diff options
Diffstat (limited to 'FSF-2020')
%3dk.gif?id=0aba6d36ed8aee098edbb01bff0e1cc0577770f9){kind=link}
/file6_Horizontal_Shear_gif.gif?id=0aba6d36ed8aee098edbb01bff0e1cc0577770f9){kind=link}
/file7_Vertical_Shear_gif.gif?id=0aba6d36ed8aee098edbb01bff0e1cc0577770f9){kind=link}
153 files changed, 5507 insertions, 610 deletions
diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/README.md b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/README.md new file mode 100644 index 0000000..05ff51d --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/README.md @@ -0,0 +1,20 @@ +<h1><div align=”center”><b>SubTopic: Lagrange Multipliers</b></h1></div> +<br/></br> + +<tab>file1_Extrema_over_g(x,y)=k + +%3Dk.gif?raw=true) +<br/></br> +<br/></br> + +<tab>file2_Geometric_Proof + + +<br/></br> +<br/></br> + +<tab>file3_Constraints_g_and_h + + +<br/></br> +<br/></br> diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.gif b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.gif Binary files differindex 9d64d50..d423943 100644 --- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.gif +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.gif diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.py b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.py index da17aac..a01efb0 100644 --- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.py +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.py @@ -5,33 +5,26 @@ import math as m class ConstrainedExtrema(ThreeDScene): def construct(self): axes = ThreeDAxes().fade(0.4) - label_x = TextMobject("$x$").shift([5.5,-0.5,0]).fade(0.4) #---- x axis - label_y = TextMobject("$y$").shift([-0.5,5.5,0]).rotate(-4.5).fade(0.4) #---- y axis + label_x = TextMobject("$x$").shift([5.5,-0.5,0]) #---- x axis + label_y = TextMobject("$y$").shift([-0.5,5.5,0]).rotate(-4.5) #---- y axis surface = ParametricSurface( lambda u, v: np.array([ u, v, u**2+v**2+u**3-v**3 - ]),u_min=-0.5,u_max=0.5, v_min=-0.5,v_max=0.5).scale(5).shift([0,1,2.5]).set_color(TEAL).fade(0.4) + ]),u_min=-0.5,u_max=0.5, v_min=-0.5,v_max=0.5).scale(5).shift([0,1,2.5]).set_color(TEAL).fade(0.2) - c = Circle().set_color('#FF00FF').shift([-0.4,0,1.5]).rotate(1.9,UP).scale(0.7) + c = Circle(color='#FF00FF',fill_opacity=0.3).shift([-0.4,0,1.5]).rotate(1.9,UP).scale(0.7) minima = Dot(color = '#4169E1').shift([-0.5,0.5,1]).rotate(1.571,UP) - maxima = Dot(color = '#4169E1').shift([0.1,0,2.2]).rotate(1.571,UP) + maxima = Dot(color = '#4169E1').shift([0.1,0,2.2]).rotate(1.571,UP) - l1 = DashedLine([-0.5,0.5,0.9],[-0.5,0.5,0],color = '#F08080') - l2 = DashedLine([0.1,0,2.1],[0.1,0,0],color = '#F08080') - - c2 = Circle(fill_opacity= 0.5).shift([-0.3,0.2,0]).scale(0.4) - - minima_refl = Dot(color = '#4682B4').shift([-0.5,0.5,0]).rotate(1.571,UP) - maxima_refl = Dot(color = '#4682B4').shift([0.1,0,0]).rotate(1.571,UP) - - max_text = TextMobject("maximum over $g(x,y)=k$",color = '#FFA074').shift([-1.7,0,0]).scale(0.5).shift(2.2*UP) - min_text = TextMobject("minimum over $g(x,y)=k$",color = '#FFA074').shift([2.5,0.5,1]).scale(0.5).shift(0.5*UP) - label_f = TextMobject("$z=f(x,y)$",color = '#8A2BE2').scale(0.5).shift(3*UP+3*RIGHT) - label_g = TextMobject("$g(x,y)=k$",color = '#8A2BE2').scale(0.5).shift(2*RIGHT) + max_text = TextMobject("maximum over $g(x,y)=k$",color = '#FFA074').scale(0.6).shift(2.3*UP+2*LEFT) + min_text = TextMobject("minimum over $g(x,y)=k$",color = '#FFA074').shift([2.5,0.5,1]).scale(0.6).shift(0.5*UP) + label_f = TextMobject("$z=f(x,y)$",color=TEAL).scale(0.8).shift(3*UP+3*RIGHT) + label_g = TextMobject("g(x,y)=k",color = PURPLE).scale(0.5).shift(1.5*UP+0.8*LEFT) + self.add(axes) self.add(label_x) @@ -42,16 +35,11 @@ class ConstrainedExtrema(ThreeDScene): self.wait(2) self.play(Write(c)) self.wait(1) + self.add_fixed_in_frame_mobjects(label_g) + self.wait(1) self.play(Write(maxima)) self.add_fixed_in_frame_mobjects(max_text) self.wait(1) self.play(Write(minima)) self.add_fixed_in_frame_mobjects(min_text) - self.wait(1) - self.play(ShowCreation(l1),ShowCreation(l2)) - self.play(Write(c2)) - self.add_fixed_in_frame_mobjects(label_g) - self.wait(1) - self.play(Write(maxima_refl)) - self.play(Write(minima_refl)) - self.wait(1) + self.wait(1) diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Geometric_Proof.gif b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Geometric_Proof.gif Binary files differnew file mode 100644 index 0000000..e028a81 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Geometric_Proof.gif diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Geometric_Proof.py b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Geometric_Proof.py index 2c2a9de..2c1d668 100644 --- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Geometric_Proof.py +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Geometric_Proof.py @@ -1,7 +1,7 @@ from manimlib.imports import* #---- visualization of geometric proof of Lagrange multiplier -class GeometricProof(ThreeDScene): +class firstScene(ThreeDScene): def construct(self): axes = ThreeDAxes().scale(0.7).rotate(math.radians(180)) label_x = TextMobject("$x$").shift(4*RIGHT).fade(0.4) #---- x axis @@ -12,19 +12,18 @@ class GeometricProof(ThreeDScene): 1*np.sin(u)*np.cos(v), 1*np.sin(u)*np.sin(v), -1*np.sin(u)*np.sin(u)+2 - ]),u_min=0,u_max=PI/2,v_min=0,v_max=2*PI,checkerboard_colors=[GREEN_C, GREEN_E]).scale(1).shift([-1.5,-1.5,0]) + ]),u_min=0,u_max=PI/2,v_min=0,v_max=2*PI).set_color(GREEN).scale(1).shift([-1.5,-1.5,0]) d = Dot([-2,-2.55,0],color = '#800000') - a_df = Arrow(color = '#00FFFF').rotate(-2).shift(3.2*DOWN+2.3*LEFT) #---- f parallel to g at maxima - a_dg = Arrow(color = '#FF00FF').scale(0.8).shift(3.2*DOWN+2.3*LEFT).rotate(-2) #---- g parallel to f at maxima + a_df = Arrow(color = '#00FFFF').rotate(-2).shift(3.2*DOWN+2.3*LEFT) #---- f parallel to g + a_dg = Arrow(color = '#FF00FF').scale(0.8).shift(3.2*DOWN+2.3*LEFT).rotate(-2) #---- f parallel to g - b_dg = Arrow(color = '#00FFFF').rotate(1.1).shift(0.82*LEFT+0.15*UP) #---- g parallel to f at minima - b_df = Arrow(color = '#FF00FF').scale(0.6).rotate(-2).shift(1.43*LEFT+1.1*DOWN) #---- f parallel to g at minima + b_dg = Arrow(color = '#00FFFF').rotate(1.1).shift(0.82*LEFT+0.15*UP) #---- f parallel to g + b_df = Arrow(color = '#FF00FF').scale(0.6).rotate(-2).shift(1.43*LEFT+1.1*DOWN) #---- f parallel to g qd = Dot(color = '#800000').shift(1.2*LEFT+0.6*DOWN) - #---- level curves l1 = Line([-1,-3.1,0],[-4,-3.1,0],color = PINK).rotate(-0.3).fade(0.6) l2 = Line([-0.9,-2.9,0],[-4,-2.9,0],color = PINK).rotate(-0.3).fade(0.6) l3= Line([-0.8,-2.7,0],[-4,-2.7,0],color = PINK).rotate(-0.3).fade(0.6) @@ -48,7 +47,6 @@ class GeometricProof(ThreeDScene): p_text= TextMobject("$P$").shift([1.8,2.6,0]).scale(0.5) - #---- labelling of level curves l1_text = TextMobject("$w=$ 17").rotate(math.radians(180)).scale(0.4).shift(2.7*DOWN+4.36*LEFT) l2_text = TextMobject("$w=$ 16").rotate(math.radians(180)).scale(0.4).shift(2.46*DOWN+4.36*LEFT) l3_text = TextMobject("$w=$ 15").rotate(math.radians(180)).scale(0.4).shift(2.2*DOWN+4.36*LEFT) @@ -70,8 +68,9 @@ class GeometricProof(ThreeDScene): self.set_camera_orientation(phi=0 * DEGREES, theta = 90*DEGREES) self.add(axes) self.add(label_x) - self.add(label_y) - self.play(Write(surface)) + self.add(label_y) + self.wait(1) + self.add(surface) self.wait(1) self.play(ShowCreation(level_Curve)) self.wait(1) diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file3_Constraints_g_and_h.gif b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file3_Constraints_g_and_h.gif Binary files differnew file mode 100644 index 0000000..0da30ad --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file3_Constraints_g_and_h.gif diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file3_Constraints_g_and_h.py b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file3_Constraints_g_and_h.py new file mode 100644 index 0000000..742d6b5 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file3_Constraints_g_and_h.py @@ -0,0 +1,41 @@ +from manimlib.imports import* +import math as m + +class firstScene(ThreeDScene): + def construct(self): + axes = ThreeDAxes() + label_x = TextMobject("$x$").shift([5.5,-0.5,0]).fade(0.4) #---- x axis + label_y = TextMobject("$y$").shift([-0.5,5.5,0]).rotate(-4.5).fade(0.4) #---- y axis + + #---- constraint g(x,y) + cylinder = ParametricSurface( + lambda u, v: np.array([ + np.cos(TAU * u), + np.sin(TAU * u), + 2 * (v) + ]),checkerboard_colors=[YELLOW_C,YELLOW_D,YELLOW_E]).rotate(m.radians(-40),RIGHT).shift([0.5,0.5,0]).scale(0.8) + + #---- constraint h(x,y) + plane = ParametricSurface( + lambda u, v: np.array([ + u, + v, + u+v + ]),checkerboard_colors=[TEAL_C,TEAL_D,TEAL_E]).shift([0,0,0]).rotate(m.radians(-40),RIGHT).scale(2).fade(0.3) + + figure = VGroup(cylinder,plane).rotate(m.radians(-45),DOWN).scale(1.5) + + self.set_camera_orientation(phi=65*DEGREES,theta=45*DEGREES) + self.add(axes) + self.add(label_x) + self.add(label_y) + self.wait(1) + self.play(Write(cylinder)) + self.play(Write(plane)) + self.wait(1) + self.begin_ambient_camera_rotation(rate=0.4) + self.wait(1) + self.wait(1) + self.play(FadeOut(label_x),FadeOut(label_y)) + self.wait(1) + self.wait(1) diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file3_Optimizing_function_w.r.t_one_constraint.gif b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file3_Optimizing_function_w.r.t_one_constraint.gif Binary files differdeleted file mode 100644 index 9602283..0000000 --- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file3_Optimizing_function_w.r.t_one_constraint.gif +++ /dev/null diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file3_Optimizing_function_w.r.t_one_constraint.py b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file3_Optimizing_function_w.r.t_one_constraint.py deleted file mode 100644 index bf75dd8..0000000 --- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file3_Optimizing_function_w.r.t_one_constraint.py +++ /dev/null @@ -1,29 +0,0 @@ -from manimlib.imports import* - -class firstScene(ThreeDScene): - def construct(self): - axes = ThreeDAxes() - cylinder = ParametricSurface( - lambda u, v: np.array([ - np.cos(TAU * v), - np.sin(TAU * v), - 2 * (u) - ]),checkerboard_colors=[YELLOW_C,YELLOW_D,YELLOW_E] - ).fade(0.4) #Resolution of the surfaces - - plane = ParametricSurface( - lambda u, v: np.array([ - u, - v, - u+v - ]),checkerboard_colors=[TEAL_C,TEAL_D,TEAL_E] - ).scale(2.5) - self.add(axes) - self.set_camera_orientation(phi=75*DEGREES,theta=45*DEGREES) - self.play(Write(cylinder)) - self.play(Write(plane)) - self.wait(1) - self.begin_ambient_camera_rotation(rate=0.7) - self.wait(5) - self.move_camera(phi=35*DEGREES,theta=-45*DEGREES) - self.wait(2) diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Critical_Points_mcq_questions.pdf b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/MCQ-Questions/Critical_Points_mcq_questions.pdf Binary files differindex 25c4e4d..25c4e4d 100644 --- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Critical_Points_mcq_questions.pdf +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/MCQ-Questions/Critical_Points_mcq_questions.pdf diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/MCQ-Questions/Lagrange_Multipliers_mcq_questions.pdf b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/MCQ-Questions/Lagrange_Multipliers_mcq_questions.pdf Binary files differnew file mode 100644 index 0000000..3ba7d1c --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/MCQ-Questions/Lagrange_Multipliers_mcq_questions.pdf diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/MCQ-Questions/Tangent_Plane_Approximations_mcq_questions.pdf b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/MCQ-Questions/Tangent_Plane_Approximations_mcq_questions.pdf Binary files differnew file mode 100644 index 0000000..2a77b15 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/MCQ-Questions/Tangent_Plane_Approximations_mcq_questions.pdf diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The_Second_Derivative_Test_MCQ.pdf b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/MCQ-Questions/The_Second_Derivative_Test_mcq_questions.pdf Binary files differindex ca60cbf..ca60cbf 100644 --- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The_Second_Derivative_Test_MCQ.pdf +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/MCQ-Questions/The_Second_Derivative_Test_mcq_questions.pdf diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/MCQ-Questions/Total_Differential_mcq_questions.pdf b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/MCQ-Questions/Total_Differential_mcq_questions.pdf Binary files differnew file mode 100644 index 0000000..b1a679d --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/MCQ-Questions/Total_Differential_mcq_questions.pdf diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Tangent-Plane-Approximations/README.md b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Tangent-Plane-Approximations/README.md new file mode 100644 index 0000000..2a274d0 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Tangent-Plane-Approximations/README.md @@ -0,0 +1,26 @@ +<h1><div align=”center”><b>SubTopic: Tangent Plane Approximations</b></h1></div> +<br/></br> + +<tab>file1_Tangent_Plane + + +<br/></br> +<br/></br> + +<tab>file2_Tangent_plane_approximation_visualization + + +<br/></br> +<br/></br> + +<tab>file3_Non_Differentiable_Function + + +<br/></br> +<br/></br> + +<tab>file4_Tangent_plane_at_extrema_and_saddle_point + + +<br/></br> +<br/></br> diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Tangent-Plane-Approximations/file1_Tangent_Plane.py b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Tangent-Plane-Approximations/file1_Tangent_Plane.py