0.6*DOWN+4*RIGHT)
+ rect2 = Rectangle(height=0.5)
+ rect2.surround(text20)
+ self.play(ShowCreation(text20),ShowCreation(rect2))
+ self.wait(3)
+
+ self.play(FadeOut(text14),FadeOut(text15),FadeOut(text19),FadeOut(text16),FadeOut(text18),FadeOut(rect2),FadeOut(curve10),FadeOut(area5),FadeOut(curve12),FadeOut(area7),FadeOut(text20))
+ curve1 = self.get_graph(lambda x : sin(x), x_min=0,x_max=2,color=YELLOW)
+ text1 = TextMobject(r"$f(x)$").scale(0.5).shift(1.77*DOWN)
+ self.play(ShowCreation(curve1),ShowCreation(text1))
+ self.wait(1.5)
+ self.play(ShowCreation(curve2),ShowCreation(text2))
+ self.wait(1.7)
+ text21 = TextMobject(r"\text{$<f(x), g(x)>$ = ",r"\text{$\int_{0}^{2} f(x)g(x)$ $dx$}",r"\text{= 1.74}").scale(0.57).shift(3.5*RIGHT+3*UP)
+ text21[1].set_color(GREEN)
+ self.play(ShowCreation(text21))
+ self.wait(2)
+ curve13 = self.get_graph(lambda x : sin(x)*x, x_min=0,x_max=2,color=GREEN)
+ area8 = self.get_area(curve13,0,2)
+ area8.set_color(GREEN)
+ text22 = TextMobject(r"$f(x)\cdot g(x)$").scale(0.5).shift(0.32*RIGHT+0.7*DOWN)
+ self.play(ShowCreation(curve13),ShowCreation(area8),ShowCreation(text22),FadeOut(curve1),FadeOut(text1),FadeOut(curve2),FadeOut(text2))
+ self.wait(2.2)
+ curve14 = self.get_graph(lambda x : sin(x)*x, x_min=0,x_max=2,color=RED)
+ area9 = self.get_area(curve14,0,2)
+ area9.set_color(RED)
+ self.play(ShowCreation(curve14),ShowCreation(area9))
+ text23 = TextMobject(r"= $\overline{f(x)\cdot g(x)}$").scale(0.5).shift(0.7*DOWN+1.7*RIGHT)
+ self.play(ShowCreation(text23))
+ self.wait(2)
+ text24 = TextMobject(r"For all the real functions").scale(0.5).shift(2*RIGHT+2*UP)
+ text25 = TextMobject(r"$<\overline{f(x), g(x)}>$ = $<f(x), g(x)>$").scale(0.5).shift(2*RIGHT+1.4*UP)
+ rect3 = Rectangle(height=0.7)
+ rect3.surround(text25)
+ self.play(ShowCreation(text24),ShowCreation(text25),ShowCreation(rect3))
+ self.wait(3)
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Inner_product.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Inner_product.py new file mode 100644 index 0000000..e1344f7 --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Inner_product.py @@ -0,0 +1,28 @@ +from manimlib.imports import *
+import numpy as np
+class InnerProduct(Scene):
+ def construct(self):
+ big_box=Rectangle().scale(2.7)
+ box = Rectangle(height=2,width=2,color=DARK_GREY).set_fill(color=BLUE_B,opacity=350)
+ arrow1 = Arrow(color=RED).shift(1.8*LEFT+0.5*UP)
+ arrow2 = Arrow(color=RED).shift(1.8*LEFT+0.5*DOWN)
+ arrow3 = Arrow(color=GREEN).shift(1.8*RIGHT)
+ Inner = TextMobject("INNER",color=BLACK).scale(0.65).shift(0.2*UP)
+ Product = TextMobject("PRODUCT",color=BLACK).scale(0.65).shift(0.2*DOWN)
+ u = TextMobject(r"$\vec{u}$",color=YELLOW).scale(0.7).shift(2.8*LEFT+0.5*UP)
+ v = TextMobject(r"$\vec{v}$",color=YELLOW).scale(0.7).shift(2.8*LEFT+0.5*DOWN)
+ scalar = TextMobject("(Scalar)").scale(0.55).shift(3.3*RIGHT+0.4*DOWN)
+ u.v = TextMobject(r"$<\vec{u}, \vec{v}>$",color=YELLOW).scale(0.7).shift(3.3*RIGHT)
+ V = TextMobject("V").scale(0.7).shift(2*UP+3.8*RIGHT)
+ text = TextMobject(r"The Inner Product is an operation that takes $\vec{u}, \vec{v} \in$ V as inputs and gives a scalar as an output.").scale(0.55).shift(2*DOWN)
+ self.play(ShowCreation(big_box),ShowCreation(V))
+ self.play(ShowCreation(box))
+ self.play(ShowCreation(Product),ShowCreation(Inner))
+ self.wait(2)
+ self.play(ShowCreation(arrow1),ShowCreation(u))
+ self.play(ShowCreation(arrow2),ShowCreation(v))
+ self.wait(1.5)
+ self.play(ShowCreation(arrow3),ShowCreation(scalar),ShowCreation(u.v))
+ self.wait(1)
+ self.play(ShowCreation(text))
+ self.wait(10)
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Instances_of_Topological_Spaces.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Instances_of_Topological_Spaces.py new file mode 100644 index 0000000..2b3cf14 --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Instances_of_Topological_Spaces.py @@ -0,0 +1,36 @@ +from manimlib.imports import *
+class InnerProduct(Scene):
+ def construct(self):
+
+ circle1 = Circle(color=DARK_GREY).scale(3.7)
+ circle1.set_fill(color=GOLD,opacity=350)
+ square1 = Square(color=DARK_GREY).scale(2.5)
+ square1.set_fill(color=DARK_BLUE,opacity=350)
+ square2=Square(color=DARK_GREY).scale(1.6).shift(0.2*DOWN)
+ square2.rotate(np.pi/4).set_fill(color=YELLOW,opacity=350)
+ square3 = Square(color=DARK_GREY).scale(1).shift(0.3*DOWN)
+ square3.set_fill(color=BLACK,opacity=350)
+ circle2 = Circle(color=DARK_GREY).scale(0.5).shift(0.45*DOWN)
+ circle2.set_fill(color=MAROON_A,opacity=350)
+ text1 = TextMobject("Topological Spaces",color=BLACK).scale(0.5).shift(3*UP)
+ text2 = TextMobject("Metric Spaces",color=BLACK).scale(0.5).shift(2.2*UP)
+ text3 = TextMobject("Normed",color=BLACK).scale(0.44).shift(1.4*UP)
+ text4 = TextMobject("Vector Spaces",color=BLACK).scale(0.44).shift(1.17*UP)
+ text5 = TextMobject("Inner Product",color=WHITE).scale(0.37).shift(0.5*UP)