index 4c17f90..8efdbd2 100644 --- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Tangent-Plane-Approximations/file1_Tangent_Plane.py +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Tangent-Plane-Approximations/file1_Tangent_Plane.py @@ -1,7 +1,7 @@ from manimlib.imports import* #---- tangent plane is parallel to the surface of the funtion at a point -class firstScene(ThreeDScene): +class tangentplane(ThreeDScene): def construct(self): s1_text=TextMobject("Suppose, the point $(x,y)$ lies on the surface of the function.").scale(0.5).shift(2*UP) diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Tangent-Plane-Approximations/file2_Tangent_plane_approximation_visualization.gif b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Tangent-Plane-Approximations/file2_Tangent_plane_approximation_visualization.gif Binary files differindex d23405d..6d5a67a 100644 --- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Tangent-Plane-Approximations/file2_Tangent_plane_approximation_visualization.gif +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Tangent-Plane-Approximations/file2_Tangent_plane_approximation_visualization.gif diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Tangent-Plane-Approximations/file2_Tangent_plane_approximation_visualization.py b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Tangent-Plane-Approximations/file2_Tangent_plane_approximation_visualization.py index d1ecf8c..02576d9 100644 --- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Tangent-Plane-Approximations/file2_Tangent_plane_approximation_visualization.py +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Tangent-Plane-Approximations/file2_Tangent_plane_approximation_visualization.py @@ -1,12 +1,13 @@ from manimlib.imports import* +import math as m -#---- tangent plane is parallel to the x-y plane -class MaximaScene(ThreeDScene): +#---- tangent plane approximation visualization +class ApproximationScene(ThreeDScene): def construct(self): - axes = ThreeDAxes().scale(1.2) - label_x= TextMobject("$x$").shift([5.4,-0.5,0]) #---- x axis - label_y= TextMobject("$y$").shift([-0.5,5.2,0]).rotate(-4.5) #---- y axis + axes = ThreeDAxes().scale(1.2).fade(0.7) + label_x= TextMobject("$x$").shift([5.4,-0.5,0]).fade(0.7) #---- x axis + label_y= TextMobject("$y$").shift([-0.5,5.2,0]).rotate(-4.5).fade(0.7) #---- y axis #---- graph of the function s = ParametricSurface( @@ -14,61 +15,71 @@ class MaximaScene(ThreeDScene): 1.5*np.cos(u)*np.cos(v), 1.5*np.cos(u)*np.sin(v), 1.5*np.sin(u) - ]),u_min=0,u_max=PI,v_min=PI,v_max=2*PI,checkerboard_colors=[BLUE_B,BLUE_C,BLUE_D,BLUE_E]).scale(1.5).shift([-0.8,0.5,1.5]) - + ]),u_min=0,u_max=PI,v_min=PI,v_max=2*PI,checkerboard_colors=[BLUE_B,BLUE_C,BLUE_D,BLUE_E]).shift([0,1,2.4]).scale(1.3) + d1 = Dot([0.2,2.01,2.24],color = '#800000').rotate(1.1,LEFT) #---- point(x_0,y_0) - d1_copy = Dot([1.1,2.2,-0.45],color = '#800000') #---- projection of point(x_0,y_0) on x-y plane - d1_text = TextMobject("$(x_0,y_0)$",color = "#8B0000").scale(0.4).shift(1.3*RIGHT+1.1*UP) + d1_copy = Dot([0.2,2.01,0],color = '#800000') #---- projection of point(x_0,y_0) on x-y plane - d2 = Dot([1.1,2.2,2.7],color = '#800000').rotate(1,LEFT) #---- point(x,y) - d2_copy = Dot([0.1,1.95,0.4],color = '#800000') #---- projection of point(x,y) on x-y plane - d2_text = TextMobject("$(x,y)$",color = "#8B0000").scale(0.4).shift(0.6*RIGHT+0.8*UP) + d1_text = TextMobject("$f(x_0,y_0)$",color=ORANGE).scale(0.5).shift([0.2,2.01,2.3]) + d1_copy_text = TextMobject("$(x_0,y_0)$",color=ORANGE).scale(0.5).shift([0.2,2.01,0],4.1*DOWN) - t_plane = Rectangle(color = PURPLE, fill_opacity=0.3).scale(0.4).rotate(1,LEFT).shift([1.1,2.5,2.9]) #---- tangent plane + d2 = Dot([2,2.6,3.5],color = '#800000').rotate(1,LEFT) #---- point(x,y) + d2_copy = Dot([2,2.6,0],color = '#800000') #---- projection of point(x,y) on x-y plane - t_text= TextMobject("Tangent Plane",color = RED).scale(0.5).shift(0.3*RIGHT+1.3*UP).rotate(math.radians(5),LEFT) + d2_text = TextMobject("$f(x,y)$",color=ORANGE).scale(0.5).shift([0.8,1.4,1.5]) + d2_copy_text = TextMobject("$(x,y)$",color=ORANGE).scale(0.5).shift([0.8,1.4,0],2.4*DOWN) - l1 = Line([1.1,2.2,2.6],[1.1,2.2,-0.45]).fade(0.2) - l2 = Line([0.1,1.95,2.05],[0.1,1.95,0.4]).fade(0.2) + l1 = Line([0.2,2.01,2.21],[0.2,2.01,0],color= YELLOW).fade(0.2) + l2 = Line([2,2.6,3.4],[2,2.6,0],color= YELLOW).fade(0.2) - a1 = Line([0.1,1.95,0.4],[1.1,2.2,-0.45],color ="#00FF7F") - a_x = Line([0.1,1.95,0.4],[1.7,1.95,0.4],color ="#9400D3") - a_y = Line([0.1,1.95,0.4],[0.1,2.75,0.4],color ="#8B4513") - a2 = Line([1.7,1.95,0.4],[1.7,2.75,0.4]) - a3 = Line([0.1,2.75,0.4],[1.7,2.75,0.4]) - - #---- transition of tangent plane + t_plane = Rectangle(color = PURPLE, fill_opacity=0.3).scale(0.6).rotate(m.radians(45),LEFT).shift([1.1,2.5,3.1]) #---- tangent plane + t_text= TextMobject("Tangent Plane",color = PINK).scale(0.5).shift(0.3*RIGHT+2.6*UP).rotate(math.radians(5),LEFT) + + a1 = Line([0.2,2.01,0],[2,2.6,0],color ="#00FF7F") + a_x = Line([0.2,2.01,0],[2,2.01,0],color ="#9400D3") + a_y = Line([0.2,2.01,0],[0.2,2.6,0],color ="#8B4513") + a2 = Line([2,2.01,0],[2,2.6,0]) + a3 = Line([0.2,2.6,0],[2,2.6,0]) + + ax_text = TextMobject("$f_x (x_0 , y_0 )(x – x_0 ) $").scale(0.5).shift(DOWN+0.8*LEFT).rotate(0.4) + ay_text = TextMobject("$ f_y (x_0 , y_0 )(y – y_0 ) $").scale(0.5).shift(0.8*DOWN+2.7*RIGHT).rotate(-0.6) + a1_text = TextMobject("$f_x (x_0 , y_0 )(x – x_0 ) + f_y (x_0 , y_0 )(y – y_0 )$ ").scale(0.4).rotate(0.7).shift(1.7*DOWN+0.6*RIGHT) + + lines = VGroup(a1,a_y,a_x,a2,a3,d1_copy,d2_copy) - t2_plane = Rectangle(color = PURPLE, fill_opacity=0.3).scale(0.4).rotate(1,LEFT).shift([1.1,2.5,2]) - t3_plane = Rectangle(color = PURPLE, fill_opacity=0.3).scale(0.4).rotate(math.radians(180),LEFT).shift([1.1,2.5,2]) - t4_plane = Rectangle(color = PURPLE, fill_opacity=0.3).scale(0.4).rotate(math.radians(180),LEFT).shift([0.9,2.35,0.4]) - #------------------------------------------- - self.set_camera_orientation(phi = 50 * DEGREES, theta = 45 * DEGREES) + self.set_camera_orientation(phi = 60 * DEGREES, theta = 55 * DEGREES) self.wait(1) self.add(axes) self.add(label_x) self.add(label_y) self.play(Write(s)) self.wait(1) - self.play(Write(d1)) + self.play(Write(d2)) self.add_fixed_in_frame_mobjects(d1_text) - self.play(ShowCreation(t_plane)) + self.wait(1) + self.play(Write(t_plane)) self.add_fixed_in_frame_mobjects(t_text) self.wait(1) - self.play(FadeOut(t_text),Write(d2)) - self.add_fixed_in_frame_mobjects(d2_text) + self.play(Write(d1)) + self.add_fixed_in_frame_mobjects(d2_text) + self.wait(1) + self.play(Write(l1),Write(d1_copy)) + self.add_fixed_in_frame_mobjects(d2_copy_text) + self.wait(1) + self.play(Write(l2),Write(d2_copy)) + self.add_fixed_in_frame_mobjects(d1_copy_text) + self.wait(2) + self.play(FadeOut(d1_text),FadeOut(d1_copy_text),FadeOut(d2_text),FadeOut(d2_copy_text),FadeOut(t_text)) self.wait(1) - self.play(Write(l1),Write(l2)) - self.play(Write(d2_copy),Write(d1_copy)) + self.play(Write(a1),Write(a_x),Write(a_y),Write(a2),Write(a3)) self.wait(1) - self.play(Write(a1),Write(a_x),Write(a_y)) + self.play(FadeOut(s),FadeOut(d1),FadeOut(d2),FadeOut(l1),FadeOut(l2),FadeOut(t_plane),FadeOut(label_x),FadeOut(label_y)) self.wait(1) - self.play(Write(a2),Write(a3)) - self.wait(1) - self.play(ReplacementTransform(t_plane,t2_plane)) + lines.scale(2) + axes.scale(1.5) self.wait(1) - self.play(ReplacementTransform(t2_plane,t3_plane)) + self.add_fixed_in_frame_mobjects(ax_text) + self.add_fixed_in_frame_mobjects(ay_text) + self.add_fixed_in_frame_mobjects(a1_text) self.wait(1) - self.play(ReplacementTransform(t3_plane,t4_plane)) - self.wait(1) diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Tangent-Plane-Approximations/file4_Tangent plane_at_extrema_and_saddle_point.gif b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Tangent-Plane-Approximations/file4_Tangent plane_at_extrema_and_saddle_point.gif Binary files differdeleted file mode 100644 index cfe054b..0000000 --- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Tangent-Plane-Approximations/file4_Tangent plane_at_extrema_and_saddle_point.gif +++ /dev/null diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Tangent-Plane-Approximations/file4_Tangent_plane_at_extrema_and_saddle_point.gif b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Tangent-Plane-Approximations/file4_Tangent_plane_at_extrema_and_saddle_point.gif Binary files differnew file mode 100644 index 0000000..3fe7992 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Tangent-Plane-Approximations/file4_Tangent_plane_at_extrema_and_saddle_point.gif diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/README.md b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/README.md index a2f71d7..10786d6 100644 --- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/README.md +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/README.md @@ -4,5 +4,8 @@ **file2_circle_curvature.py** <br>  +**file3_curvature_interpretation.py** <br> + + **file4_different_curvature_single_curve.py** <br>  diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file1_simple_visualization.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file1_simple_visualization.gif Binary files differindex 858a8de..3f7ecd1 100644 --- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file1_simple_visualization.gif +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file1_simple_visualization.gif diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file1_simple_visualization.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file1_simple_visualization.py index 7ab8908..45058d7 100644 --- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file1_simple_visualization.py +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file1_simple_visualization.py @@ -32,6 +32,8 @@ class randomcurve(GraphScene): dot6 = Dot(tgt6.get_start(), color = RED) dot7 = Dot(tgt7.get_start(), color = RED) + arc = ArcBetweenPoints(dot1.get_center(), dot2.get_center(), color = GREEN_SCREEN, angle = 10*DEGREES).rotate(180*DEGREES) + dots = VGroup(*[dot1, dot2, dot3, dot4, dot5, dot6, dot7]) ds = CurvedArrow((-4, 2, 0), (tgt1.get_start() + tgt2.get_start()) / 2, color = YELLOW) @@ -43,15 +45,13 @@ class randomcurve(GraphScene): self.wait(2) self.play(FadeOut(intro)) self.setup_axes(hideaxes=False) - self.play(ShowCreation(graphobj), FadeIn(dots), FadeIn(ds), FadeIn(ds_text)) + self.play(ShowCreation(graphobj), FadeIn(dots), FadeIn(ds), FadeIn(ds_text), FadeIn(arc)) self.wait(1) - self.play(FadeOut(self.axes), FadeOut(graphobj),FadeIn(mid), FadeOut(dots), FadeOut(ds), FadeOut(ds_text)) - self.wait(2) + self.play(FadeOut(self.axes), FadeOut(arc), FadeOut(graphobj),FadeIn(mid), FadeOut(dots), FadeOut(ds), FadeOut(ds_text)) + self.wait(3) self.play(FadeOut(mid)) self.play(FadeIn(self.axes), FadeIn(graphobj), FadeIn(dots)) - - tangents = [tgt1, tgt2, tgt3, tgt4, tgt5, tgt6, tgt7] for tangent in tangents: self.play(ShowCreation(tangent), run_time = 0.2) @@ -60,7 +60,7 @@ class randomcurve(GraphScene): self.play(FadeOut(self.axes), FadeOut(graphobj), FadeOut(tangents), FadeOut(dots)) self.wait(1) self.play(FadeIn(outro)) - self.wait(2) + self.wait(3) self.play(FadeOut(outro)) self.wait(1) diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.gif Binary files differnew file mode 100644 index 0000000..22a450a --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.gif diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.py new file mode 100644 index 0000000..d8dd0a4 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.py @@ -0,0 +1,42 @@ +from manimlib.imports import * + +class interpretation(Scene): + def construct(self): + tgt = Vector((1, 2, 0), color = YELLOW) + tgtText = TextMobject(r'$r\prime (t)$').next_to(tgt, UP, buff = 0).scale(0.7) + tgt2 = DashedLine((0,0,0),(1, 2, 0), color = GRAY).shift(DOWN + 2*RIGHT) + + nm = Vector((2, -1, 0), color = BLUE) + nmText = TextMobject(r'$r\prime\prime (t)$').next_to(nm, DOWN+RIGHT, buff = 0).scale(0.7) + nm2 = DashedLine((0,0,0),(2, -1, 0), color = GRAY).shift(2*UP + RIGHT) + square = Square(fill_color = WHITE, fill_opacity = 0.2).rotate(63*DEGREES).shift(0.5*UP +1.5*RIGHT).scale(1.1) + square.set_stroke(width = 0.1) + arrow = CurvedArrow(square.get_center() + np.array([2,1,0]), square.get_center() + np.array([0.5,0,0])) + arrowText = TextMobject(r'$r\prime (t)\times r\prime\prime (t)$').next_to(arrow.get_start(), DOWN+1*RIGHT, buff = 0).scale(0.7) + + text1 = TextMobject(r'$\left|\frac{dT}{ds}\right| = \frac{\left|\frac{dT}{dt}\right|}{\left|\frac{ds}{dt}\right|}$').shift(UP+3*LEFT) + text2 = TextMobject(r'$\left|\frac{dT}{ds}\right| = \frac{\frac{r\prime\prime (t)}{\left| r\prime (t)\right|}\times\frac{r\prime (t)}{\left| r\prime (t)\right|}}{\left|r\prime (t)\right|}$').next_to(text1, DOWN, buff = 0.1) + unit = VGroup(*[tgt, tgt2, nm, nm2]) + + # self.play(FadeIn(VGroup(*[tgt, tgt2, nm, nm2, nmText, tgtText, square, arrow, arrowText]))) + tgt2text = TextMobject(r'$\frac{r\prime (t)}{\left| r\prime (t)\right|}$').shift(1.1*UP).scale(0.7).rotate(63*DEGREES ) + nm2text = TextMobject(r'$\frac{r\prime\prime (t)}{\left| r\prime (t)\right|}$').scale(0.7).shift(0.7*RIGHT+0.8*DOWN).rotate(-25*DEGREES) + unit2 = unit.copy().scale(0.5).shift(0.75*LEFT+0.25*DOWN) + + self.play(FadeIn(VGroup(*[tgt, tgtText]))) + self.wait(1) + self.play(FadeIn(VGroup(*[nm, nmText]))) + self.wait(1) + self.play(FadeIn(VGroup(*[tgt2, nm2]))) + self.wait(1) + self.play(FadeIn(VGroup(*[square, arrow, arrowText]))) + self.wait(1) + self.play(FadeIn(unit2)) + self.wait(1) + self.play(FadeIn(VGroup(*[tgt2text, nm2text]))) + self.wait(1) + self.play(FadeIn(text1)) + self.wait(1) + self.play(FadeIn(text2)) + self.wait(2) + self.play(FadeOut(VGroup(*[tgt2text, nm2text, text1, text2, tgt, tgtText,nm, nmText,tgt2, nm2,square, arrow, arrowText,unit2]))) diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_intuition.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_intuition.gif Binary files differdeleted file mode 100644 index 0d6fdcf..0000000 --- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_intuition.gif +++ /dev/null diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file4_different_curvature_single_curve.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file4_different_curvature_single_curve.py index d71adda..56b7fbb 100644 --- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file4_different_curvature_single_curve.py +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file4_different_curvature_single_curve.py @@ -8,7 +8,9 @@ class GR(GraphScene): "x_max": 6, "y_min": -6, "y_max": 10, - "graph_origin": ORIGIN + "graph_origin": ORIGIN, + 'x_tick_frequency': 20, + 'y_tick_frequency': 20 } def construct(self): @@ -21,7 +23,7 @@ class GR(GraphScene): tracker = ValueTracker(-3) - text = TextMobject(r'The curvature at point $P_{1}$ is \\ lesser than that at point $P_{2}$: \\ as $\kappa = \frac{1}{R}$').shift(3.2*RIGHT+3*UP).scale(0.6) + text = TextMobject(r'$\because R_{1} > R_{2}$, the curvature at \\ point $P_{1}$ is less than that \\ at point $P_{2}$ as $\kappa = \frac{1}{R}$').shift(3.2*RIGHT+3*UP).scale(0.6) dot1 = Dot((0,3,0), color = YELLOW) dot1label = TextMobject(r'$P_{1}$').next_to(dot1, UP+RIGHT, buff = 0.1) @@ -47,10 +49,30 @@ class GR(GraphScene): line.move_to(p0) return line + circle1 = Circle(radius = 0.8, color = GREY, opacity = 0.2).shift(2.2*UP) + tgt1 = Line((-2,3,0), (2,3,0), color = GREY, opacity = 0.2).scale(0.4) + + r1 = Line(circle1.get_center(), circle1.get_center() + np.array([0,0.8,0]), color=GREEN_SCREEN) + r1label = TextMobject(r'$R_{1}$',color=WHITE).next_to(r1, RIGHT, buff = 0.1).scale(0.6) + + curvature1 = VGroup(*[circle1, tgt1, r1, r1label]) + + circle2 = Circle(radius = 0.6, color = GREY, opacity = 0.2).shift(0.4*DOWN + 4*RIGHT) + tgt2 = Line((4,-2,0), (6, -2, 0), color = GREY, opacity = 0.2).scale(0.5).shift(LEFT + UP) + + r2 = Line(circle2.get_center(), circle2.get_center() + np.array([0,-0.6,0]), color=GREEN_SCREEN) + r2label = TextMobject(r'$R_{2}$', color=WHITE).next_to(r2, 0.9*RIGHT, buff = 0).scale(0.6) + + curvature2 = VGroup(*[circle2, tgt2, r2, r2label]) + line = always_redraw(get_tangent_line) self.add(graph,line, dots, text) self.wait(1.2) - self.play(tracker.set_value, 6, rate_func=smooth, run_time=13) - self.play(FadeOut(VGroup(*[graph, self.axes, line, dots, text]))) + self.play(tracker.set_value, 0, rate_func=smooth, run_time=5) + self.play(FadeIn(curvature1)) + self.play(tracker.set_value, 4, rate_func=smooth, run_time=5) + self.play(FadeIn(curvature2)) + self.play(tracker.set_value, 6, rate_func=smooth, run_time=3) + self.play(FadeOut(VGroup(*[curvature1, curvature2, graph, self.axes, line, dots, text]))) self.wait() diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file1_parametric_circle.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file1_parametric_circle.py index 40b5150..37d079e 100644 --- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file1_parametric_circle.py +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file1_parametric_circle.py @@ -11,12 +11,15 @@ class parametricCircle(ThreeDScene, GraphScene): self.y_axis_label = "" self.x_axis_width = 10 self.y_axis_height = 10 + self.y_tick_frequency = 1.9 + self.x_tick_frequency = 1.4 axes = [] - self.setup_axes() - self.axes.scale(0.5).shift(3*LEFT) - axes.append(self.axes) + # self.setup_axes() + ax = Axes(y_tick_frequency = 1, x_axis_width = 10, y_axis_height = 10, y_min = -5, x_max = 5, y_max = 5, x_tick_frequency = 1, x_axis_label = "", y_axis_label = "", x_min = -5, ) + ax.scale(0.5).shift(3*LEFT) + axes.append(ax) self.setup_axes() self.axes.scale(0.3).shift(3*RIGHT + 2*UP) axes.append(self.axes) @@ -38,7 +41,7 @@ class parametricCircle(ThreeDScene, GraphScene): asint = ParametricFunction( lambda t: np.array([ t, - np.sin(t), + 2*np.sin(t), 0 ]), t_min = -np.pi, t_max = np.pi, color = GREEN_E ).shift(3*RIGHT + 2*UP).scale(0.4) @@ -50,7 +53,7 @@ class parametricCircle(ThreeDScene, GraphScene): acost = ParametricFunction( lambda t: np.array([ t, - np.cos(t), + 2*np.cos(t), 0 ]), t_min = -np.pi, t_max = np.pi, color = BLUE ).shift(3*RIGHT + 2*DOWN).scale(0.4) diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file2_cycloid.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file2_cycloid.gif Binary files differdeleted file mode 100644 index 39656de..0000000 --- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file2_cycloid.gif +++ /dev/null diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/README.md b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/README.md index 34885b2..7874f43 100644 --- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/README.md +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/README.md @@ -1,2 +1,15 @@ -**file2_tnb_frame_manim.py** <br> - +**file1_tnb_creation.py**<br> + + + +**file2_tnb_basic.py** <br> + + +**file3_tnb_frame_manim.py** <br> + + +**file4_fs1.py** <br> + + +**file5_fs2.py** <br> + diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_prescribed_plane.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_prescribed_plane.gif Binary files differdeleted file mode 100644 index c8668e3..0000000 --- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_prescribed_plane.gif +++ /dev/null diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_creation.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_creation.gif Binary files differnew file mode 100644 index 0000000..eae8686 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_creation.gif diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_creation.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_creation.py new file mode 100644 index 0000000..80372ee --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_creation.py @@ -0,0 +1,66 @@ +from manimlib.imports import * + +class tnb(ThreeDScene): + def construct(self): + self.set_camera_orientation(phi = 75*DEGREES, theta=45*DEGREES) + + helix1 = ParametricFunction( + lambda t: np.array([ + np.cos(TAU*t), + np.sin(TAU*t), + 0.4*t + ]), t_min = -2*np.pi/3, t_max = -1.638*np.pi/3, color = WHITE + ) + + helix2 = ParametricFunction( + lambda t: np.array([ + np.cos(TAU*t), + np.sin(TAU*t), + 0.4*t + ]), t_min = -1.638*np.pi/3, t_max = -1.33*np.pi/3, color = WHITE + ) + + pointText = TextMobject(r'Consider an arbitrary point \\ on the given curve.').scale(0.8).shift(1.5*UP) + tgtText = TextMobject(r'Unit', ' tangent ', r'vector at \\ this point is given as:').scale(0.8).shift(1.5*UP) + tgtText.set_color_by_tex_to_color_map({ + "tangent": YELLOW + }) + normalText = TextMobject(r'Unit', ' normal ', r'vector at \\ this point is given as:').scale(0.8).shift(1.5*UP) + normalText.set_color_by_tex_to_color_map({ + "normal": BLUE + }) + planeText = TextMobject(r'$\overrightarrow{T}$ and $\overrightarrow{N}$ \\ prescribe a plane.').scale(0.8).shift(1.5*UP) + bnmText = TextMobject(r'The vector normal to this plane \\ is called the', ' binormal ', 'vector.').scale(0.8).shift(1.5*UP) + bnmText.set_color_by_tex_to_color_map({ + "binormal": GREEN_E + }) + + dot1 = Dot(np.array([np.cos(-np.pi/3), np.sin(-np.pi/3), -0.4*np.pi/3]) + np.array([0,0.2,0]), radius = 0.16, color=RED) + tgt1 = Arrow((0,0,0), (-2,-0.55,0), color = YELLOW).shift(dot1.get_center() + np.array([0.18,0.04,0])) + nm1 = Arrow((0,0,0), (0.4,-2,0), color = BLUE).shift(dot1.get_center() + np.array([0,0.26,0])) + bnm1 = Arrow((0,0,0), (0,2,0), color=GREEN_E).shift(2.1*RIGHT+2*DOWN) + plane1 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(dot1.get_center() + np.array([-0.4, -0.6, 0])).rotate(13*DEGREES).scale(1.2) + point1 = VGroup(*[dot1, tgt1, nm1, plane1]).scale(0.8).shift(np.array([1,4.86,0])).rotate(-15*DEGREES) + + + + helix = VGroup(*[helix1, helix2]) + self.play(FadeIn(helix)) + self.play(ApplyMethod(helix.scale, 4)) + self.add_fixed_in_frame_mobjects(pointText) + self.play(FadeIn(dot1), FadeIn(pointText)) + self.wait(2) + self.add_fixed_in_frame_mobjects(tgtText) + self.play(Write(tgt1), ReplacementTransform(pointText, tgtText)) + self.wait(2) + self.add_fixed_in_frame_mobjects(normalText) + self.play(Write(nm1), ReplacementTransform(tgtText, normalText)) + self.wait(2) + self.add_fixed_in_frame_mobjects(planeText) + self.play(FadeIn(plane1), ReplacementTransform(normalText, planeText)) + self.wait(2) + self.add_fixed_in_frame_mobjects(bnmText) + self.add_fixed_in_frame_mobjects(bnm1) + self.play(ReplacementTransform(planeText, bnmText), Write(bnm1)) + self.wait(2) + self.play(FadeOut(VGroup(*[helix, bnm1, bnmText, dot1, tgt1, nm1, plane1]))) diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_basic.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_basic.gif Binary files differnew file mode 100644 index 0000000..67aaea2 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_basic.gif diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_basic.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_basic.py new file mode 100644 index 0000000..c870210 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_basic.py @@ -0,0 +1,36 @@ +from manimlib.imports import * + +class tnb(ThreeDScene): + def construct(self): + t = TextMobject(r'T', color = YELLOW) + n = TextMobject(r'N', color = BLUE).next_to(t, RIGHT, buff=0) + b = TextMobject(r'B', color = GREEN_E).next_to(n, RIGHT, buff=0) + frame = TextMobject(r'Frame').next_to(b, RIGHT, buff=0.2) + f1 = TextMobject(r'$\overrightarrow{B}$ ', color = GREEN_E) + f2 = TextMobject(r' = $\overrightarrow{T}$', color = YELLOW).next_to(f1, RIGHT, buff=0.2) + f3 = TextMobject(r'$\times\overrightarrow{N}$', color = BLUE).next_to(f2, RIGHT, buff=0.1) + formula = VGroup(*[f1, f2, f3]).move_to(ORIGIN).shift(3*UP) + + # text = VGroup(*[t,n,b,frame]).move_to(ORIGIN).shift(3*UP) + curve = ParametricFunction( + lambda t: np.array([ + np.sin(TAU*t), + np.cos(TAU*t), + 0 + ]) + ).scale(2.5) + dot = Dot(color = RED).scale(1.5).shift(1.05*LEFT) + tgt = Arrow(dot.get_center(), (-2, 2, 0), color = YELLOW).shift(0.3*DOWN + 0.09*RIGHT) + normal = Arrow(tgt.get_start(), (1, 1, 0), color = BLUE).shift(0.2*LEFT + 0.05*DOWN) + binormal = Arrow(dot.get_center() - np.array([0,0,0.3]), (tgt.get_start()[0], tgt.get_start()[1],2), color = GREEN) + square = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).move_to(tgt.get_start()).rotate(27*DEGREES).shift(UP+0.4*RIGHT).scale(1.2) + group = VGroup(*[dot, tgt, normal, square, binormal]).shift(np.array([-1.24,-1,0])) + + self.add_fixed_in_frame_mobjects(formula) + self.add(curve, group) + self.wait(1) + self.move_camera(phi = 75*DEGREES, theta=45*DEGREES, run_time = 2) + self.add_fixed_in_frame_mobjects(formula) + self.begin_ambient_camera_rotation(rate = 0.5) + self.wait(5) + self.play(FadeOut(VGroup(*[formula, curve, dot, tgt, normal, square, binormal]))) diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame.gif Binary files differdeleted file mode 100644 index 097652f..0000000 --- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame.gif +++ /dev/null diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.gif Binary files differdeleted file mode 100644 index 784b6a6..0000000 --- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.gif +++ /dev/null diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file3_tnb_frame_manim.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file3_tnb_frame_manim.gif Binary files differnew file mode 100644 index 0000000..78e3aa3 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file3_tnb_frame_manim.gif diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file3_tnb_frame_manim.py index ee5e717..176cac5 100644 --- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.py +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file3_tnb_frame_manim.py @@ -79,15 +79,16 @@ class tnb(ThreeDScene): self.play(FadeIn(helix), FadeIn(text)) self.play(ApplyMethod(helix.scale, 4)) self.add_fixed_in_frame_mobjects(bnm0) - self.play(FadeIn(point0), MoveAlongPath(helix_dot, helix1, run_time=5)) + self.play(FadeIn(point0)) + self.play(ApplyMethod(point0.set_color, GRAY, opacity = 0.1), MoveAlongPath(helix_dot, helix1, run_time=5)) self.add_fixed_in_frame_mobjects(bnm1) - self.play(ApplyMethod(point0.set_color, GRAY), FadeIn(point1)) - self.play(MoveAlongPath(helix_dot, helix2, run_time = 5)) + self.play(FadeIn(point1)) + self.play(ApplyMethod(point1.set_color, GRAY, opacity = 0.1), ApplyMethod(bnm1.set_color, GRAY, opacity = 0.1), MoveAlongPath(helix_dot, helix2, run_time = 5)) self.add_fixed_in_frame_mobjects(bnm2) - self.play(ApplyMethod(point1.set_color, GRAY), ApplyMethod(bnm1.set_color, GRAY), FadeIn(point2)) - self.play(MoveAlongPath(helix_dot, helix3, run_time=5)) + self.play(FadeIn(point2)) + self.play(ApplyMethod(point2.set_color, GRAY, opacity = 0.1), MoveAlongPath(helix_dot, helix3, run_time=5)) dot3 = Dot(np.array([np.cos(-np.pi/3), np.sin(-np.pi/3), -0.4*np.pi/3]) + np.array([3.3,-0.25,0]), radius = 0.16, color=RED) tgt3 = Arrow((0,0,0), (0,2,0), color = YELLOW).shift(helix_dot.get_center() - np.array([-0.05,0.2,0])) @@ -111,15 +112,15 @@ class tnb(ThreeDScene): point5 = VGroup(*[tgt5, nm5, bnm5, plane5]) self.add_fixed_in_frame_mobjects(bnm3) - self.play(ApplyMethod(point2.set_color, GRAY), FadeIn(point3)) - self.play(MoveAlongPath(helix_dot, helix4, run_time=5)) + self.play(FadeIn(point3)) + self.play(ApplyMethod(point3.set_color, GRAY, opacity = 0.1), MoveAlongPath(helix_dot, helix4, run_time=5)) self.add_fixed_in_frame_mobjects(bnm4) - self.play(ApplyMethod(point3.set_color, GRAY), FadeIn(point4)) - self.play(MoveAlongPath(helix_dot, helix5, run_time=5)) + self.play(FadeIn(point4)) + self.play(ApplyMethod(point4.set_color, GRAY, opacity = 0.1), MoveAlongPath(helix_dot, helix5, run_time=5)) self.add_fixed_in_frame_mobjects(bnm5) - self.play(ApplyMethod(point4.set_color, GRAY), FadeIn(point5)) + self.play(FadeIn(point5)) self.wait(2) - self.play(FadeOut(VGroup(*[helix, bnm1, point0, point1, point2, point3, point4, point5, helix_dot]))) + self.play(FadeOut(VGroup(*[text, helix, bnm1, point0, point1, point2, point3, point4, point5, helix_dot]))) diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file4_fs1.