+ text6 = TextMobject("Spaces",color=WHITE).scale(0.37).shift(0.27*UP)
+ text7 = TextMobject("Dot",color=BLACK).scale(0.37).shift(0.3*DOWN)
+ text8 = TextMobject("Product",color=BLACK).scale(0.32).shift(0.5*DOWN)
+
+
+
+
+ self.play(ShowCreation(circle1),ShowCreation(text1))
+ self.wait(1.5)
+ self.play(ShowCreation(square1),ShowCreation(text2))
+ self.wait(1.5)
+ self.play(ShowCreation(square2),ShowCreation(text3),ShowCreation(text4))
+ self.wait(1.5)
+ self.play(ShowCreation(square3),ShowCreation(text5),ShowCreation(text6))
+ self.wait(1.5)
+ self.play(ShowCreation(circle2),ShowCreation(text7),ShowCreation(text8))
+ self.wait(4)
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Interpretation_of_Norm_as_Length.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Interpretation_of_Norm_as_Length.py new file mode 100644 index 0000000..23c568d --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Interpretation_of_Norm_as_Length.py @@ -0,0 +1,42 @@ +from manimlib.imports import *
+import numpy as np
+class Interpretation_of_norm_as_length(GraphScene):
+ CONFIG = {
+ "x_min" : 0,
+ "x_max" : 5,
+ "y_min" : 0,
+ "y_max" : 5,
+ "y_tick_frequency" : 1,
+ "x_tick_frequency" : 1,
+ "axes_color":LIGHT_GRAY,
+ "x_axis_width": 5,
+ "y_axis_height":5,
+ "graph_origin" : ORIGIN + 2*DOWN + 2*LEFT,
+ "enclude_zero_label": False
+
+ }
+ def construct(self):
+ self.setup_axes(animate=False)
+ dot = Dot().scale(0.5)
+ self.play(ShowCreation(dot))
+ origin = TextMobject(r"(0, 0)").scale(0.5).shift(2.5*LEFT+2.2*DOWN)
+ line1 = self.get_graph(lambda x : x, x_min=0,x_max=2,color=WHITE)
+ line2 = Line().rotate(np.pi/2).shift(1*DOWN)
+ text1 = TextMobject(r"$(v_1, 0)$").scale(0.5).shift(2.2*DOWN+0.2*RIGHT)
+ text2 = TextMobject(r"$(0, v_2)$").scale(0.5).shift(2.5*LEFT)
+ text3 = TextMobject(r"$(v_1, v_2)$").scale(0.5).shift(0.5*RIGHT)
+ text4 = TextMobject(r"$| v_1 |$",color=RED_B).scale(0.5).shift(1*LEFT+2.3*DOWN)
+ text5 = TextMobject(r"$| v_2 |$",color=RED_B).scale(0.5).shift(0.3*RIGHT+1*DOWN)
+ text6 = TextMobject(r"$\sqrt{{v_1}^2 + {v_2}^2}$",color=RED_B).scale(0.5).rotate(np.pi/4).shift(1.3*LEFT+1*DOWN)
+ line3 = Line(color=YELLOW).shift(1*LEFT+2*DOWN)
+ self.play(ShowCreation(line1),ShowCreation(line2),ShowCreation(text1),ShowCreation(text2),ShowCreation(text3),ShowCreation(origin))
+ self.wait(1.5)
+ self.play(ShowCreation(line3),ShowCreation(text4))
+ self.wait(1.5)
+ line2 = Line(color=YELLOW).rotate(np.pi/2).shift(1*DOWN)
+ self.play(ShowCreation(line2),ShowCreation(text5))
+ self.wait(1.5)
+ line1 = self.get_graph(lambda x : x, x_min=0,x_max=2,color=YELLOW)
+ self.play(ShowCreation(text6),ShowCreation(line1))
+ self.wait(4)
+
\ No newline at end of file diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Linearity_of_Inner_Product.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Linearity_of_Inner_Product.py new file mode 100644 index 0000000..e1344f7 --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Linearity_of_Inner_Product.py @@ -0,0 +1,28 @@ +from manimlib.imports import *
+import numpy as np
+class InnerProduct(Scene):
+ def construct(self):
+ big_box=Rectangle().scale(2.7)
+ box = Rectangle(height=2,width=2,color=DARK_GREY).set_fill(color=BLUE_B,opacity=350)
+ arrow1 = Arrow(color=RED).shift(1.8*LEFT+0.5*UP)
+ arrow2 = Arrow(color=RED).shift(1.8*LEFT+0.5*DOWN)
+ arrow3 = Arrow(color=GREEN).shift(1.8*RIGHT)
+ Inner = TextMobject("INNER",color=BLACK).scale(0.65).shift(0.2*UP)
+ Product = TextMobject("PRODUCT",color=BLACK).scale(0.65).shift(0.2*DOWN)
+ u = TextMobject(r"$\vec{u}$",color=YELLOW).scale(0.7).shift(2.8*LEFT+0.5*UP)
+ v = TextMobject(r"$\vec{v}$",color=YELLOW).scale(0.7).shift(2.8*LEFT+0.5*DOWN)
+ scalar = TextMobject("(Scalar)").scale(0.55).shift(3.3*RIGHT+0.4*DOWN)
+ u.v = TextMobject(r"$<\vec{u}, \vec{v}>$",color=YELLOW).scale(0.7).shift(3.3*RIGHT)
+ V = TextMobject("V").scale(0.7).shift(2*UP+3.8*RIGHT)
+ text = TextMobject(r"The Inner Product is an operation that takes $\vec{u}, \vec{v} \in$ V as inputs and gives a scalar as an output.").scale(0.55).shift(2*DOWN)
+ self.play(ShowCreation(big_box),ShowCreation(V))
+ self.play(ShowCreation(box))
+ self.play(ShowCreation(Product),ShowCreation(Inner))
+ self.wait(2)
+ self.play(ShowCreation(arrow1),ShowCreation(u))
+ self.play(ShowCreation(arrow2),ShowCreation(v))
+ self.wait(1.5)
+ self.play(ShowCreation(arrow3),ShowCreation(scalar),ShowCreation(u.v))
+ self.wait(1)
+ self.play(ShowCreation(text))
+ self.wait(10)
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Projection-in-3D-space.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Projection-in-3D-space.py new file mode 100644 index 0000000..e99202f --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Projection-in-3D-space.py @@ -0,0 +1,31 @@ +from manimlib.imports import *
+class ThreeDSpace(ThreeDScene):
+
+ def construct(self):
+ axes = ThreeDAxes()
+ axes.set_stroke(width=1,color=GOLD)