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file4_fs1.gif Binary files differnew file mode 100644 index 0000000..6b4b438 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file4_fs1.gif diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file4_fs1.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file4_fs1.py new file mode 100644 index 0000000..c719a1d --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file4_fs1.py @@ -0,0 +1,23 @@ +from manimlib.imports import * + +class fs1(ThreeDScene): + def construct(self): + + + self.set_camera_orientation(phi = 75*DEGREES, theta=45*DEGREES) + dot1 = Dot(np.array([np.cos(-np.pi/3), np.sin(-np.pi/3), -0.4*np.pi/3]) + np.array([0,0.2,0]), radius = 0.16, color=RED) + tgt1 = Arrow((0,0,0), (-2,-0.55,0), color = YELLOW).shift(dot1.get_center() + np.array([0.18,0.04,0])) + nm1 = Arrow((0,0,0), (0.4,-2,0), color = BLUE).shift(dot1.get_center() + np.array([0,0.26,0])).shift(np.array([0.8,4.76,0])).rotate(-15*DEGREES).scale(0.8) + bnm1 = Arrow((0,0,0), (0,2,0), color=GREEN_E).shift(2.1*RIGHT+2*DOWN) + plane1 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(dot1.get_center() + np.array([-0.4, -0.6, 0])).rotate(13*DEGREES).scale(1.2) + point1 = VGroup(*[dot1, tgt1, plane1]).scale(0.8).shift(np.array([1,4.86,0])).rotate(-15*DEGREES) + t = TextMobject(r'$T$', color = YELLOW).move_to(ORIGIN).shift(3.2*RIGHT + DOWN) + n = TextMobject(r'$N$', color = BLUE).shift(DOWN + RIGHT) + b = TextMobject(r'$B$', color = GREEN_E).next_to(bnm1, UP, buff = 0.1) + text = VGroup(*[t, n, b]) + self.add_fixed_in_frame_mobjects(bnm1, text) + self.play(FadeIn(point1), FadeIn(bnm1), FadeIn(text)) + self.wait() + self.play(TransformFromCopy(tgt1, nm1, run_time = 2)) + self.wait(2) + self.play(FadeOut(VGroup(*[bnm1, text, point1, nm1]))) diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file5_fs2.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file5_fs2.gif Binary files differnew file mode 100644 index 0000000..ce367b6 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file5_fs2.gif diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file5_fs2.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file5_fs2.py new file mode 100644 index 0000000..0261fed --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file5_fs2.py @@ -0,0 +1,28 @@ +from manimlib.imports import * + +class fs1(ThreeDScene): + def construct(self): + + + self.set_camera_orientation(phi = 75*DEGREES, theta=45*DEGREES) + dot1 = Dot(np.array([np.cos(-np.pi/3), np.sin(-np.pi/3), -0.4*np.pi/3]) + np.array([0,0.2,0]), radius = 0.16, color=RED) + tgt1 = Arrow((0,0,0), (-2,-0.55,0), color = YELLOW).shift(dot1.get_center() + np.array([0.18,0.04,0])) + nm1 = Arrow((0,0,0), (0.4,-2,0), color = BLUE).shift(dot1.get_center() + np.array([0,0.26,0])).shift(np.array([0.8,4.76,0])).rotate(-15*DEGREES).scale(0.8) + bnm1 = Arrow((0,0,0), (0,2,0), color=GREEN_E).shift(2.1*RIGHT+2*DOWN) + + bnms = Line((0,0,0), (0,0,1.6), color = GREEN_E).shift(np.array([3.1,5.2,0])).scale(0.6) + bnmsa = ArrowTip(color = GREEN_E).next_to(bnms, np.array([0,0,1]), buff = 0).rotate(45*DEGREES) + bns = VGroup(*[bnms, bnmsa]) + + plane1 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(dot1.get_center() + np.array([-0.4, -0.6, 0])).rotate(13*DEGREES).scale(1.2) + point1 = VGroup(*[dot1, tgt1, plane1]).scale(0.8).shift(np.array([1,4.86,0])).rotate(-15*DEGREES) + t = TextMobject(r'$T$', color = YELLOW).move_to(ORIGIN).shift(3.2*RIGHT + DOWN) + n = TextMobject(r'$N$', color = BLUE).shift(DOWN + RIGHT) + b = TextMobject(r'$B$', color = GREEN_E).next_to(bnm1, UP, buff = 0.1) + text = VGroup(*[t, n, b]) + self.add_fixed_in_frame_mobjects(bnm1, text) + self.play(FadeIn(point1), FadeIn(text), FadeIn(bnm1)) + self.wait() + self.play(TransformFromCopy(bnms, nm1, run_time = 3)) + self.wait(2) + self.play(FadeOut(VGroup(*[bnms, text, point1, nm1, bnm1]))) diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/README.md b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/README.md index 7ff6b61..97a0fb7 100644 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/README.md +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/README.md @@ -4,6 +4,6 @@ Github Account : <a href="https://github.com/nishanpoojary">nishanpoojary</a> ## Sub-Topics Covered:
+ Scalar Functions
+ Multivariable Functions
-+ Limits and Continuity of Multivariable Functions
++ Multivariable Limits and Continuity
+ Partial Derivatives
+ Directonal Derivatives
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/README.md b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/README.md new file mode 100644 index 0000000..a62369d --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/README.md @@ -0,0 +1,8 @@ +**file1_directional_deriv** + + +**file2_gradient** + + +**file3_gradient_level_curves** + diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/file1_directional_deriv.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/file1_directional_deriv.py new file mode 100644 index 0000000..677d821 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/file1_directional_deriv.py @@ -0,0 +1,85 @@ +from manimlib.imports import *
+
+class GeomRepresen(ThreeDScene):
+ def construct(self):
+ axes = ThreeDAxes()
+
+ paraboloid = ParametricSurface(
+ lambda u, v: np.array([
+ 3*np.sin(u)*np.cos(v),
+ 3*np.sin(u)*np.sin(v),
+ -0.25*3*3*np.sin(u)*np.sin(u)+2
+ ]),u_min=0,u_max=PI/4,v_min=0,v_max=2*PI, color = BLUE_C, fill_color = BLUE_C, fill_opacity = 0.7,
+ resolution=(15, 32)).scale(1)
+
+ parabola_curve = ParametricFunction(
+ lambda u : np.array([
+ u,
+ -u,
+ -0.5*(u*u)+2
+ ]),color=PINK,t_min=-1.5,t_max=1.5,
+ )
+
+ circle = Circle(radius = 2.22 , color = BLACK, fill_color = BLUE_C, fill_opacity= 0.3, stroke_width=0.1)
+
+ plane = Polygon(np.array([2.5,-2.5,0]),np.array([-2.5,2.5,0]),np.array([-2.5,2.5,2.5]),np.array([2.5,-2.5,2.5]),np.array([2.5,-2.5,0]), color = BLACK, fill_color = PINK, fill_opacity= 0.2, stroke_width=0.1)
+
+ line = DashedLine(np.array([1,-1,0]), np.array([1,-1,1.5]), color = YELLOW_C)
+
+ tangent_line = Line(np.array([1.5,-1.5,1]), np.array([0.5,-0.5,2]), color = RED_C)
+
+ vector = Arrow(np.array([1,-1,0]), np.array([0.5,-0.5,0]), buff=0.01, color = GREEN_C)
+
+ dot1 =Sphere(radius=0.08).move_to(np.array([1,-1,0])).set_fill(YELLOW_C)
+ dot2 =Sphere(radius=0.08).move_to(np.array([1,-1,1.5])).set_fill(YELLOW_C)
+
+ dot1_lab = TextMobject(r"$P_0$").scale(0.6).move_to(np.array([1,-1,1.8])).set_color(RED_C)
+ dot2_lab = TextMobject(r"$(x_0,y_0)$").scale(0.6).move_to(np.array([1.6,-1,0])).set_color(PURPLE)
+ vector_lab = TextMobject(r"$\hat{u}$").scale(0.8).move_to(np.array([1.2,-0.5,0])).set_color(GREEN_C)
+ domain_lab = TextMobject(r"$D$").scale(0.6).move_to(np.array([1,1,0])).set_color(GREEN_C)
+ func_lab = TextMobject(r"$z = f(x,y)$").scale(0.6).move_to(1*UP + 2.8*RIGHT).set_color(BLUE_C)
+ directional_deriv_lab = TextMobject(r"Slope = $D_{\hat{u}}f(x_0,y_0)$").scale(0.6).move_to(2.2*UP + 1.5*RIGHT).set_color(YELLOW_C)
+
+ self.add(axes)
+
+ axis = TextMobject(r"X",r"Y",r"Z")
+ axis[0].move_to(6*RIGHT)
+ axis[1].move_to(6*UP)
+ axis[2].move_to(np.array([0,0,3.7]))
+
+ self.add_fixed_orientation_mobjects(axis[2])
+ self.add_fixed_orientation_mobjects(axis[0])
+ self.add_fixed_orientation_mobjects(axis[1])
+
+ self.set_camera_orientation(phi=65 * DEGREES, theta = 20*DEGREES)
+
+ self.play(ShowCreation(paraboloid))
+ self.add_fixed_in_frame_mobjects(func_lab)
+ self.wait()
+
+ #self.play(ShowCreation(circle))
+ self.bring_to_front(circle)
+ self.wait()
+ self.add_fixed_orientation_mobjects(domain_lab)
+ self.wait()
+
+ self.play(ShowCreation(plane), ShowCreation(parabola_curve))
+ self.play(ShowCreation(dot1), GrowArrow(line), ShowCreation(dot2))
+ self.add_fixed_orientation_mobjects(dot1_lab)
+ self.wait()
+ self.add_fixed_orientation_mobjects(dot2_lab)
+ self.wait()
+
+ self.play(ShowCreation(tangent_line))
+ self.add_fixed_in_frame_mobjects(directional_deriv_lab)
+ self.wait()
+
+ self.play(GrowArrow(vector))
+ self.add_fixed_orientation_mobjects(vector_lab)
+ self.wait()
+
+
+ self.begin_ambient_camera_rotation(rate=0.1)
+ self.wait(3)
+
+
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/file2_gradient.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/file2_gradient.py new file mode 100644 index 0000000..e9fef50 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/file2_gradient.py @@ -0,0 +1,103 @@ +from manimlib.imports import *
+
+class Gradient(ThreeDScene):
+ def construct(self):
+ axes = ThreeDAxes() # creates a 3D Axis
+
+
+ quadrant = ParametricSurface(
+ lambda u, v: np.array([
+ 2*np.sin(u)*np.cos(v),
+ 2*np.sin(u)*np.sin(v),
+ 2*np.cos(u)
+ ]),u_min=0,u_max=PI/3,v_min=0,v_max=PI/2,checkerboard_colors=[GREEN_C, GREEN_E],
+ resolution=(15, 32)).scale(1)
+
+ quadrant_curve = ParametricSurface(
+ lambda u, v: np.array([
+ 2*np.sin(u)*np.cos(v),
+ 2*np.sin(u)*np.sin(v),
+ 2*np.cos(u)
+ ]),u_min=34*DEGREES,u_max=38*DEGREES,v_min=0,v_max=PI/2,checkerboard_colors=[YELLOW_C, YELLOW_E],
+ resolution=(15, 32)).scale(1)
+
+
+
+ dot1 =Sphere(radius=0.05).move_to(np.array([1,1,0])).set_fill(YELLOW_C)
+ dot2 =Sphere(radius=0.05).move_to(np.array([1,1,1.732])).set_fill(YELLOW_C)
+
+ dot1_line = DashedLine(np.array([1,1,1.732]), np.array([0,2,2]), color = WHITE)
+ dot1_lab = TextMobject(r"$P_0(x_0,y_0,z_0)$").move_to(np.array([0,2.1,2.2])).set_color(YELLOW_C).scale(0.6)
+ #dot2_line = Line(np.array([0.8,0.8,0]), np.array([1,0.6,0]), color = PINK)
+
+ positive_vector = Arrow(np.array([1,1,0]), np.array([0.5,0.5,0]), buff=0.001, color = BLUE_C)
+ positive_gradient = Arrow(np.array([1,1,1.732]), np.array([0.5,0.5,1.9362]), buff=0.001, color = BLUE_C)
+ positive_gradient_lab = TextMobject(r"$\nabla f$").move_to(np.array([0.5,0.3,0])).set_color(BLUE_C).scale(0.5)
+
+ negative_vector = Arrow(np.array([1,1,0]), np.array([1.5,1.5,0]), buff=0.001, color = RED_C)
+ negative_gradient = Arrow(np.array([1,1,1.732]), np.array([1.5,1.5,1.322]), buff=0.001, color = RED_C)
+ negative_gradient_lab = TextMobject(r"$-\nabla f$").move_to(np.array([1.6,1.6,0])).set_color(RED_C).scale(0.5)
+
+ positive_vector_line = DashedLine(np.array([0.8,0.8,0]), np.array([1,-2,0]), color = WHITE)
+ positive_vector_lab = TextMobject(r"Most Rapid increase in $f$").move_to(np.array([1.6,-3.6,0])).set_color(BLUE_C).scale(0.6)
+ negative_vector_line = DashedLine(np.array([1.2,1.2,0]), np.array([3,-1.5,0]), color = WHITE)
+ negative_vector_lab = TextMobject(r"Most Rapid decrease in $f$").move_to(np.array([3.6,-3,0])).set_color(RED_C).scale(0.6)
+
+
+
+ line1 = DashedLine(np.array([0.5,0.5,0]), np.array([0.5,0.5,1.9362]), color = BLUE_C)
+ line2 = DashedLine(np.array([1,1,0]), np.array([1,1,1.732]), color = YELLOW_C)
+ line3 = DashedLine(np.array([1.5,1.5,0]), np.array([1.5,1.5,1.322]), color = RED_C)
+
+ curve_vector1 = Arrow(np.array([1,1,0]), np.array([1.5,0.5,0]), buff=0.001, color = YELLOW_C)
+ curve_vector2 = Arrow(np.array([1,1,0]), np.array([0.5,1.5,0]), buff=0.001, color = YELLOW_C)
+
+ curve_vector1_line = DashedLine(np.array([1.2,0.8,0]), np.array([1,2.5,0]), color = WHITE)
+ curve_vector2_line = DashedLine(np.array([0.8,1.2,0]), np.array([1,2.5,0]), color = WHITE)
+ curve_vector_lab = TextMobject(r"Zero Change in $f$").move_to(np.array([0.7,3.6,0])).set_color(PINK).scale(0.6)
+
+ #square = Square(side_length = 0.5).rotate(45*DEGREES).move_to(np.array([1.025,0.975,0]))
+ line_x = Line(np.array([0.8,0.8,0]), np.array([1,0.6,0]), color = PINK)
+ line_y = Line(np.array([1.2,0.8,0]), np.array([1,0.6,0]), color = PINK)
+
+ ninety_degree = VGroup(line_x, line_y)
+
+ self.set_camera_orientation(phi=60* DEGREES, theta = 20*DEGREES)
+
+ self.add(axes)
+
+ axis = TextMobject(r"X",r"Y",r"Z")
+ axis[0].move_to(6*RIGHT)
+ axis[1].move_to(6*UP)
+ axis[2].move_to(np.array([0,0,3.7]))
+
+ self.add_fixed_orientation_mobjects(axis[2])
+ self.add_fixed_orientation_mobjects(axis[0])
+ self.add_fixed_orientation_mobjects(axis[1])
+
+ self.play(ShowCreation(quadrant))
+ self.wait()
+ self.play(ShowCreation(dot1), ShowCreation(dot2))
+ self.wait()
+ self.play(GrowArrow(positive_vector), GrowArrow(positive_gradient))
+ self.wait()
+ self.play(GrowArrow(negative_vector), GrowArrow(negative_gradient))
+ self.wait()
+ self.play(GrowArrow(line1), GrowArrow(line2), GrowArrow(line3))
+ self.wait()
+ self.play(ShowCreation(quadrant_curve))
+ self.wait()
+ self.play(GrowArrow(curve_vector1), GrowArrow(curve_vector2), ShowCreation(ninety_degree))
+ self.wait()
+ self.play(GrowArrow(dot1_line))
+ self.add_fixed_orientation_mobjects(dot1_lab)
+ self.wait()
+ self.play(GrowArrow(curve_vector1_line), GrowArrow(curve_vector2_line))
+ self.add_fixed_orientation_mobjects(curve_vector_lab)
+ self.wait()
+ self.add_fixed_orientation_mobjects(positive_gradient_lab, negative_gradient_lab)
+ self.wait()