+ self.add(axes)
+ self.set_camera_orientation(phi = 70*DEGREES,theta =110*DEGREES)
+ line1 = Line(color = YELLOW,opacity=350,start = ORIGIN,end = [0.5,2,2])
+ self.play(ShowCreation(line1))
+ self.wait(1)
+ line2 = Line(color = BLUE,opacity=350,start = ORIGIN,end = [2,2,-1])
+ self.play(ShowCreation(line2))
+ self.wait(1)
+ line3 = Line(opacity=350,start=axes.c2p(0.5,2,2) ,end=axes.c2p(0.5,1.14,-0.17))
+ self.play(ShowCreation(line3))
+ self.wait(1)
+ line4 = Line(color=RED,opacity=350,start = ORIGIN,end=[0.5,1.14,-0.145])
+ self.play(ShowCreation(line4))
+ self.wait(2)
+ text1 = TextMobject(r"\text{Projection on }",r"\text{$\vec{v}$}",r"\text{ onto }",r"\text{$\vec{u}$}",r"\text{ = }",r"\text{$ |\vec{v}|cos\theta$,}").scale(0.6).shift(4*LEFT+3.5*UP)
+ text1[1].set_color(YELLOW)
+ text1[3].set_color(BLUE)
+ text1[5].set_color(RED)
+ text2 = TextMobject(r"\text{where $\theta$ is the angle between the vectors.}").scale(0.6).shift(4*LEFT+3*UP)
+ self.add_fixed_in_frame_mobjects(text1)
+ self.add_fixed_in_frame_mobjects(text2)
+ self.play(ShowCreation(text1),ShowCreation(text2))
+ self.wait(3)
+
+
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Vector_Projection.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Vector_Projection.py new file mode 100644 index 0000000..b1724c1 --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Vector_Projection.py @@ -0,0 +1,43 @@ +from manimlib.imports import *
+VECTORS = [[3,1],
+ [1,3],
+ [1.96,0.65]]
+class Projection(LinearTransformationScene):
+ CONFIG = {
+ "include_background_plane": True,
+ "include_foreground_plane": False,
+ "show_coordinates": False,
+ "show_basis_vectors": False,
+ "basis_vector_stroke_width": 3,
+ }
+ def construct(self):
+ v1 = self.add_vector(VECTORS[0],color = YELLOW, stroke_width = 3.5)
+ u = TextMobject(r"$\vec{u}$",color=YELLOW).scale(0.65).shift(3.2*RIGHT,1*UP)
+ self.play(ShowCreation(u))
+ self.wait(0.7)
+ v2 = self.add_vector(VECTORS[1],color = RED, stroke_width = 3.5)
+ v = TextMobject(r"$\vec{v}$",color=RED).scale(0.65).shift(1.2*RIGHT,3*UP)
+ self.play(ShowCreation(v))
+ self.wait(0.7)
+ angle = Arc(radius=0.6).scale(0.5)
+ theta = TextMobject(r"$\theta$").scale(0.65).shift(0.5*UP+0.5*RIGHT).rotate(np.pi/6)
+ self.play(ShowCreation(angle),ShowCreation(theta))
+ self.wait(1)
+ line1 = Line().scale(1.25).rotate(np.pi/(2)).shift(1.8*UP+1.47*RIGHT)
+ line1.rotate(np.pi/8)
+ self.play(ShowCreation(line1))
+ self.wait(1.3)
+ v3 = self.add_vector(VECTORS[2],color = BLUE, stroke_width = 3.5)
+ text1 = TextMobject(r"$\vec{v}$cos$\theta$",color=BLUE).scale(0.55).shift(1.25*RIGHT+0.26*UP).rotate(np.pi/9)
+ self.play(ShowCreation(text1))
+ self.wait(2)
+ text2 = TextMobject(r"\text{Projection on }",r"\text{$\vec{v}$}",r"\text{ onto }",r"\text{$\vec{u}$}",r"\text{ = }",r"\text{$ |\vec{v}|cos\theta$}").scale(0.6).shift(4*RIGHT+3*UP)
+ text2[1].set_color(RED)
+ text2[3].set_color(YELLOW)
+ text2[5].set_color(BLUE)
+ text2.add_background_rectangle()
+ self.play(ShowCreation(text2))
+ self.wait(4)
+
+
+
\ No newline at end of file diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Conjugate_Symmetry_and_Positivity_of_Inner_Product.mp4 b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Conjugate_Symmetry_and_Positivity_of_Inner_Product.mp4 Binary files differnew file mode 100644 index 0000000..6b44c55 --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Conjugate_Symmetry_and_Positivity_of_Inner_Product.mp4 diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/InnerProduct.gif b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/InnerProduct.gif Binary files differnew file mode 100644 index 0000000..55b6546 --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/InnerProduct.gif diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Inner_Product_Space_Example.mp4 b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Inner_Product_Space_Example.mp4 Binary files differnew file mode 100644 index 0000000..edecd88 --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Inner_Product_Space_Example.mp4 diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Instances_of_Topological_Spaces.gif b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Instances_of_Topological_Spaces.gif Binary files differnew file mode 100644 index 0000000..82d5c75 --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Instances_of_Topological_Spaces.gif diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Interpretation_of_norm_as_length.gif b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Interpretation_of_norm_as_length.gif Binary files differnew file mode 100644 index 0000000..9eda7c5 --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Interpretation_of_norm_as_length.gif diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Linerity_of_Inner_Product.mp4 b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Linerity_of_Inner_Product.mp4 Binary files differnew file mode 100644 index 0000000..a1e7b29 --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Linerity_of_Inner_Product.mp4 diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Projection.gif b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Projection.gif Binary files differnew file mode 100644 index 0000000..c32fd6b --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Projection.gif diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Projection_of_vectors_in-3D_plane.mp4 b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Projection_of_vectors_in-3D_plane.mp4 Binary files differnew file mode 100644 index 0000000..bdca5f9 --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Projection_of_vectors_in-3D_plane.mp4 diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Basis.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Basis.py new file mode 100644 index 0000000..6d2edc8 --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Basis.py @@ -0,0 +1,174 @@ +from manimlib.imports import *
+
+
+VECTORS = [[1, 2],
+ [-4, 2],
+ [-3, -3],
+ [3,-2],
+ [3,3],
+ [-2,1],
+ [-1,-3]]
+
+class Scene1(LinearTransformationScene):
+
+ CONFIG = {
+ "include_background_plane": True,
+ "include_foreground_plane": False,
+ "show_coordinates": False,
+ "show_basis_vectors": True,
+ "basis_vector_stroke_width": 3,
+
+ }
+ def construct(self):
+ self.setup()
+ ihat, jhat = self.get_basis_vectors()
+ labels = self.get_basis_vector_labels()
+ self.add(ihat, jhat)
+ self.add(*labels)
+
+ self.show_vector_as_basis_sum()
+ self.wait(2)
+
+ def show_vector_as_basis_sum(self):
+ text1 = TextMobject(r"Vector Space $\mathbb{R}^2$}").scale(0.8).shift(3*UP)
+ text1.add_background_rectangle()
+ self.play(ShowCreation(text1))
+ text2 = TextMobject(r"$\mathbb{R}^2$",color=BLUE_E).scale(0.8).shift(6.5*LEFT+3.5*UP)
+ text3 = TextMobject(r"\text{Basis Vectors:}",r"\text{$\hat{i}$}",r"\text{,}",r"\text{$\hat{j}$}").scale(0.7).shift(2*UP+2.5*RIGHT)
+ text3[1].set_color(GREEN_C)
+ text3[3].set_color(RED_C)
+
+ self.wait(2)
+ self.play(Transform(text1,text2))
+ self.wait(1)
+ self.play(ShowCreation(text3))
+ self.wait(1.7)
+ self.play(FadeOut(text3))
+
+ for i in range(len(VECTORS)):
+ v = self.add_vector(VECTORS[i], stroke_width = 3,color=YELLOW_D)
+
+ linei = Line(start = ORIGIN, end = VECTORS[i][0]*RIGHT)
+ linei.set_color(GREEN_C)
+ linej = Line(start = linei.get_end(),
+ end = linei.get_end() + VECTORS[i][1]*UP)
+ linej.set_color(RED_C)
+ self.play(ShowCreation(linei))
+ self.play(ShowCreation(linej))
+ vlabel = self.get_vector_label(v, str(VECTORS[i][0]) +
+ r"\imath" + "+" +
+ str(VECTORS[i][1]) +
+ r"\jmath", at_tip = True)
+ self.play(ShowCreation(vlabel))
+
+ self.play(FadeOut(linei),FadeOut(linej))
+ self.wait(1)
+ dot = Dot(v.get_end(), fill_color = v.get_stroke_color())
+ self.play(ShowCreation(dot),FadeOut(v),FadeOut(vlabel))
+ self.wait(0.3)
+
+class Scene2(LinearTransformationScene):
+ CONFIG = {
+ "num_vectors" : 16,
+ "start_color" : GREY,
+ "end_color" : YELLOW_D,
+ "include_background_plane": True,
+ "include_foreground_plane": False,
+ }
+
+ def get_vectors(self):
+ return [
+ Vector([x, y], stroke_width = 3.5)
+ for x in np.arange(-int(FRAME_X_RADIUS), int(FRAME_X_RADIUS)+0.5, 0.5)
+ for y in np.arange(-int(FRAME_Y_RADIUS), int(FRAME_Y_RADIUS)+0.5, 0.5)
+ ]
+
+ def lock_in_faded_grid(self, dimness=0.7, axes_dimness=0.5):
+ plane = self.add_plane()
+ axes = plane.get_axes()
+ plane.fade(dimness)
+ axes.set_color(WHITE)
+ axes.fade(axes_dimness)
+ self.add(axes)
+
+ def construct(self):
+ self.lock_in_faded_grid()
+
+ vectors = self.get_vectors()
+ colors = Color(self.start_color).range_to(
+ self.end_color, len(vectors)
+ )
+ for vect, color in zip(vectors, colors):
+ vect.set_color(color)
+
+ vector_group = VGroup(*vectors)
+ self.play(
+ ShowCreation(
+ vector_group,
+ run_time = 3
+ )
+ )
+
+ self.wait(1)
+
+ vectors.sort(key=lambda v: v.get_length())
+ def v_to_dot(vector):
+ return Dot(vector.get_end(), fill_color = vector.get_stroke_color())
+ self.wait()
+ rate_functions = [
+ squish_rate_func(smooth, float(x)/(len(vectors)+2), 1)
+ for x in range(len(vectors))
+ ]
+ self.play(*[
+ Transform(v, v_to_dot(v), rate_func = rf, run_time = 3)
+ for v, rf in zip(vectors, rate_functions)
+ ])
+ self.wait(2)
+ self.play_final_animation(vectors, rate_functions)
+ self.wait(2)
+
+ text1 = TextMobject(" Basis is the minimum information required to ").shift(3.1*UP).scale(0.8)
+ text2 = TextMobject("generate the whole space.").scale(0.8).shift(2.6*UP)
+
+ text1.add_background_rectangle()
+ text2.add_background_rectangle()
+
+
+
+ self.play(ShowCreation(text1),ShowCreation(text2))
+
+ self.play(ShowCreation(self.get_basis_vectors()))
+ self.wait(3)
+
+ def play_final_animation(self, vectors, rate_functions):
+
+ h_line = Line(
+ FRAME_X_RADIUS*RIGHT, FRAME_X_RADIUS*LEFT,
+ stroke_width = 0.5,
+ color = BLUE_E
+ )
+ v_line = Line(
+ FRAME_Y_RADIUS*UP, FRAME_Y_RADIUS*DOWN,