+ self.play(GrowArrow(positive_vector_line), GrowArrow(negative_vector_line))
+ self.add_fixed_orientation_mobjects(positive_vector_lab, negative_vector_lab)
+ self.begin_ambient_camera_rotation(rate=0.1)
+ self.wait(3)
\ No newline at end of file diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/file3_gradient_level_curves.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/file3_gradient_level_curves.py new file mode 100644 index 0000000..a3b88e5 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/file3_gradient_level_curves.py @@ -0,0 +1,107 @@ +from manimlib.imports import *
+
+class GradientLevelCurves(ThreeDScene):
+ def construct(self):
+ axes = ThreeDAxes()
+
+ paraboloid = ParametricSurface(
+ lambda u, v: np.array([
+ u*np.cos(v),
+ u*np.sin(v),
+ -u*u+2
+ ]),u_min=-1.414,u_max=1.414,v_min=0,v_max=2*PI, color = BLUE_C, fill_color = BLUE_C, fill_opacity = 0.1,
+ resolution=(15, 32)).scale(1)
+
+ plane_0 = Polygon(np.array([2,-2,0]),np.array([2,2,0]),np.array([-2,2,0]),np.array([-2,-2,0]),np.array([2,-2,0]), color = BLUE_E, fill_color = BLUE_E, fill_opacity = 0.3)
+ plane_0_lab = TextMobject("C = 0").move_to(0.4*UP+3.2*RIGHT).set_color(BLUE_E).scale(0.6)
+ circle_0 = Circle(radius = 1.414 , color = BLUE_E)
+ circle_0_lab = TextMobject("0").move_to(1.1*DOWN+1.1*RIGHT).set_color(BLUE_E).scale(0.6)
+
+ plane_0_5 = Polygon(np.array([2,-2,0.5]),np.array([2,2,0.5]),np.array([-2,2,0.5]),np.array([-2,-2,0.5]),np.array([2,-2,0.5]), color = GREEN_C, fill_color = GREEN_C, fill_opacity = 0.3)
+ plane_0_5_lab = TextMobject("C = 0.5").move_to(0.8*UP+3.4*RIGHT).set_color(GREEN_C).scale(0.6)
+ circle_0_5 = Circle(radius = 1.224 , color = GREEN_C)
+ circle_0_5_lab = TextMobject("0.5").move_to(0.9*DOWN+0.9*RIGHT).set_color(GREEN_C).scale(0.6)
+ circle_0_5_copy = circle_0_5.copy().move_to(np.array([0,0,0.5]))
+
+ plane_1 = Polygon(np.array([2,-2,1]),np.array([2,2,1]),np.array([-2,2,1]),np.array([-2,-2,1]),np.array([2,-2,1]), color = YELLOW_C, fill_color = YELLOW_C, fill_opacity = 0.3)
+ plane_1_lab = TextMobject("C = 1").move_to(1.2*UP+3.3*RIGHT).set_color(YELLOW_C).scale(0.6)
+ circle_1 = Circle(radius = 1 , color = YELLOW_C)
+ circle_1_lab = TextMobject("1").move_to(0.7*DOWN+0.7*RIGHT).set_color(YELLOW_C).scale(0.6)
+ circle_1_copy = circle_1.copy().move_to(np.array([0,0,1]))
+
+ plane_1_5 = Polygon(np.array([2,-2,1.5]),np.array([2,2,1.5]),np.array([-2,2,1.5]),np.array([-2,-2,1.5]),np.array([2,-2,1.5]), color = ORANGE, fill_color = ORANGE, fill_opacity = 0.3)
+ plane_1_5_lab = TextMobject("C = 1.5").move_to(1.7*UP+3.4*RIGHT).set_color(ORANGE).scale(0.6)
+ circle_1_5 = Circle(radius = 0.707 , color = ORANGE)
+ circle_1_5_lab = TextMobject("1.5").move_to(0.5*DOWN+0.5*RIGHT).set_color(ORANGE).scale(0.6)
+ circle_1_5_copy = circle_1_5.copy().move_to(np.array([0,0,1.5]))
+
+ plane_2 = Polygon(np.array([2,-2,2]),np.array([2,2,2]),np.array([-2,2,2]),np.array([-2,-2,2]),np.array([2,-2,2]), color = RED_C, fill_color = RED_C, fill_opacity = 0.3)
+ plane_2_lab = TextMobject("C = 2").move_to(2.1*UP+3.3*RIGHT).set_color(RED_C).scale(0.6)
+ dot_2 = Dot().set_fill(RED_C)
+ circle_2_lab = TextMobject("2").move_to(0.2*DOWN+0.2*RIGHT).set_color(RED_C).scale(0.6)
+ dot_2_copy = dot_2.copy().move_to(np.array([0,0,2]))
+
+ vector1 = Arrow(np.array([0.99,-0.99,0]), np.array([0.865,-0.865,0.5]), buff=0.01, color = RED_C).set_stroke(width=3)
+ gradient1 = Arrow(np.array([0.99,-0.99,0]), np.array([0.865,-0.865,0]), buff=0.01, color = RED_C).set_stroke(width=3)
+
+ vector2 = Arrow(np.array([0.865,-0.865,0.5]), np.array([0.707,-0.707,1]), buff=0.01, color = RED_C).set_stroke(width=3)
+ gradient2 = Arrow(np.array([0.865,-0.865,0]), np.array([0.707,-0.707,0]), buff=0.01, color = RED_C).set_stroke(width=3)
+
+ vector3 = Arrow(np.array([0.707,-0.707,1]), np.array([0.499,-0.499,1.5]), buff=0.01, color = RED_C).set_stroke(width=3)
+ gradient3 = Arrow(np.array([0.707,-0.707,0]), np.array([0.499,-0.499,0]), buff=0.01, color = RED_C).set_stroke(width=3)
+
+ vector4 = Arrow(np.array([0.499,-0.499,1.5]), np.array([0,0,2]), buff=0.01, color = RED_C).set_stroke(width=3)
+ gradient4 = Arrow(np.array([0.499,-0.499,0]), np.array([0,0,0]), buff=0.01, color = RED_C).set_stroke(width=3)
+
+
+ self.set_camera_orientation(phi=80 * DEGREES, theta = 0*DEGREES)
+ #self.set_camera_orientation(phi=45 * DEGREES, theta = -20*DEGREES)
+
+ self.add(axes)
+
+ axis = TextMobject(r"X",r"Y",r"Z")
+ axis[0].move_to(6*RIGHT)
+ axis[1].move_to(6*UP)
+ axis[2].move_to(np.array([0,0,3.7]))
+
+ self.add_fixed_orientation_mobjects(axis[2])
+ self.add_fixed_orientation_mobjects(axis[0])
+ self.add_fixed_orientation_mobjects(axis[1])
+
+ self.play(Write(paraboloid))
+ self.wait()
+ self.play(ShowCreation(plane_0), ShowCreation(circle_0))
+ self.add_fixed_in_frame_mobjects(plane_0_lab)
+ self.wait()
+ self.play(ShowCreation(plane_0_5), ShowCreation(circle_0_5_copy), ShowCreation(circle_0_5))
+ self.add_fixed_in_frame_mobjects(plane_0_5_lab)
+ self.wait()
+ self.play(ShowCreation(plane_1), ShowCreation(circle_1_copy), ShowCreation(circle_1))
+ self.add_fixed_in_frame_mobjects(plane_1_lab)
+ self.wait()
+ self.play(ShowCreation(plane_1_5), ShowCreation(circle_1_5_copy), ShowCreation(circle_1_5))
+ self.add_fixed_in_frame_mobjects(plane_1_5_lab)
+ self.wait()
+ self.play(ShowCreation(plane_2), ShowCreation(dot_2_copy), ShowCreation(dot_2))
+ self.add_fixed_in_frame_mobjects(plane_2_lab)
+ self.wait()
+ self.move_camera(phi=60 * DEGREES, theta = 30*DEGREES,run_time=3)
+ self.play(FadeOut(plane_0), FadeOut(plane_0_lab), FadeOut(plane_0_5), FadeOut(plane_0_5_lab), FadeOut(plane_1), FadeOut(plane_1_lab), FadeOut(plane_1_5), FadeOut(plane_1_5_lab), FadeOut(plane_2), FadeOut(plane_2_lab))
+ self.play(FadeOut(circle_0_5_copy), FadeOut(circle_1_copy), FadeOut(circle_1_5_copy), FadeOut(dot_2_copy))
+
+ self.move_camera(phi=45 * DEGREES, theta = -20*DEGREES,run_time=3)
+ self.play(Write(vector1), Write(gradient1))
+ self.wait()
+ self.play(Write(vector2), Write(gradient2))
+ self.wait()
+ self.play(Write(vector3), Write(gradient3))
+ self.wait()
+ self.play(Write(vector4), Write(gradient4))
+ self.wait()
+ self.move_camera(phi=0 * DEGREES, theta = 0*DEGREES,run_time=3)
+ self.play(FadeOut(paraboloid))
+ self.play(FadeOut(vector1), FadeOut(vector2), FadeOut(vector3), FadeOut(vector4))
+ self.wait()
+ self.add_fixed_in_frame_mobjects(circle_0_lab, circle_0_5_lab, circle_1_lab, circle_1_5_lab,circle_2_lab)
+ self.wait(4)
+
\ No newline at end of file diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/gifs/file1_directional_deriv.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/gifs/file1_directional_deriv.gif Binary files differnew file mode 100644 index 0000000..39305d5 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/gifs/file1_directional_deriv.gif diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/gifs/file2_gradient.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/gifs/file2_gradient.gif Binary files differnew file mode 100644 index 0000000..d96f330 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/gifs/file2_gradient.gif diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/gifs/file3_gradient_level_curves.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/gifs/file3_gradient_level_curves.gif Binary files differnew file mode 100644 index 0000000..f1bf06a --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/gifs/file3_gradient_level_curves.gif diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file1_epsilon_delta_defn.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file1_epsilon_delta_defn.py deleted file mode 100644 index 63b6165..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file1_epsilon_delta_defn.py +++ /dev/null @@ -1,120 +0,0 @@ -from manimlib.imports import *
-
-class EpsilonDelta(ThreeDScene):
- def construct(self):
- axes = ThreeDAxes() # creates a 3D Axis
-
-
- sphere = ParametricSurface(
- lambda u, v: np.array([
- 2*np.sin(u)*np.cos(v),
- 2*np.sin(u)*np.sin(v),
- 2*np.cos(u)
- ]),u_min=0,u_max=PI/4,v_min=0,v_max=PI/2,checkerboard_colors=[RED_D, RED_E],
- resolution=(15, 32)).scale(2)
- #sphere.shift(0.5*RIGHT+0.5*UP)
-
- #self.set_camera_orientation(phi=0*DEGREES,theta=270*DEGREES)
- self.set_camera_orientation(phi=75 * DEGREES)
-
-
-
- circle = Circle(radius= 0.4,color = GREEN)
- circle.shift(0.5*RIGHT+0.5*UP)
-
- line1 = DashedLine(np.array([0.5, 0.1,0]), np.array([0.5, 0.1,2.1]), color = BLUE_E)
- line2 = DashedLine(np.array([0.5, 0.9,0]), np.array([0.5, 0.9,1.7]), color = BLUE_E)
- line3 = DashedLine(np.array([0, 0,2.1]), np.array([0.5, 0.1,2.1]), color = YELLOW_C)
- line4 = DashedLine(np.array([0, 0,1.7]), np.array([0.5, 0.9,1.7]), color = YELLOW_C)
-
- dot1 = Sphere()
- dot1.scale(0.01)
- dot1.move_to(np.array([0,0,1.9]))
- dot1.set_fill(BLUE_E)
-
- temp_func1 = TextMobject(r"$L$")
- temp_func1.scale(0.6)
- temp_func1.set_color(BLUE_E)
-
- dot2 = Sphere()
- dot2.scale(0.01)
- dot2.move_to(np.array([0,0,1.7]))
- dot2.set_fill(PURPLE)
-
- temp_func2 = TextMobject(r"$L - \epsilon$")
- temp_func2.scale(0.6)
- temp_func2.set_color(PURPLE)
-
- dot3 = Sphere()
- dot3.scale(0.01)
- dot3.move_to(np.array([0,0,2.1]))
- dot3.set_fill(PURPLE)
-
- temp_func3 = TextMobject(r"$L + \epsilon$")
- temp_func3.scale(0.6)
- temp_func3.set_color(PURPLE)
-
- self.add(axes)
-
- self.play(ShowCreation(dot1))
- self.add_fixed_in_frame_mobjects(temp_func1)
- temp_func1.move_to(1.9*UP)
- self.play(Write(temp_func1))
-
- self.play(ShowCreation(dot2))
- self.add_fixed_in_frame_mobjects(temp_func2)
- temp_func2.move_to(1.7*UP)
- self.play(Write(temp_func2))
-
- self.play(ShowCreation(dot3))
- self.add_fixed_in_frame_mobjects(temp_func3)
- temp_func3.move_to(2.1*UP)
- self.play(Write(temp_func3))
-
-
- circle_center = Sphere()
- circle_center.scale(0.05)
- circle_center.move_to(np.array([0.5,0.5,0]))
- circle_center.set_fill(GREEN)
-
- temp_circle_center = TextMobject(r"$(a,b,0)$")
- temp_circle_center.scale(0.5)
- temp_circle_center.set_color(GREEN)
-
- curve_circle_center = Sphere()
- curve_circle_center.scale(0.05)
- curve_circle_center.move_to(np.array([0.5,0.5,1.9]))
- curve_circle_center.set_fill(BLUE_E)
-
- temp_curve_circle_center = TextMobject(r"$(a,b,L)$")
- temp_curve_circle_center.scale(0.5)
- temp_curve_circle_center.set_color(BLUE)
-
- delta_lab = TextMobject(r"$\delta - disk$")
- delta_lab.scale(0.5)
- delta_lab.set_color(PINK)
-
- self.play(ShowCreation(circle_center))
- self.add_fixed_in_frame_mobjects(temp_circle_center)
- temp_circle_center.move_to(1.5*RIGHT)
- self.play(Write(temp_circle_center))
-
- self.play(ShowCreation(curve_circle_center))
- self.add_fixed_in_frame_mobjects(temp_curve_circle_center)
- temp_curve_circle_center.move_to(1.9*UP+1*RIGHT)
- self.play(Write(temp_curve_circle_center))
-
-
- self.add_fixed_in_frame_mobjects(delta_lab)
- delta_lab.move_to(0.4*DOWN+1.7*RIGHT)
- self.play(Write(delta_lab))
-
-
-
-
-
- self.begin_ambient_camera_rotation(rate=0.2)
- self.play(Write(sphere))
- self.play(ShowCreation(circle), ShowCreation(line1), ShowCreation(line2))
- self.play(ShowCreation(line3), ShowCreation(line4))
- self.wait(8)
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file3_limit_func.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file3_limit_func.py deleted file mode 100644 index 02e00e8..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file3_limit_func.py +++ /dev/null @@ -1,30 +0,0 @@ -from manimlib.imports import *
-
-class LimitFunc(ThreeDScene):
- def construct(self):
- axes = ThreeDAxes()
-
- text3d = TextMobject(r"$f(x,y) = \frac{x^2 - y^2}{x^2 + y^2}$")
- self.add_fixed_in_frame_mobjects(text3d)
-
- text3d.to_corner(UL)
-
- text3d.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
-
- self.play(Write(text3d))
- self.wait(1)
-
- limit_func = ParametricSurface(
- lambda u, v: np.array([
- u*np.cos(v),
- u*np.sin(v),
- (np.cos(v)*np.cos(v) - np.sin(v)*np.sin(v))/3
- ]),u_min=-3,u_max=3,v_min=0,v_max=2*PI,checkerboard_colors=[YELLOW_C, YELLOW_E],
- resolution=(15, 32)).scale(2)
-
- self.set_camera_orientation(phi=80 * DEGREES)
- self.begin_ambient_camera_rotation(rate=0.3)
-
- self.add(axes)
- self.play(Write(limit_func))
- self.wait(10)
\ No newline at end of file diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file4_continuity_func.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file4_continuity_func.py deleted file mode 100644 index 551c8a8..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file4_continuity_func.py +++ /dev/null @@ -1,32 +0,0 @@ -from manimlib.imports import *
-
-class ContinuityFunc(ThreeDScene):
- def construct(self):
- axes = ThreeDAxes()
-
- text3d = TextMobject(r"$f(x,y) = \frac{3x^2y}{x^2 + y^2}$")
- self.add_fixed_in_frame_mobjects(text3d)
-
- text3d.to_corner(UL)
-
- text3d.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
-
- self.play(Write(text3d))
- self.wait(1)
-
- continuity_func = ParametricSurface(
- lambda u, v: np.array([
- u*np.cos(v),
- u*np.sin(v),
- 3*u*np.cos(v)*np.cos(v)*np.sin(v)
- ]),u_min=-1.5,u_max=1.5,v_min=0,v_max=2*PI,checkerboard_colors=[YELLOW_C, YELLOW_E],
- resolution=(15, 32)).scale(2)
-
-
-
- self.set_camera_orientation(phi=80 * DEGREES)
- self.begin_ambient_camera_rotation(rate=0.3)
-
- self.add(axes)
- self.play(Write(continuity_func))
- self.wait(8)
\ No newline at end of file diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file1_epsilon_delta_defn.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file1_epsilon_delta_defn.gif Binary files differdeleted file mode 100644 index 68f637e..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file1_epsilon_delta_defn.gif +++ /dev/null diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file2_limit_approach_point.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file2_limit_approach_point.gif Binary files differdeleted file mode 100644 index 830b6f1..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file2_limit_approach_point.gif +++ /dev/null diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file3_limit_func.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file3_limit_func.gif Binary files differdeleted file mode 100644 index 07b23be..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file3_limit_func.gif +++ /dev/null diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file4_continuity_func.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file4_continuity_func.gif Binary files differdeleted file mode 100644 index 560e0f1..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file4_continuity_func.gif +++ /dev/null diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/README.md b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/README.md new file mode 100644 index 0000000..0e6e8d3 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/README.md @@ -0,0 +1,17 @@ +**file1_multivar_func_examples** + + +**file2_multivariable_func_respresentation** + + +**file3_sphere** + + +**file4_vectorvf_sine** + + +**file5_vectorvf_helix** + + +**file6_derivative_vectorvf** + diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file1_multivar_func_examples.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file1_multivar_func_examples.py new file mode 100644 index 0000000..55b2b7e --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file1_multivar_func_examples.py @@ -0,0 +1,167 @@ +from manimlib.imports import *
+
+class Examples1(GraphScene):
+ def construct(self):
+
+ rectangle = Rectangle(height = 3, width = 4, color = GREEN)
+ rectangle_area_func = TexMobject("Area", "=", "f(", "Length", ",", "Breadth", ")").scale(0.6)
+ rectangle_area_func[0].set_color(RED_C)
+ rectangle_area_func[2].set_color(ORANGE)
+ rectangle_area_func[3].set_color(YELLOW_C)
+ rectangle_area_func[5].set_color(BLUE_C)
+ rectangle_area_func[6].set_color(ORANGE)
+
+
+ rectangle_area = TexMobject("Area", "=", "Length", "\\times", "Breadth").scale(0.6)
+ rectangle_area[0].set_color(RED_C)
+ rectangle_area[2].set_color(YELLOW_C)
+ rectangle_area[4].set_color(BLUE_C)
+
+
+ square = Square(side_length = 5, color = PURPLE)
+ square_area_func = TexMobject("Area", "=", "f(", "Length", ")")
+ square_area_func[0].set_color(GREEN_C)
+ square_area_func[2].set_color(ORANGE)
+ square_area_func[3].set_color(BLUE_C)
+ square_area_func[4].set_color(ORANGE)
+
+ square_area = TexMobject("Area", "=", "Length^2")
+ square_area[0].set_color(GREEN_C)
+ square_area[2].set_color(BLUE_C)
+
+
+ circle = Circle(radius = 2, color = PINK)
+ circle_area_func = TexMobject("Area", "=", "f(", "r", ")")
+ circle_area_func[0].set_color(YELLOW_C)
+ circle_area_func[2].set_color(ORANGE)
+ circle_area_func[3].set_color(GREEN_C)
+ circle_area_func[4].set_color(ORANGE)
+
+ circle_area = TexMobject("Area", "=", "\\pi", "r^2")
+ circle_area[0].set_color(YELLOW_C)
+ circle_area[2].set_color(BLUE_C)
+ circle_area[3].set_color(GREEN_C)
+
+ radius = Line(ORIGIN,2*RIGHT, color = RED_C)
+
+
+
+ braces_rect1 = Brace(rectangle, LEFT)
+ eq_text1 = braces_rect1.get_text("Length").set_color(YELLOW_C)
+ braces_rect2 = Brace(rectangle, UP)
+ eq_text2 = braces_rect2.get_text("Breadth").set_color(BLUE_C)
+
+ braces_square = Brace(square, LEFT)
+ braces_square_text = braces_square.get_text("Length").set_color(BLUE_C)
+
+ radius_text = TexMobject("r", color = GREEN_C).next_to(radius,UP)
+
+
+
+ self.play(ShowCreation(rectangle))
+ self.wait(1)
+ self.play(GrowFromCenter(braces_rect1),Write(eq_text1),GrowFromCenter(braces_rect2),Write(eq_text2))
+ self.wait(1)
+ self.play(Write(rectangle_area_func))
+ self.wait(1)
+ self.play(Transform(rectangle_area_func, rectangle_area))
+ self.wait(1)
+ self.play(FadeOut(braces_rect1),FadeOut(eq_text1),FadeOut(braces_rect2),FadeOut(eq_text2),FadeOut(rectangle_area_func))
+
+
+ self.play(Transform(rectangle, square))
+ self.wait(1)
+ self.play(GrowFromCenter(braces_square),Write(braces_square_text))
+ self.wait(1)
+ self.play(Write(square_area_func))
+ self.wait(1)
+ self.play(Transform(square_area_func, square_area))
+ self.wait(1)
+ self.play(FadeOut(braces_square),FadeOut(braces_square_text),FadeOut(square_area_func))
+
+
+ self.play(Transform(rectangle, circle))
+ self.wait(1)
+ self.play(ShowCreation(radius),Write(radius_text))
+ self.wait(1)
+ self.play(FadeOut(radius_text),FadeOut(radius))
+ self.wait(1)
+ self.play(Write(circle_area_func))
+ self.wait(1)
+ self.play(Transform(circle_area_func, circle_area))
+ self.wait(1)
+ self.play(FadeOut(circle_area_func))
+
+
+
+class Examples2(ThreeDScene):
+ def construct(self):
+ axes = ThreeDAxes()
+
+ rectangle_x_y_0 = Polygon(np.array([-1,-2,0]),np.array([-1,2,0]),np.array([1,2,0]),np.array([1,-2,0]),np.array([-1,-2,0]), color = RED_E, fill_color = RED_C, fill_opacity = 0.1)
+ rectangle_x_y_3 = Polygon(np.array([-1,-2,3]),np.array([-1,2,3]),np.array([1,2,3]),np.array([1,-2,3]),np.array([-1,-2,3]), color = RED_E, fill_color = RED_C, fill_opacity = 0.1)
+
+ rectangle_y_z_1 = Polygon(np.array([1,-2,3]),np.array([1,2,3]),np.array([1,2,0]),np.array([1,-2,0]),np.array([1,-2,3]), color = RED_E, fill_color = RED_C, fill_opacity = 0.1)
+ rectangle_y_z_minus_1 = Polygon(np.array([-1,-2,3]),np.array([-1,2,3]),np.array([-1,2,0]),np.array([-1,-2,0]),np.array([-1,-2,3]), color = RED_E, fill_color = RED_C, fill_opacity = 0.1)
+
+ rectangle_x_z_2 = Polygon(np.array([1,2,3]),np.array([-1,2,3]),np.array([-1,2,0]),np.array([1,2,0]),np.array([1,2,3]), color = RED_E, fill_color = RED_C, fill_opacity = 0.1)
+ rectangle_x_z_minus_2 = Polygon(np.array([1,-2,3]),np.array([-1,-2,3]),np.array([-1,-2,0]),np.array([1,-2,0]),np.array([1,-2,3]), color = RED_E, fill_color = RED_C, fill_opacity = 0.1)
+
+ box = VGroup(rectangle_x_y_0, rectangle_x_y_3, rectangle_y_z_1, rectangle_y_z_minus_1, rectangle_x_z_2, rectangle_x_z_minus_2)
+
+ braces_rectangle_x_y_0 = Line(np.array([1,2,0]), np.array([1,-2,0]), color = BLUE_C)
+ braces_rectangle_x_y_0_text = TextMobject("Length").set_color(BLUE_C).move_to(np.array([2,-1,0]))
+
+ braces_rectangle_y_z_1 = Line(np.array([1,2,0]), np.array([1,2,3]), color = YELLOW_C)
+ braces_rectangle_y_z_1_text = TextMobject("Height").set_color(YELLOW_C).move_to(np.array([2,3.8,2]))
+
+ braces_rectangle_x_z_2 = Line(np.array([1,2,3]), np.array([-1,2,3]), color = PURPLE)
+ braces_rectangle_x_z_2_text = TextMobject("Breadth").set_color(PURPLE).move_to(np.array([0,3.8,3.3]))
+
+ box_area_func = TexMobject("Area =", "f(", "Length", ",", "Breadth", ",", "Height", ")").move_to(4*LEFT+3.5*UP).scale(0.6)
+ box_area_func[0].set_color(GREEN_C)
+ box_area_func[1].set_color(ORANGE)
+ box_area_func[2].set_color(BLUE_C)
+ box_area_func[4].set_color(PURPLE)
+ box_area_func[6].set_color(YELLOW_C)
+ box_area_func[7].set_color(ORANGE)
+
+ box_area_func_2 = TexMobject("Area =", "Length", "\\times", "Breadth", "\\times", "Height").move_to(4*LEFT+3.5*UP).scale(0.6)
+ box_area_func_2[0].set_color(GREEN_C)
+ box_area_func_2[1].set_color(BLUE_C)
+ box_area_func_2[3].set_color(PURPLE)
+ box_area_func_2[5].set_color(YELLOW_C)
+
+
+ self.set_camera_orientation(phi=70 * DEGREES, theta = 45*DEGREES)
+
+ self.add(axes)
+
+ axis = TextMobject(r"X",r"Y",r"Z")
+ axis[0].move_to(6*RIGHT)
+ axis[1].move_to(6*UP)
+ axis[2].move_to(3.7*UP)
+
+ self.add_fixed_in_frame_mobjects(axis[2])
+ self.add_fixed_orientation_mobjects(axis[0])
+ self.add_fixed_orientation_mobjects(axis[1])
+
+ self.play(ShowCreation(box), ShowCreation(braces_rectangle_x_y_0))
+ self.add_fixed_orientation_mobjects(braces_rectangle_x_y_0_text)
+ self.play(ShowCreation(braces_rectangle_y_z_1))
+ self.add_fixed_orientation_mobjects(braces_rectangle_y_z_1_text)
+ self.play(ShowCreation(braces_rectangle_x_z_2))
+ self.add_fixed_orientation_mobjects(braces_rectangle_x_z_2_text)
+ self.wait(2)
+
+ self.move_camera(phi=60* DEGREES,theta=80*DEGREES)
+ self.add_fixed_in_frame_mobjects(box_area_func)
+ self.play(Write(box_area_func))
+ self.wait()
+
+
+ self.play(ReplacementTransform(box_area_func,box_area_func_2))
+ self.add_fixed_in_frame_mobjects(box_area_func_2)
+
+
+ self.wait(3)
\ No newline at end of file diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file1_multivariable_func_respresentation.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file1_multivariable_func_respresentation.py deleted file mode 100644 index 4bfcf21..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file1_multivariable_func_respresentation.py +++ /dev/null @@ -1,80 +0,0 @@ -from manimlib.imports import *
-
-class MultivariableFunc(Scene):
- def construct(self):
-
- topic = TextMobject("Multivariable Functions")
- topic.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
- topic.scale(2)
-
- self.play(Write(topic))
- self.wait(1)
- self.play(FadeOut(topic))
-
-
- circle = Circle()
- circle.scale(3)
-
- eqn1 = TextMobject(r"f(x,y) = $x^2y$")
- eqn1.set_color(YELLOW)
-
-
-
- number1 = TextMobject("(2,1)")
- number1.move_to(3*UP+ 3*LEFT)
- number1.scale(1.2)
- number1.set_color(GREEN)
-
- output1 = TextMobject("4")
- output1.scale(1.5)
- output1.set_color(BLUE)
-
- eqn1_1 = TextMobject(r"f(2,1) = $2^2(1)$")
- eqn1_1.set_color(YELLOW)
-
-
- self.play(ShowCreation(circle),Write(eqn1))
- self.wait(1)
- self.play(ApplyMethod(number1.move_to, 0.6*LEFT))
- self.play(FadeOut(number1))
- self.play(Transform(eqn1, eqn1_1))
- self.wait(1)
- self.play(ApplyMethod(output1.move_to, 3*DOWN+4*RIGHT))
- self.wait(1)
- self.play(FadeOut(output1))
-
-
- eqn2 = TextMobject(r"f(x,y,z) = $x^2y+2yz$")
- eqn2.set_color(YELLOW)
-
- number2 = TextMobject("(2,1,3)")
- number2.move_to(3*UP+ 3*LEFT)
- number2.scale(1.2)
- number2.set_color(GREEN)
-
- output2 = TextMobject("8")
- output2.scale(1.5)
- output2.set_color(BLUE)
-
- eqn2_1 = TextMobject(r"f(2,1,3) = $2^2(1) + 2(1)(3)$")
- eqn2_1.set_color(YELLOW)
-
- eqn2_2 = TextMobject(r"f(2,1,3) = $2 + 6$")
- eqn2_2.set_color(YELLOW)
-
-
-
- self.play(FadeOut(eqn1))
- self.play(Write(eqn2))
-
- self.wait(1)
- self.play(ApplyMethod(number2.move_to, 1.2*LEFT))
- self.play(FadeOut(number2))
- self.play(Transform(eqn2, eqn2_1))
- self.wait(1)
- self.play(Transform(eqn2, eqn2_2))
- self.wait(1)
- self.play(ApplyMethod(output2.move_to, 3*DOWN+4*RIGHT))
- self.wait(1)
- self.play(FadeOut(output2),FadeOut(eqn2),FadeOut(circle))
- self.wait(2)
\ No newline at end of file diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file2_multivariable_func_examples.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file2_multivariable_func_examples.py deleted file mode 100644 index 7322e47..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file2_multivariable_func_examples.py +++ /dev/null @@ -1,69 +0,0 @@ -from manimlib.imports import *
-
-class Examples(GraphScene):
- def construct(self):
-
- rectangle = Rectangle(height = 3, width = 4, color = GREEN)
- square = Square(side_length = 5, color = PURPLE)
- circle = Circle(radius = 2, color = PINK)
- radius = Line(ORIGIN,2*RIGHT)
-
- radius.set_color(RED)
-
- rectangle_area_func = TextMobject(r"$Area = f(Length, Breadth)$")
- rectangle_area_func.scale(0.6)
- square_area_func = TextMobject(r"$Area = f(Length)$")
- circle_area_func = TextMobject(r"$Area = f(r)$")
-
-
- rectangle_area = TextMobject(r"$Area = Length \times Breadth$")
- rectangle_area.scale(0.6)
- square_area = TextMobject(r"$Area = Length^2$")
- circle_area = TextMobject(r"$Area = \pi r^2$")
-
- braces_rect1 = Brace(rectangle, LEFT)
- eq_text1 = braces_rect1.get_text("Length")
- braces_rect2 = Brace(rectangle, UP)
- eq_text2 = braces_rect2.get_text("Breadth")
-
- braces_square = Brace(square, LEFT)
- braces_square_text = braces_square.get_text("Length")
-
- radius_text = TextMobject("r")
- radius_text.next_to(radius,UP)
-
-
-
- self.play(ShowCreation(rectangle))
- self.wait(1)
- self.play(GrowFromCenter(braces_rect1),Write(eq_text1),GrowFromCenter(braces_rect2),Write(eq_text2))
- self.wait(1)
- self.play(Write(rectangle_area_func))
- self.wait(1)
- self.play(Transform(rectangle_area_func, rectangle_area))
- self.wait(1)
- self.play(FadeOut(braces_rect1),FadeOut(eq_text1),FadeOut(braces_rect2),FadeOut(eq_text2),FadeOut(rectangle_area_func))
-
-
- self.play(Transform(rectangle, square))
- self.wait(1)
- self.play(GrowFromCenter(braces_square),Write(braces_square_text))
- self.wait(1)
- self.play(Write(square_area_func))
- self.wait(1)
- self.play(Transform(square_area_func, square_area))
- self.wait(1)
- self.play(FadeOut(braces_square),FadeOut(braces_square_text),FadeOut(square_area_func))
-
-
- self.play(Transform(rectangle, circle))
- self.wait(1)
- self.play(ShowCreation(radius),Write(radius_text))
- self.wait(1)
- self.play(FadeOut(radius_text),FadeOut(radius))
- self.wait(1)
- self.play(Write(circle_area_func))
- self.wait(1)
- self.play(Transform(circle_area_func, circle_area))
- self.wait(1)
- self.play(FadeOut(circle_area_func))
\ No newline at end of file diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file2_multivariable_func_respresentation.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file2_multivariable_func_respresentation.py new file mode 100644 index 0000000..d10ff0a --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file2_multivariable_func_respresentation.py @@ -0,0 +1,98 @@ +from manimlib.imports import *
+
+class MultivariableFunc(Scene):
+ def construct(self):
+
+ topic = TextMobject("Multivariable Functions")
+ topic.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
+ topic.scale(1.5)
+
+ self.play(Write(topic))
+ self.wait()
+ self.play(FadeOut(topic))
+