+ stroke_width = 0.5,
+ color = BLUE_E
+ )
+ line_pairs = [
+ VGroup(h_line.copy().shift(y), v_line.copy().shift(x))
+ for v in vectors
+ for x, y, z in [v.get_center()]
+ ]
+ plane = NumberPlane()
+
+ self.play(
+ ShowCreation(plane),
+ *[
+ Transform(v, p, rate_func = rf)
+ for v, p, rf in zip(vectors, line_pairs, rate_functions)
+ ]
+ )
+ self.remove(*vectors)
+
+
+
+
+
\ No newline at end of file diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Intersection_of_Subspaces.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Intersection_of_Subspaces.py new file mode 100644 index 0000000..ec82daa --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Intersection_of_Subspaces.py @@ -0,0 +1,52 @@ +from manimlib.imports import *
+class ThreeDSpace(ThreeDScene):
+
+
+ def construct(self):
+ axes = ThreeDAxes()
+ self.set_camera_orientation(phi = 80*DEGREES,theta =110*DEGREES)
+ self.begin_ambient_camera_rotation(rate=0.09)
+
+
+
+
+ cube = Cube(stroke_width=5,color=WHITE).shift([1.5,1.5,1.5]).scale(1.5)
+ cube.set_fill(TEAL)
+
+ cube.set_opacity(0.4)
+
+
+ plane1 = Polygon([0,0,3],[3,0,3],[3,3,0],[0,3,0])
+ plane1.set_opacity(0.65)
+ plane1.set_fill(PURPLE)
+ plane1.set_color(PURPLE)
+
+
+ plane2 = Polygon([0,3,3],[3,3,3],[3,0,0],[0,0,0])
+ plane2.set_opacity(0.7)
+ plane2.set_fill(RED)
+ plane2.set_color(RED)
+ line = Line(color=YELLOW,set_opacity=100).shift([1.5,1.5,1.5]).scale(1.5)
+
+ vgroup = VGroup(plane1,plane2,line,cube)
+ vgroup.shift([-1,-1,-1])
+
+ dot = Dot(color=BLACK).shift([0.5,0.5,0.5]).scale(1)
+ text = TextMobject(r"\text{The}",r"\text{line}",r"\text{representing the intersection of the two planes is a Subspace.}",opacity = 0.6).scale(0.7).shift(3*UP)
+ text[1].set_color(YELLOW)
+ self.add_fixed_in_frame_mobjects(text)
+ self.play(ShowCreation(text))
+
+
+ self.play(ShowCreation(cube))
+ self.play(ShowCreation(plane1))
+ self.play(ShowCreation(plane2))
+
+ self.play(ShowCreation(line),ShowCreation(dot))
+
+
+ self.wait(15)
+
+
+
+
\ No newline at end of file diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Subspace_Example.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Subspace_Example.py deleted file mode 100644 index ada173e..0000000 --- a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Subspace_Example.py +++ /dev/null @@ -1,82 +0,0 @@ -from manimlib.imports import *
-class Subspace_Example(Scene):
- def construct(self):
- sq = Square(side = 2, color=BLACK).shift(2*LEFT)
- sq.set_fill(color=RED,opacity=350)
- line1=Line(color=BLACK).shift(2*LEFT)
- line1.rotate(np.pi/2)
- line2=Line(color=BLACK).shift(2.5*LEFT+0.5*UP)
- line2.scale(0.5)
- line3=Line(color=BLACK).shift(+1.5*LEFT)
- line3.scale(0.5)
- a1=TextMobject(r"$a_1$",color=BLACK).scale(0.5).shift(3.4*LEFT+0.7*UP)
- a2=TextMobject(r"$a_2$",color=BLACK).scale(0.5).shift(3.4*LEFT+0.3*DOWN)
- a3=TextMobject(r"$a_3$",color=BLACK).scale(0.5).shift(0.7*LEFT+0.5*DOWN)
- a4=TextMobject(r"$a_4$",color=BLACK).scale(0.5).shift(0.7*LEFT+0.5*UP)
- big_rect=Rectangle().scale(3).shift(0.5*DOWN)
- big_rect.set_fill(color=GREY,opacity=350)
- vec_space=TextMobject("$Vector Space$").scale(0.77).shift(4.5*RIGHT+3.5*UP)
- sub=TextMobject(r"$Subspace$",color=BLACK).scale(0.77).shift(3.8*RIGHT+2*UP)
- self.play(ShowCreation(vec_space))
- self.play(ShowCreation(big_rect),ShowCreation(sub))
- self.play(ShowCreation(sq),ShowCreation(line1),ShowCreation(line2),ShowCreation(line3),ShowCreation(a1),ShowCreation(a2),ShowCreation(a3),ShowCreation(a4))
- rec = Rectangle(color=BLACK).scale(0.5).shift(1*RIGHT)
- rec.rotate(np.pi/2)
- rec.set_fill(color=BLUE,opacity=350)
- line4=Line(color=BLACK).shift(1*RIGHT).rotate(np.pi/2)
- line5=Line(color=BLACK).scale(0.25).shift(0.75*RIGHT)
- line6=Line(color=BLACK).scale(0.25).shift(0.5*DOWN+1.25*RIGHT)
- b1=TextMobject(r"$b_1$",color=BLACK).scale(0.5).shift(0.3*RIGHT+0.5*UP)
- b2=TextMobject(r"$b_2$",color=BLACK).scale(0.5).shift(0.3*RIGHT+0.5*DOWN)
- b3=TextMobject(r"$b_3$",color=BLACK).scale(0.5).shift(1.67*RIGHT+0.8*DOWN)
- b4=TextMobject(r"$b_4$",color=BLACK).scale(0.5).shift(1.67*RIGHT+0.5*UP)
- self.play(ShowCreation(rec),ShowCreation(line4),ShowCreation(line5),ShowCreation(line6),ShowCreation(b1),ShowCreation(b2),ShowCreation(b3),ShowCreation(b4))
- self.wait(1)
- text1=TextMobject(r"$a_1 + a_2 = a_3 + a_4$",color=BLACK).scale(0.5).shift(2*LEFT+1.5*DOWN)
- text2=TextMobject(r"$b_1 + b_2 = b_3 + b_4$",color=BLACK).scale(0.5).shift(1.5*RIGHT+1.5*DOWN)
- self.play(ShowCreation(text1),ShowCreation(text2))
- self.wait(3)
- self.play(FadeOut(text1),FadeOut(text2))
- rec.shift(3*LEFT+2.01*DOWN)
- line4.shift(3*LEFT+2*DOWN)
- line5.shift(3*LEFT+2*DOWN)
- line6.shift(3*LEFT+2*DOWN)
- b1.shift(3.1*LEFT+2.1*DOWN)
- b2.shift(3.1*LEFT+2.1*DOWN)
- b3.shift(2.9*LEFT+2*DOWN)
- b4.shift(2.9*LEFT+2.3*DOWN)
- self.play(ShowCreation(rec),ShowCreation(line4),ShowCreation(line5),ShowCreation(line6),ShowCreation(b1),ShowCreation(b2),ShowCreation(b3),ShowCreation(b4))