+
+ #circle = Circle()
+ #circle.scale(3)
+
+ scalar_function = TextMobject("Scalar Valued Function")
+ scalar_function.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
+ scalar_function.scale(1.5)
+ scalar_function.move_to(2.5*UP)
+
+ rectangle = Rectangle(height = 2, width = 4)
+ rectangle.set_color(PURPLE)
+
+ eqn1 = TextMobject(r"f(x,y) = $x^2y$")
+ eqn1.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE)
+
+
+
+ number1 = TextMobject("(2,1)")
+ number1.move_to(2.5*UP+ 4*LEFT)
+ number1.scale(1.2)
+ number1.set_color(ORANGE)
+
+ output1 = TextMobject("4")
+ output1.scale(1.5)
+ output1.set_color(BLUE_C)
+ output1.move_to(3*RIGHT)
+
+ eqn1_1 = TextMobject(r"f(2,1) = $2^2(1)$")
+ eqn1_1.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE)
+
+
+ self.play(Write(eqn1),ShowCreation(rectangle))
+ self.wait()
+ self.play(ApplyMethod(number1.move_to, 3*LEFT))
+ self.play(FadeOut(number1))
+ self.play(Transform(eqn1, eqn1_1))
+ self.wait()
+ self.play(ApplyMethod(output1.move_to, 2.5*DOWN+4*RIGHT))
+ self.wait()
+ self.play(Write(scalar_function))
+ self.play(FadeOut(output1), FadeOut(scalar_function), FadeOut(eqn1))
+
+
+ vector_function = TextMobject("Vector Valued Function")
+ vector_function.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
+ vector_function.scale(1.5)
+ vector_function.move_to(2.5*UP)
+
+
+ eqn2 = TextMobject(r"f(x,y,z) = $ \begin{bmatrix} x^2y \\ 2yz \end{bmatrix}$")
+ eqn2.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
+
+ number2 = TextMobject("(2,1,3)")
+ number2.move_to(2.5*UP+ 4*LEFT)
+ number2.scale(1.2)
+ number2.set_color(ORANGE)
+
+ output2 = TextMobject(r"$ \begin{bmatrix} 4 \\ 6 \end{bmatrix}$")
+ #output2.scale(1.5)
+ output2.set_color(BLUE_C)
+ output2.move_to(3*RIGHT)
+
+ #eqn2_1 = TextMobject(r"f(2,1,3) = $2^2(1) + 2(1)(3)$")
+ #eqn2_1.set_color(YELLOW)
+
+ #eqn2_2 = TextMobject(r"f(2,1,3) = $2 + 6$")
+ #eqn2_2.set_color(YELLOW)
+
+
+ self.play(Write(eqn2))
+
+ self.wait()
+ self.play(ApplyMethod(number2.move_to, 3*LEFT))
+ self.play(FadeOut(number2))
+
+ #self.play(Transform(eqn2, eqn2_1))
+ #self.wait(1)
+ #self.play(Transform(eqn2, eqn2_2))
+ #self.wait(1)
+
+ self.play(ApplyMethod(output2.move_to, 2.5*DOWN+4*RIGHT))
+ self.wait()
+ self.play(Write(vector_function))
+ self.play(FadeOut(output2),FadeOut(eqn2), FadeOut(vector_function), FadeOut(rectangle))
+ self.wait()
\ No newline at end of file diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file3_plot_sphere.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file3_plot_sphere.py deleted file mode 100644 index baf08b1..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file3_plot_sphere.py +++ /dev/null @@ -1,42 +0,0 @@ -from manimlib.imports import *
-
-class Sphere(ThreeDScene):
- def construct(self):
- axes = ThreeDAxes() # creates a 3D Axis
-
- sphere = ParametricSurface(
- lambda u, v: np.array([
- np.sin(u)*np.cos(v),
- np.sin(u)*np.sin(v),
- np.cos(u)
- ]),u_min=0,u_max=PI,v_min=0,v_max=2*PI,checkerboard_colors=[RED_D, RED_E],
- resolution=(15, 32)).scale(2)
-
-
-
- #self.set_camera_orientation(phi=0 * DEGREES,theta=270*DEGREES)
-
- text3d = TextMobject(r"$f(x,y) \rightarrow Point(x,y,z)$")
- text3d1 = TextMobject(r"$f(x,y) \rightarrow Point(x,y, 1 - x^2 - y^2)$")
- self.add_fixed_in_frame_mobjects(text3d)
- text3d.scale(0.7)
- text3d1.scale(0.7)
- text3d.to_corner(UL)
- text3d1.to_corner(UL)
- text3d.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
- text3d1.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
- self.play(Write(text3d))
- self.wait(1)
-
- self.play(Transform(text3d,text3d1))
- self.add_fixed_in_frame_mobjects(text3d1)
- self.play(FadeOut(text3d))
-
-
- self.set_camera_orientation(phi=75 * DEGREES)
- self.begin_ambient_camera_rotation(rate=0.3)
-
-
- self.add(axes)
- self.play(Write(sphere))
- self.wait(5)
\ No newline at end of file diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file3_sphere.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file3_sphere.py new file mode 100644 index 0000000..86239ae --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file3_sphere.py @@ -0,0 +1,177 @@ +from manimlib.imports import *
+
+class Sphere(ThreeDScene):
+ def construct(self):
+ axes = ThreeDAxes() # creates a 3D Axis
+
+ text3d = TextMobject(r"$f(x,y) \rightarrow Point(x,y,z)$")
+ text3d1 = TextMobject(r"$f(x,y) \rightarrow Point(x,y, \sqrt{r^2 - x^2 - y^2})$")
+ self.add_fixed_in_frame_mobjects(text3d)
+ text3d.scale(0.7)
+ text3d1.scale(0.7)
+ text3d.to_corner(UL)
+ text3d1.to_corner(UL)
+ text3d.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
+ text3d1.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
+ self.play(Write(text3d))
+ self.wait(1)
+
+ self.play(Transform(text3d,text3d1))
+ self.add_fixed_in_frame_mobjects(text3d1)
+ self.play(FadeOut(text3d))
+
+ sphere = ParametricSurface(
+ lambda u, v: np.array([
+ 2*np.sin(u)*np.cos(v),
+ 2*np.sin(u)*np.sin(v),
+ 2*np.cos(u)
+ ]),u_min=0,u_max=PI,v_min=0,v_max=2*PI,checkerboard_colors=[RED_D, RED_E],
+ resolution=(15, 32)).scale(1)
+
+
+ #Experiment with circles by changing difference value of u and v
+ '''
+ sphere_points = [np.array([2*np.sin(u*DEGREES)*np.cos(v*DEGREES), 2*np.sin(u*DEGREES)*np.sin(v*DEGREES), 2*np.cos(u*DEGREES)]) for u in range(0, 185, 5) for v in range(0, 365, 5)]
+
+ sphere_spheres = [Dot().move_to(pts) for pts in sphere_points]
+
+ sphere = VGroup(*sphere_spheres)
+ '''
+
+ self.set_camera_orientation(phi=75 * DEGREES, theta = 45*DEGREES)
+
+ self.add(axes)
+
+ axis = TextMobject(r"X",r"Y",r"Z")
+ axis[0].move_to(6*RIGHT)
+ axis[1].move_to(6*UP)
+ axis[2].move_to(np.array([0,0,3.7]))
+
+ self.add_fixed_orientation_mobjects(axis[2])
+ self.add_fixed_orientation_mobjects(axis[0])
+ self.add_fixed_orientation_mobjects(axis[1])
+
+ dot_x_y1 = Dot().scale(0.75).set_fill(RED_C).move_to(np.array([-1,1,0]))
+ dot_x_y_z1 = Dot().scale(0.75).set_fill(RED_C).move_to(np.array([-1,1,1.414]))
+ dot_x_y_z_1 = Dot().scale(0.75).set_fill(RED_C).move_to(np.array([-1,1,-1.414]))
+ line1 = DashedLine(np.array([-1,1,-1.414]), np.array([-1,1,1.414]), color = YELLOW_C)
+
+ point_x_y1 = TexMobject("(-1,1,0)").set_color(BLUE_C).move_to(np.array([-1.5,1.5,0])).scale(0.5)
+ point_x_y_z1 = TexMobject("(-1,1,\\sqrt{r^2 - x^2 - y^2})").set_color(BLUE_C).move_to(np.array([-1.5,1.5,1.414])).scale(0.5)
+ point_x_y_z1_2 = TexMobject("(-1,1,\\sqrt{4 - x^2 - y^2})").set_color(BLUE_C).move_to(np.array([-1.5,1.5,1.414])).scale(0.5)
+ point_x_y_z1_3 = TexMobject("(-1,1,\\sqrt{4 - 1 - 1})").set_color(BLUE_C).move_to(np.array([-1.5,1.5,1.414])).scale(0.5)
+ point_x_y_z1_4 = TexMobject("(-1,1,\\sqrt{2})").set_color(BLUE_C).move_to(np.array([-1.5,1.5,1.414])).scale(0.5)
+ point_x_y_z1_5 = TexMobject("(-1,1,1.414)").set_color(BLUE_C).move_to(np.array([-1.5,1.5,1.414])).scale(0.5)
+
+ point_x_y_z_1 = TexMobject("(-1,1,\\sqrt{r^2 - x^2 - y^2})").set_color(BLUE_C).move_to(np.array([-1.5,1.5,-1.414])).scale(0.5)
+ point_x_y_z_1_2 = TexMobject("(-1,1,\\sqrt{4 - x^2 - y^2})").set_color(BLUE_C).move_to(np.array([-1.5,1.5,-1.414])).scale(0.5)
+ point_x_y_z_1_3 = TexMobject("(-1,1,\\sqrt{4 - 1 - 1})").set_color(BLUE_C).move_to(np.array([-1.5,1.5,-1.414])).scale(0.5)
+ point_x_y_z_1_4 = TexMobject("(-1,1,\\sqrt{2})").set_color(BLUE_C).move_to(np.array([-1.5,1.5,-1.414])).scale(0.5)
+ point_x_y_z_1_5 = TexMobject("(-1,1,-1.414)").set_color(BLUE_C).move_to(np.array([-1.5,1.5,-1.414])).scale(0.5)
+
+
+ self.play(ShowCreation(dot_x_y1))
+ self.add_fixed_orientation_mobjects(point_x_y1)
+ self.play(ShowCreation(dot_x_y_z1), ShowCreation(dot_x_y_z_1), ShowCreation(line1))
+ self.add_fixed_orientation_mobjects(point_x_y_z1, point_x_y_z_1)
+ self.wait(0.5)
+ self.play(ReplacementTransform(point_x_y_z1,point_x_y_z1_2), ReplacementTransform(point_x_y_z_1,point_x_y_z_1_2))
+ self.add_fixed_orientation_mobjects(point_x_y_z1_2, point_x_y_z_1_2)
+
+ self.wait(0.5)
+ self.play(ReplacementTransform(point_x_y_z1_2,point_x_y_z1_3), ReplacementTransform(point_x_y_z_1_2,point_x_y_z_1_3))
+ self.add_fixed_orientation_mobjects(point_x_y_z1_3, point_x_y_z_1_3)
+ self.wait(0.5)
+ self.play(ReplacementTransform(point_x_y_z1_3,point_x_y_z1_4), ReplacementTransform(point_x_y_z_1_3,point_x_y_z_1_4))
+ self.add_fixed_orientation_mobjects(point_x_y_z1_4, point_x_y_z_1_4)
+ self.wait(0.5)
+ self.play(ReplacementTransform(point_x_y_z1_4,point_x_y_z1_5), ReplacementTransform(point_x_y_z_1_4,point_x_y_z_1_5))
+ self.add_fixed_orientation_mobjects(point_x_y_z1_5, point_x_y_z_1_5)
+
+
+
+ dot_x_y2 = Dot().scale(0.75).set_fill(RED_C).move_to(np.array([0.5,-0.5,0]))
+ dot_x_y_z2 = Dot().scale(0.75).set_fill(RED_C).move_to(np.array([0.5,-0.5,1.87]))
+ dot_x_y_z_2 = Dot().scale(0.75).set_fill(RED_C).move_to(np.array([0.5,-0.5,-1.87]))
+ line2 = DashedLine(np.array([0.5,-0.5,-1.87]), np.array([0.5,-0.5,1.87]), color = YELLOW_C)
+
+ point_x_y2 = TexMobject("(0.5,-0.5,0)").set_color(BLUE_C).move_to(np.array([1.5,-1.5,0])).scale(0.5)
+ point_x_y_z2 = TexMobject("(0.5,-0.5,\\sqrt{r^2 - x^2 - y^2})").set_color(BLUE_C).move_to(np.array([1.5,-1.5,1.87])).scale(0.5)
+ point_x_y_z2_2 = TexMobject("(0.5,-0.5,\\sqrt{4 - x^2 - y^2})").set_color(BLUE_C).move_to(np.array([1.5,-1.5,1.87])).scale(0.5)
+ point_x_y_z2_3 = TexMobject("(0.5,-0.5,\\sqrt{4 - 0.25 - 0.25})").set_color(BLUE_C).move_to(np.array([1.5,-1.5,1.87])).scale(0.5)
+ point_x_y_z2_4 = TexMobject("(0.5,-0.5,\\sqrt{3.5})").set_color(BLUE_C).move_to(np.array([1.5,-1.5,1.87])).scale(0.5)
+ point_x_y_z2_5 = TexMobject("(0.5,-0.5,1.87)").set_color(BLUE_C).move_to(np.array([1.5,-1.5,1.87])).scale(0.5)
+
+ point_x_y_z_2 = TexMobject("(0.5,-0.5,\\sqrt{r^2 - x^2 - y^2})").set_color(BLUE_C).move_to(np.array([1.5,-1.5,-1.87])).scale(0.5)
+ point_x_y_z_2_2 = TexMobject("(0.5,-0.5,\\sqrt{4 - x^2 - y^2})").set_color(BLUE_C).move_to(np.array([1.5,-1.5,-1.87])).scale(0.5)
+ point_x_y_z_2_3 = TexMobject("(0.5,-0.5,\\sqrt{4 - 0.25 - 0.25})").set_color(BLUE_C).move_to(np.array([1.5,-1.5,-1.87])).scale(0.5)
+ point_x_y_z_2_4 = TexMobject("(0.5,-0.5,\\sqrt{3.5})").set_color(BLUE_C).move_to(np.array([1.5,-1.5,-1.87])).scale(0.5)
+ point_x_y_z_2_5 = TexMobject("(0.5,-0.5,-1.87)").set_color(BLUE_C).move_to(np.array([1.5,-1.5,-1.87])).scale(0.5)
+
+
+ self.play(ShowCreation(dot_x_y2))
+ self.add_fixed_orientation_mobjects(point_x_y2)
+ self.play(ShowCreation(dot_x_y_z2), ShowCreation(dot_x_y_z_2), ShowCreation(line2))
+ self.add_fixed_orientation_mobjects(point_x_y_z2, point_x_y_z_2)
+ self.wait(0.5)
+ self.play(ReplacementTransform(point_x_y_z2,point_x_y_z2_2), ReplacementTransform(point_x_y_z_2,point_x_y_z_2_2))
+ self.add_fixed_orientation_mobjects(point_x_y_z2_2, point_x_y_z_2_2)
+
+ self.wait(0.5)
+ self.play(ReplacementTransform(point_x_y_z2_2,point_x_y_z2_3), ReplacementTransform(point_x_y_z_2_2,point_x_y_z_2_3))
+ self.add_fixed_orientation_mobjects(point_x_y_z2_3, point_x_y_z_2_3)
+ self.wait(0.5)
+ self.play(ReplacementTransform(point_x_y_z2_3,point_x_y_z2_4), ReplacementTransform(point_x_y_z_2_3,point_x_y_z_2_4))
+ self.add_fixed_orientation_mobjects(point_x_y_z2_4, point_x_y_z_2_4)
+ self.wait(0.5)
+ self.play(ReplacementTransform(point_x_y_z2_4,point_x_y_z2_5), ReplacementTransform(point_x_y_z_2_4,point_x_y_z_2_5))
+ self.add_fixed_orientation_mobjects(point_x_y_z2_5, point_x_y_z_2_5)
+
+ self.play(FadeOut(point_x_y1), FadeOut(point_x_y_z1_5), FadeOut(point_x_y_z_1_5), FadeOut(dot_x_y1), FadeOut(dot_x_y_z1), FadeOut(dot_x_y_z_1), FadeOut(line1))
+ self.play(FadeOut(point_x_y2), FadeOut(point_x_y_z2_5), FadeOut(point_x_y_z_2_5), FadeOut(dot_x_y2), FadeOut(dot_x_y_z2), FadeOut(dot_x_y_z_2), FadeOut(line2))
+
+
+
+
+ sphere_final = []
+
+ for u in range(0, 180, 15):
+ sphere_points1 = [np.array([2*np.sin(u*DEGREES)*np.cos(v*DEGREES), 2*np.sin(u*DEGREES)*np.sin(v*DEGREES), 2*np.cos(u*DEGREES)]) for v in range(0, 370, 10)]
+ sphere_dots1 = [Dot().scale(0.75).set_fill(RED_C).move_to(pts) for pts in sphere_points1]
+
+ sphere_points2 = [np.array([2*np.sin((u+5)*DEGREES)*np.cos(v*DEGREES), 2*np.sin((u+5)*DEGREES)*np.sin(v*DEGREES), 2*np.cos((u+5)*DEGREES)]) for v in range(0, 370, 10)]
+ sphere_dots2 = [Dot().scale(0.75).set_fill(RED_C).move_to(pts) for pts in sphere_points2]
+
+ sphere_points3 = [np.array([2*np.sin((u+10)*DEGREES)*np.cos(v*DEGREES), 2*np.sin((u+10)*DEGREES)*np.sin(v*DEGREES), 2*np.cos((u+10)*DEGREES)]) for v in range(0, 370, 10)]
+ sphere_dots3 = [Dot().scale(0.75).set_fill(RED_C).move_to(pts) for pts in sphere_points3]
+
+ sphere_final = sphere_final + sphere_dots1 + sphere_dots2 + sphere_dots3
+
+ sphere_dots = sphere_dots1 + sphere_dots2 + sphere_dots3
+
+ sphere_with_dots = VGroup(*sphere_dots)
+ self.play(ShowCreation(sphere_with_dots))
+
+ sphere_final_with_dots = VGroup(*sphere_final)
+
+
+ self.begin_ambient_camera_rotation(rate=0.5)
+ self.wait(3)
+ self.play(ReplacementTransform(sphere_final_with_dots, sphere))
+ self.wait(5)
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file5_vectorvf_helix.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file5_vectorvf_helix.py new file mode 100644 index 0000000..fc151ac --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file5_vectorvf_helix.py @@ -0,0 +1,92 @@ +from manimlib.imports import *
+
+class Helix(ThreeDScene):
+ def construct(self):
+ axes = ThreeDAxes() # creates a 3D Axis
+
+ helix1=ParametricFunction(
+ lambda u : np.array([
+ 1.5*np.cos(u),
+ 1.5*np.sin(u),
+ u/4
+ ]),color=PURPLE,t_min=-TAU,t_max=TAU,
+ )
+
+ helix2=ParametricFunction(
+ lambda u : np.array([
+ 2*np.cos(u),
+ 2*np.sin(u),
+ u/2
+ ]),color=GREEN_C,t_min=-TAU,t_max=TAU,
+ )
+
+ function = TexMobject("f(", "r", ",", "\\theta", ")", "=", "[", "r", "\\cos", "\\theta", ",", "r", "\\sin" ,"\\theta", ",", "h" ,"\\theta", "]" ).scale(0.6).to_corner(UL)