- self.wait(2)
-
- text3=TextMobject(r"$(a_1 + a_2) + (b_1 + b_2) = (a_3 + a_4) + (b_3 + b_4)$",color=BLACK).scale(0.5).shift(2.5*RIGHT+0.5*DOWN)
- text3=TextMobject(r"$(a_1 + a_2) + (b_1 + b_2) = (a_3 + a_4) + (b_3 + b_4)$",color=BLACK).scale(0.5).shift(2.5*RIGHT+0.5*DOWN)
- text4=TextMobject("Vector Addition",color=BLACK).scale(0.8).shift(2.5*RIGHT+0.5*UP)
- self.play(ShowCreation(text3),ShowCreation(text4))
- self.wait(3)
- rec.set_fill(color=GREY,opacity=350)
- self.play(FadeOut(text3),FadeOut(text4),FadeOut(line4),FadeOut(line5),FadeOut(line6),FadeOut(rec),FadeOut(b4),FadeOut(b3),FadeOut(b2),FadeOut(b1))
- sq1=Square(color=BLACK).scale(0.5).shift(1.5*LEFT+1.5*UP)
- sq1.set_fill(color=RED,opacity=350)
- sq2=Square(color=BLACK).scale(0.5).shift(1.5*LEFT+1.5*DOWN)
- sq2.set_fill(color=RED,opacity=350)
- rec1=Rectangle(height=0.5,width=1,color=BLACK).shift(2.5*LEFT+1.2*UP)
- rec1.set_fill(color=RED,opacity=350)
- rec2=Rectangle(height=1.5,width=1,color=BLACK)
- rec2.set_fill(color=RED,opacity=350).shift(2.5*LEFT+1.5*DOWN)
- self.play(ShowCreation(sq1),ShowCreation(sq2),ShowCreation(rec1),ShowCreation(rec2))
- a=TextMobject(r"$a_1$",color=BLACK).scale(0.5).shift(3.4*LEFT+1.2*UP)
- b=TextMobject(r"$a_2$",color=BLACK).scale(0.5).shift(3.4*LEFT+1.4*DOWN)
- c=TextMobject(r"$a_3$",color=BLACK).scale(0.5).shift(0.7*LEFT+1.4*DOWN)
- d=TextMobject(r"$a_4$",color=BLACK).scale(0.5).shift(0.7*LEFT+1.4*UP)
- self.play(ShowCreation(a),ShowCreation(b),ShowCreation(c),ShowCreation(d))
- self.wait(2.3)
- text4=TextMobject("Scalar Multiplication",color=BLACK).scale(0.8).shift(2.5*RIGHT+0.5*UP)
- text5=TextMobject(r"$\implies 2(a_1 + a_2) = 2(a_3 + a_4)$",color=BLACK).scale(0.5).shift(2*RIGHT+0.5*DOWN)
- text6=TextMobject(r"$(a_1 + a_1) + (a_2 + a_2) = (a_3 + a_3) + (a_4 +a_4)$",color=BLACK).scale(0.5).shift(2.5*RIGHT)
- self.play(ShowCreation(text4),ShowCreation(text5),ShowCreation(text6))
- self.wait(3)
-
-
-
-
-
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Subspace_Non_Example.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Subspace_Non_Example.py new file mode 100644 index 0000000..115a722 --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Subspace_Non_Example.py @@ -0,0 +1,25 @@ +from manimlib.imports import *
+class ThreeDSpace(ThreeDScene):
+
+
+ def construct(self):
+ axes = ThreeDAxes()
+ self.add(axes)
+ self.set_camera_orientation(phi = 80*DEGREES,theta =110*DEGREES)
+ self.begin_ambient_camera_rotation(rate=0.09)
+ plane1 = Polygon([-1.5,1.5,-1.5],[1.5,1.5,-1.5],[1.5,-1.5,1.5],[-1.5,-1.5,1.5])
+ plane1.set_opacity(0.65)
+ plane1.set_fill(GREEN)
+ plane1.set_color(GREEN)
+
+
+ plane2 = Polygon([-1.5,1.5,1.5],[1.5,1.5,1.5],[1.5,-1.5,-1.5],[-1.5,-1.5,-1.5])
+ plane2.set_opacity(0.7)
+ plane2.set_fill(MAROON_A)
+ plane2.set_color(MAROON_A)
+ line = Line(color=YELLOW,set_opacity=100,start=[1.5,1.2,1.2],end=[-1.5,1.2,1.2])
+
+
+ self.play(ShowCreation(plane1),ShowCreation(plane2),ShowCreation(line))
+ self.wait(10)
+
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Basis_of_a_Subspace.mp4 b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Basis_of_a_Subspace.mp4 Binary files differnew file mode 100644 index 0000000..d384f80 --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Basis_of_a_Subspace.mp4 diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Intersection_of_Subspaces.mp4 b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Intersection_of_Subspaces.mp4 Binary files differnew file mode 100644 index 0000000..d43bfbe --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Intersection_of_Subspaces.mp4 diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Example.gif b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Example.gif Binary files differdeleted file mode 100644 index 32b02be..0000000 --- a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Example.gif +++ /dev/null diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Non_Example.mp4 b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Non_Example.mp4 Binary files differnew file mode 100644 index 0000000..390f4cf --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Non_Example.mp4 diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/Vector_Addition_and_Scalar_Multiplication.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/Vector_Addition_and_Scalar_Multiplication.py new file mode 100644 index 0000000..12c9bce --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/Vector_Addition_and_Scalar_Multiplication.py @@ -0,0 +1,177 @@ +from manimlib.imports import *
+VECTORS = [[1, 2],
+ [1, 1],
+ [2, 2],
+ [3, 4]]
+class Scene1(LinearTransformationScene):
+ CONFIG = {
+ "include_background_plane": True,
+ "include_foreground_plane": False,
+ "show_coordinates": True,
+ "show_basis_vectors": False,
+ "basis_vector_stroke_width": 3,
+ }
+ def construct(self):
+ self.write_stuff()
+ v1 = self.add_vector(VECTORS[0],color = YELLOW, stroke_width = 3.5)
+ line1 = Line(start = ORIGIN, end = VECTORS[0][0]*RIGHT)
+ line1.set_color(RED_B)
+ line2 = Line(start = line1.get_end(), end = line1.get_end() + VECTORS[0][1]*UP)
+ line2.set_color(GREEN_D)
+ self.play(ShowCreation(line1))
+ self.play(ShowCreation(line2))
+ self.wait(0.5)
+ text1 = TextMobject("(1, 2)",color=YELLOW).scale(0.6).shift(2*UP + 1.5*RIGHT)
+ self.play(ShowCreation(text1))
+ text2 = TextMobject(r"$\vec{a}$",color = YELLOW).scale(0.8).shift(2*UP + 1.2*RIGHT)
+ text3 = TextMobject(r"\text{$\vec{a}$}",r"\text{=}",r"\text{(1, 2)}").scale(0.7).shift(5.1*LEFT + 2.5*UP)
+ text3[0].set_color(YELLOW)
+ text3[2].set_color(YELLOW)
+ self.wait(1)
+ self.play(Transform(text1,text2),FadeOut(line1),FadeOut(line2))
+ self.wait(0.5)
+ self.play(ShowCreation(text3))
+ self.wait(1)
+
+
+ v2 = self.add_vector(VECTORS[1],color = BLUE, stroke_width = 3.5)
+ line3 = Line(start = ORIGIN, end = VECTORS[1][0]*RIGHT)
+ line3.set_color(RED_B)
+ line4 = Line(start = line3.get_end(), end = line3.get_end() + VECTORS[1][1]*UP)
+ line4.set_color(GREEN_D)
+ self.play(ShowCreation(line3))
+ self.play(ShowCreation(line4))
+ self.wait(0.5)
+ text4 = TextMobject("(2, 2)",color=BLUE).scale(0.6).shift(1*UP + 1.5*RIGHT)
+ self.play(ShowCreation(text4))
+ text5 = TextMobject(r"$\vec{b}$",color = BLUE).scale(0.8).shift(1*UP + 1.2*RIGHT)
+ text6 = TextMobject(r"\text{$\vec{b}$}",r"\text{=}",r"\text{(1, 1)}").scale(0.7).shift(5.1*LEFT + 1.8*UP)
+ text6[0].set_color(BLUE)
+ text6[2].set_color(BLUE)
+ self.wait(1)
+ self.play(Transform(text4,text5),FadeOut(line3),FadeOut(line4))
+ self.wait(0.5)
+ self.play(ShowCreation(text6))
+ self.wait(2)
+
+
+
+ text7 = TextMobject(r"\text{Scaling}",r"\text{ $\vec{b}$ }",r"\text{by 2 units}",color = GOLD).scale(0.7).shift(2.8*UP+4*RIGHT)
+ text7[1].set_color(BLUE)
+ self.play(ShowCreation(text7))
+ self.play(FadeOut(text4))
+ v3 = self.add_vector(VECTORS[2],color = BLUE, stroke_width = 3.5)
+ line7 = Line(start = ORIGIN, end = VECTORS[2][0]*RIGHT)
+ line7.set_color(RED_B)
+ line8 = Line(start = line7.get_end(), end = line7.get_end() + VECTORS[2][1]*UP)
+ line8.set_color(GREEN_D)
+ self.play(FadeOut(v2))
+ self.play(ShowCreation(line7))
+ self.play(ShowCreation(line8))
+
+
+ self.wait(0.5)
+
+ text8 = TextMobject("(2, 2)",color=BLUE).scale(0.6).shift(2.5*RIGHT + 2*UP)
+ text9 = TextMobject(r"$2\vec{b}$",color = BLUE).scale(0.8).shift(2*UP + 2.3*RIGHT)
+ self.play(ShowCreation(text8))
+ self.wait(1)
+ self.play(Transform(text8,text9),FadeOut(line7),FadeOut(line8))
+ self.wait(1)
+ text10 = TextMobject(r"\text{$2\vec{b}$}",r"\text{=}",r"\text{(2, 2)}").scale(0.7).shift(5.1*LEFT + 1.8*UP)
+ text10[0].set_color(BLUE)
+ text10[2].set_color(BLUE)
+ self.play(Transform(text6,text10))
+ self.wait(1)
+ self.play(FadeOut(text7))
+ self.wait(1.5)
+
+
+
+ text11 = TextMobject(r"Addition of vectors",color = GOLD).scale(0.7).shift(2.8*UP+5*RIGHT)
+ self.play(ShowCreation(text11))
+ v1.move_to(3*UP+2.5*RIGHT)
+ self.play(ShowCreation(v1),FadeOut(text8),FadeOut(text1))
+ v4 = self.add_vector(VECTORS[3],color = ORANGE, stroke_width = 3.5)
+ line7 = Line(start = ORIGIN, end = VECTORS[3][0]*RIGHT)
+ line7.set_color(RED_B)
+ line8 = Line(start = line7.get_end(), end = line7.get_end() + VECTORS[3][1]*UP)
+ line8.set_color(GREEN_D)
+ self.play(ShowCreation(line7))
+ self.play(ShowCreation(line8))
+ text12 = TextMobject("(3, 4)",color=ORANGE).scale(0.6).shift(3.5*RIGHT + 3.8*UP)
+ text13 = TextMobject(r"$\vec{c}$",color = ORANGE).scale(0.8).shift(3.7*UP + 3.3*RIGHT)
+ self.play(ShowCreation(text12))
+ self.wait(1)
+ self.play(Transform(text12,text13),FadeOut(line7),FadeOut(line8))
+ self.wait(1)
+ add = TextMobject("+").scale(0.8).shift(6.2*LEFT + 1.8*UP)
+ line_1= Line().shift(1.5*UP+5.1*LEFT).scale(1.5)
+ line_2= Line().shift(0.8*UP+5.1*LEFT).scale(1.5)
+
+ text14=TextMobject(r"\text{$\vec{c}$}",r"\text{=}",r"\text{$\vec{a}$}",r"\text{+}",r"\text{$2\vec{b}$}",r"\text{=}",r"\text{(3, 4)}").scale(0.7).shift(1.2*UP+5.1*LEFT)
+ text14[0].set_color(ORANGE)
+ text14[2].set_color(YELLOW)
+ text14[4].set_color(BLUE)
+ text14[6].set_color(ORANGE)
+
+
+ self.play(ShowCreation(add),ShowCreation(line_1))
+ self.play(ShowCreation(text14),ShowCreation(line_2))
+ self.wait(3)
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ def write_stuff(self):
+ self.text = []
+ text = self.text
+
+ text.append(TexMobject(r"\text{Consider the Vector Space }",
+ r"{\mathbb{R}^2}"))
+ self.add_title(text[0], 0.7, animate = True)
+ text.append(TexMobject(r"{\mathbb{R}^2}",
+ tex_to_color_map = {r"{\mathbb{R}^2}": BLUE_E}))
+ text[1].shift(6.5*LEFT+3.5*UP)
+ self.wait(0.5)
+ self.play(Transform(text[0], text[1]))
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/Vector_Addition_and_Scaling.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/Vector_Addition_and_Scaling.py deleted file mode 100644 index 70af123..0000000 --- a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/Vector_Addition_and_Scaling.py +++ /dev/null @@ -1,137 +0,0 @@ -from manimlib.imports import *
-import numpy as np
-
-class vectorspace(GraphScene):
- CONFIG={
- "x_min": -7,
- "x_max": 7,
- "y_min": -7,
- "y_max": 7,
- "graph_origin": ORIGIN,
- "x_axis_label":"$X$",
- "y_axis_label":"$Y$",
- "x_labeled_nums": list(np.arange(-7, 8,1)),
- "y_labeled_nums": list(np.arange(-7, 8,1)),
- "x_axis_width": 8,
- "y_axis_height": 7,
- "x_tick_frequency":1,
- "axes_color": GREY,
- "area_opacity": 3,
- "num_rects": 10,
- }
- def construct(self):
- XD = self.x_axis_width/(self.x_max- self.x_min)
- YD = self.y_axis_height/(self.y_max- self.y_min)
- a1=1*XD*RIGHT+2*YD*UP
- a2=1*XD*RIGHT+1*YD*UP
- vec1=Vector(direction=a1).set_color(RED_E)
- vec1.shift(self.graph_origin)
- vec2=Vector(direction=a2).set_color(YELLOW_E)
- vec2.shift(self.graph_origin)
- vec1_text=TextMobject(r"$\vec{a}$")
- vec2_text=TextMobject(r"$\vec{b}$")
- vec1_text=(vec1_text.shift(self.graph_origin+a1+0.2)).scale(.7)
- vec2_text=(vec2_text.shift(self.graph_origin+a2+0.2)).scale(.7)
- self.setup_axes(animate=True)
- self.wait(2)
- self.play(ShowCreation(vec1))
- self.play(ShowCreation(vec1_text))
- self.wait(.7)
- self.play(ShowCreation(vec2))
- self.play(ShowCreation(vec2_text))
- self.wait(.7)
- a=TextMobject(r"$\vec{a} = (1,2)$",color=RED_B).scale(.6)
- a.shift(3*LEFT+2.7*UP)
- b=TextMobject(r"$\vec{b} = (1,1)$",color=YELLOW_E).scale(.6)
- b.shift(3*LEFT+2*UP)
- self.play(ShowCreation(a))
- self.play(ShowCreation(b))
- self.wait(.5)
- c=TextMobject(r"$2\cdot\vec{a} = 2\cdot(1,2) = (2,4)$",color=RED_B)
- c.shift(3*LEFT+2.7*UP)
- c.scale(.6)
- self.play(Transform(a,c))
- scaling1=TextMobject(r"Scaling vector $\vec{a}$ by 2 units",color=GOLD).scale(.5)
- scaling1.shift(3.4*RIGHT+2.4*UP)
- self.play(ShowCreation(scaling1))
- a1=2*XD*RIGHT+4*YD*UP
- self.play(FadeOut(vec1_text))
- vec1_scaled=Vector(direction=a1).set_color(RED_E)
- vec1_scaled.shift(self.graph_origin)
- self.play(ShowCreation(vec1_scaled))
- self.play(FadeOut(vec1))
- vec1_scaled_text=TextMobject(r"$2\vec{a}$").scale(.7)
- vec1_scaled_text.shift(self.graph_origin+a1+0.2)
- self.play(ShowCreation(vec1_scaled_text))
- self.play(FadeOut(scaling1))
- d=TextMobject(r"$3\cdot\vec{b} = 3\cdot(1,1) = (3,3)$",color=YELLOW_E).scale(.6)
- d.shift(3*LEFT+2*UP)
- self.play(Transform(b,d))
- scaling2=TextMobject(r"Scaling vector $\vec{b}$ by 3 units",color=GOLD).scale(.5)
- scaling2.shift(3.4*RIGHT+2.4*UP)
- self.play(ShowCreation(scaling2))
- a2=3*XD*RIGHT+3*YD*UP
- self.play(FadeOut(vec2_text))
- vec2_2=Vector
- vec2_scaled=Vector(direction=a2).set_color(YELLOW_E)
- vec2_scaled.shift(self.graph_origin)
- self.play(ShowCreation(vec2_scaled))
- self.play(FadeOut(vec2))
- vec2_scaled_text=TextMobject(r"$3\vec{b}$").scale(.7)
- vec2_scaled_text.shift(self.graph_origin+a2+0.2)
- self.play(ShowCreation(vec2_scaled_text))
- self.wait(.7)
- self.play(FadeOut(scaling2))
- add = TextMobject("+").scale(.7)
- add.shift(4.8*LEFT+2*UP)
- self.play(ShowCreation(add))
- self.wait(.5)
- line = Line()
- line.shift(3*LEFT+1.6*UP)
- line.scale(1.8)
- self.play(ShowCreation(line))
- self.wait(1)
- e = TextMobject(r"$\vec{c} = 2\cdot\vec{a} + 3\cdot\vec{b} = (5,7)$",color=GREEN_D).scale(.6)
- e.shift(3*LEFT+1.3*UP)
- self.play(ShowCreation(e))
- self.wait(.5)
- add1=TextMobject("Addition of the scaled vectors",color=GOLD).scale(.5)
- add1.shift(4.1*RIGHT+2.4*UP)
- self.play(ShowCreation(add1))
- self.wait(.5)
- self.play(FadeOut(vec1_scaled_text))
- self.play(FadeOut(vec2_scaled_text))
- self.play(FadeOut(vec1_scaled))
- vec1_scaled2=Vector(direction=a1).set_color(RED_E)
- vec1_scaled2.shift(self.graph_origin+3*RIGHT*XD+3*UP*YD)
- self.play(ShowCreation(vec1_scaled2))
- a3=5*XD*RIGHT+7*YD*UP
- vec3=Vector(direction=a3).set_color(GREEN_C)
- vec3.shift(self.graph_origin)
- vec3_text=TextMobject(r"$\vec{c}$").scale(.7)
- vec3_text.shift(self.graph_origin+a3+0.2)
- self.play(ShowCreation(vec3))
- self.wait(.5)
- self.play(ShowCreation(vec3_text))
- self.wait(1)
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/gifs/Vector_Addition_and_Scalar_Multiplication.gif b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/gifs/Vector_Addition_and_Scalar_Multiplication.gif Binary files differdeleted file mode 100644 index ed65f8a..0000000 --- a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/gifs/Vector_Addition_and_Scalar_Multiplication.gif +++ /dev/null diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/gifs/Vector_Addition_and_Scalar_Multiplication.mp4 b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/gifs/Vector_Addition_and_Scalar_Multiplication.mp4 Binary files differnew file mode 100644 index 0000000..8acbb81 --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/gifs/Vector_Addition_and_Scalar_Multiplication.mp4 |
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