+ function.set_color_by_tex(r"\theta", BLUE_C)
+ function.set_color_by_tex(r"r", RED_C)
+ function.set_color_by_tex(r"\cos", GREEN_C)
+ function.set_color_by_tex(r"\sin", YELLOW_C)
+ function[0].set_color(ORANGE)
+ function[4].set_color(ORANGE)
+
+
+ self.add_fixed_in_frame_mobjects(function)
+
+ self.set_camera_orientation(phi=60*DEGREES, theta = 45*DEGREES)
+
+ self.add(axes)
+
+ axis = TextMobject(r"X",r"Y",r"Z")
+ axis[0].move_to(6*RIGHT)
+ axis[1].move_to(6*UP)
+ axis[2].move_to(np.array([0,0,3.7]))
+
+ self.add_fixed_orientation_mobjects(axis[2])
+ self.add_fixed_orientation_mobjects(axis[0])
+ self.add_fixed_orientation_mobjects(axis[1])
+
+
+ dot1 = Dot().rotate(PI/2).set_color(RED_C)
+ alpha1 = ValueTracker(0)
+ vector1 = self.get_vector(alpha1.get_value(),helix1)
+ dot1.add_updater(lambda m: m.move_to(vector1.get_end()))
+ self.play(
+ ShowCreation(helix1),
+ GrowFromCenter(dot1),
+ GrowArrow(vector1)
+ )
+ vector1.add_updater(
+ lambda m: m.become(
+ self.get_vector(alpha1.get_value()%1,helix1)
+ )
+ )
+ self.add(vector1,dot1)
+ self.play(alpha1.increment_value, 1, run_time=10, rate_func=linear)
+
+
+ self.play(FadeOut(vector1), FadeOut(dot1))
+ self.play(ReplacementTransform(helix1, helix2))
+
+
+ dot2 = Dot().rotate(PI/2).set_color(RED_C)
+ alpha2 = ValueTracker(0)
+ vector2 = self.get_vector(alpha2.get_value(),helix2)
+ dot2.add_updater(lambda m: m.move_to(vector2.get_end()))
+ self.play(
+ ShowCreation(helix2),
+ GrowFromCenter(dot2),
+ GrowArrow(vector2)
+ )
+ vector2.add_updater(
+ lambda m: m.become(
+ self.get_vector(alpha2.get_value()%1,helix2)
+ )
+ )
+ self.add(vector2,dot2)
+ self.play(alpha2.increment_value, 1, run_time=10, rate_func=linear)
+ self.wait()
+
+
+
+ def get_vector(self, proportion, curve):
+ vector = Line(np.array([0,0,0]), curve.point_from_proportion(proportion), color = YELLOW_C, buff=0)
+ return vector
\ No newline at end of file diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file5_derivative_vectorvf.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file6_derivative_vectorvf.py index 466e389..466e389 100644 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file5_derivative_vectorvf.py +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file6_derivative_vectorvf.py diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file1_multivar_func_examples.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file1_multivar_func_examples.gif Binary files differnew file mode 100644 index 0000000..43c3a42 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file1_multivar_func_examples.gif diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file1_multivariable_func_respresentation.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file1_multivariable_func_respresentation.gif Binary files differdeleted file mode 100644 index a173bda..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file1_multivariable_func_respresentation.gif +++ /dev/null diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file2_multivariable_func_examples.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file2_multivariable_func_examples.gif Binary files differdeleted file mode 100644 index 11f66f1..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file2_multivariable_func_examples.gif +++ /dev/null diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file2_multivariable_func_respresentation.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file2_multivariable_func_respresentation.gif Binary files differnew file mode 100644 index 0000000..8c4506c --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file2_multivariable_func_respresentation.gif diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file3_plot_sphere.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file3_plot_sphere.gif Binary files differdeleted file mode 100644 index ad7582c..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file3_plot_sphere.gif +++ /dev/null diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file3_sphere.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file3_sphere.gif Binary files differnew file mode 100644 index 0000000..3e35ec8 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file3_sphere.gif diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file4_vectorvf_sine.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file4_vectorvf_sine.gif Binary files differindex 4f6b931..215459e 100644 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file4_vectorvf_sine.gif +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file4_vectorvf_sine.gif diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file5_derivative_vectorvf.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file5_derivative_vectorvf.gif Binary files differdeleted file mode 100644 index a94de90..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file5_derivative_vectorvf.gif +++ /dev/null diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file5_vectorvf_helix.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file5_vectorvf_helix.gif Binary files differnew file mode 100644 index 0000000..c3d37f6 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file5_vectorvf_helix.gif diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file6_derivative_vectorvf.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file6_derivative_vectorvf.gif Binary files differnew file mode 100644 index 0000000..9ea94e4 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file6_derivative_vectorvf.gif diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/Limits_and_Continuity_of_Multivariable_Function_Quiz.pdf b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/Limits_and_Continuity_of_Multivariable_Function_Quiz.pdf Binary files differindex 99918e5..99918e5 100644 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/Limits_and_Continuity_of_Multivariable_Function_Quiz.pdf +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/Limits_and_Continuity_of_Multivariable_Function_Quiz.pdf diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/README.md b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/README.md new file mode 100644 index 0000000..c01ddc5 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/README.md @@ -0,0 +1,14 @@ +**file1_epsilon_delta_defn** + + +**file2_limit_approach_point** + + +**file3_limit_approach_point_3d** + + +**file4_limit_different_point** + + +**file5_continuity_func** + diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file1_epsilon_delta_defn.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file1_epsilon_delta_defn.py new file mode 100644 index 0000000..803c122 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file1_epsilon_delta_defn.py @@ -0,0 +1,179 @@ +from manimlib.imports import *
+
+class EpsilonDelta(ThreeDScene):
+ def construct(self):
+ axes = ThreeDAxes() # creates a 3D Axis
+
+
+ sphere = ParametricSurface(
+ lambda u, v: np.array([
+ 3*np.sin(u)*np.cos(v),
+ 3*np.sin(u)*np.sin(v),
+ 3*np.cos(u)
+ ]),u_min=0,u_max=PI/4,v_min=PI/2,v_max=PI,checkerboard_colors=[RED_D, RED_E],
+ resolution=(15, 32)).scale(1)
+
+
+ cylinder_z = ParametricSurface(
+ lambda u, v: np.array([
+ 0.25*np.cos(TAU * v),
+ 1.8* (1 - u),
+ 0.25*np.sin(TAU * v)
+
+ ]),
+ checkerboard_colors=[YELLOW_C, YELLOW_E], resolution=(6, 32)).fade(0.2).rotate(PI/4).move_to(np.array([-0.65,0.65,2.54]))
+
+
+ cylinder_x = ParametricSurface(
+ lambda u, v: np.array([
+ 0.3*np.cos(TAU * v)-1,
+ 0.3*np.sin(TAU * v)+1,
+ 2.6*(1 - u)
+ ]),
+ checkerboard_colors=[BLUE_C, BLUE_E], resolution=(6, 32)).fade(0.2)
+
+
+ delta_circle = Circle(radius= 0.3, color = BLACK).shift(1*LEFT+1*UP).set_fill(GREEN_E, opacity = 0.5)
+
+ epsilon_circle = [np.array([0.25*np.cos(i*DEGREES),0,0.25*np.sin(i*DEGREES)]) for i in range(361)]
+
+ epsilon_circle_polygon = Polygon(*epsilon_circle, color = RED_E, fill_color = RED_E, fill_opacity = 0.5).rotate(PI/4).move_to(np.array([0,0,2.54]))
+
+
+ dot_circle = Dot().move_to(np.array([-1,1,0])).set_fill("#000080")
+
+ dot_surface = Dot().rotate(-PI/4).scale(1.5).move_to(np.array([-1.2,1.2,2.7])).set_fill("#000080")
+
+ dot_L_epsilon1 = Polygon(*[np.array([0.05*np.cos(i*DEGREES),0,0.05*np.sin(i*DEGREES)]) for i in range(361)], color = "#000080", fill_color = "#000080", fill_opacity = 1).rotate(PI/4).move_to(np.array([0,0,2.3]))
+
+ dot_L_epsilon2 = Polygon(*[np.array([0.05*np.cos(i*DEGREES),0,0.05*np.sin(i*DEGREES)]) for i in range(361)], color = "#000080", fill_color = "#000080", fill_opacity = 1).rotate(PI/4).move_to(np.array([0,0,2.8]))
+
+ dot_L = Polygon(*[np.array([0.05*np.cos(i*DEGREES),0,0.05*np.sin(i*DEGREES)]) for i in range(361)], color = "#006400", fill_color = "#006400", fill_opacity = 1).rotate(PI/4).move_to(np.array([0,0,2.54]))
+
+
+
+ self.add(axes)
+
+ axis = TextMobject(r"X",r"Y",r"Z")
+ axis[0].move_to(6*RIGHT)
+ axis[1].move_to(6*UP)
+ axis[2].move_to(np.array([0,0,3.7]))
+
+ self.add_fixed_orientation_mobjects(axis[2])
+ self.add_fixed_orientation_mobjects(axis[0])
+ self.add_fixed_orientation_mobjects(axis[1])
+
+ self.set_camera_orientation(phi=75*DEGREES,theta=135*DEGREES)
+ #self.set_camera_orientation(phi=80*DEGREES,theta=45*DEGREES)
+
+
+ self.play(ShowCreation(sphere),ShowCreation(delta_circle), ShowCreation(dot_circle))
+
+ temp_circle_center = TextMobject(r"$(a,b,0)$").scale(0.6).set_color(BLUE_C).move_to(1.7*LEFT+1.1*UP)
+ self.add_fixed_orientation_mobjects(temp_circle_center)
+ self.wait()
+
+ delta_lab = TextMobject(r"$\delta$", r"$-$", "disk").scale(0.5).move_to(0.6*LEFT+1.7*UP)
+ delta_lab[0].set_color(PINK).scale(1.3)
+ delta_lab[1].set_color(ORANGE)
+ delta_lab[2].set_color(GREEN_E)
+
+ self.add_fixed_orientation_mobjects(delta_lab)
+
+ self.play(ShowCreation(dot_surface))
+
+ temp_curve_circle_center = TextMobject(r"$(a,b,L)$").scale(0.6).set_color("#006400").move_to(np.array([-2,1,2.7]))
+ self.add_fixed_orientation_mobjects(temp_curve_circle_center)
+
+
+ self.wait()
+ self.play(ShowCreation(cylinder_x), FadeOut(dot_surface))
+ self.wait()
+
+ self.move_camera(phi=0* DEGREES,theta=135*DEGREES)
+ self.wait()
+
+ self.move_camera(phi=80* DEGREES,theta=225*DEGREES)
+ self.wait()
+
+ self.play(FadeOut(delta_lab), ShowCreation(cylinder_z))
+ self.wait()
+
+ self.play(FadeOut(temp_circle_center), FadeOut(temp_curve_circle_center),ShowCreation(epsilon_circle_polygon))
+
+ self.move_camera(phi=80* DEGREES,theta=325*DEGREES)
+
+ dot_L_epsilon1_lab = TextMobject(r"$L$", r"$-$", r"$\epsilon$").scale(0.6).move_to(np.array([-0.4,-0.4,2.3]))
+ dot_L_epsilon1_lab[0].set_color("#D4108A")
+ dot_L_epsilon1_lab[1].set_color("#006400")
+ dot_L_epsilon1_lab[2].set_color("#4DC8A1").scale(1.5)
+
+ dot_L_epsilon2_lab = TextMobject(r"$L$", r"$+$", r"$\epsilon$").scale(0.6).move_to(np.array([-0.4,-0.4,2.8]))
+ dot_L_epsilon2_lab[0].set_color("#D4108A")
+ dot_L_epsilon2_lab[1].set_color("#006400")
+ dot_L_epsilon2_lab[2].set_color("#4DC8A1").scale(1.5)
+
+ dot_L_lab = TextMobject(r"$L$").scale(0.6).set_color("#D4108A").move_to(np.array([-0.4,-0.4,2.54]))
+
+
+ self.play(ShowCreation(dot_L_epsilon1), ShowCreation(dot_L), ShowCreation(dot_L_epsilon2))
+ self.add_fixed_orientation_mobjects(dot_L_epsilon1_lab, dot_L_epsilon2_lab, dot_L_lab)
+ self.wait(4)
+
+ self.move_camera(phi=80* DEGREES,theta=45*DEGREES)
+ self.wait(2)
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ '''
+
+
+
+
+
+
+
+
+
+
+
+ delta_lab = TextMobject(r"$\delta - disk$")
+ delta_lab.scale(0.5)
+ delta_lab.set_color(PINK)
+
+ self.play(ShowCreation(circle_center))
+ self.add_fixed_in_frame_mobjects(temp_circle_center)
+ temp_circle_center.move_to(1.5*RIGHT)
+ self.play(Write(temp_circle_center))
+
+ self.play(ShowCreation(curve_circle_center))
+ self.add_fixed_in_frame_mobjects(temp_curve_circle_center)
+ temp_curve_circle_center.move_to(1.9*UP+1*RIGHT)
+ self.play(Write(temp_curve_circle_center))
+
+
+ self.add_fixed_in_frame_mobjects(delta_lab)
+ delta_lab.move_to(0.4*DOWN+1.7*RIGHT)
+ self.play(Write(delta_lab))
+
+
+
+
+
+ self.begin_ambient_camera_rotation(rate=0.2)
+
+ self.play(ShowCreation(circle), ShowCreation(line1), ShowCreation(line2))
+ self.play(ShowCreation(line3), ShowCreation(line4))
+ self.wait(8)
+ '''
\ No newline at end of file diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file2_limit_approach_point.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file2_limit_approach_point.py index 57d1d45..57d1d45 100644 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file2_limit_approach_point.py +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file2_limit_approach_point.py diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file3_limit_approach_point_3d.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file3_limit_approach_point_3d.py new file mode 100644 index 0000000..f1007a4 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file3_limit_approach_point_3d.py @@ -0,0 +1,152 @@ +from manimlib.imports import *
+
+class Limit(ThreeDScene):
+ def construct(self):
+ axes = ThreeDAxes()
+
+ text3d = TextMobject(r"$f(x,y) = \frac{x - y}{x - 1}$")
+ self.add_fixed_in_frame_mobjects(text3d)
+
+ text3d.to_corner(UL)
+
+ text3d.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
+
+ self.play(Write(text3d))
+ self.wait(1)
+
+ limit_func = ParametricSurface(
+ lambda u, v: np.array([
+ 3*np.sin(u)*np.cos(v),
+ 3*np.sin(u)*np.sin(v),
+ (3*np.sin(u)*np.cos(v) - 3*np.sin(u)*np.sin(v))/2*(3*np.sin(u)*np.cos(v) - 1)
+ ]),u_min=0,u_max=PI,v_min=0,v_max=2*PI, color = BLUE_C, fill_color = BLUE_C, fill_opacity = 0.1,
+ resolution=(15, 32)).scale(1)
+
+ limit_y_x =ParametricFunction(
+ lambda u : np.array([
+ u,
+ u,
+ 0
+ ]),color=GREEN_D,t_min=-3,t_max=3,
+ )
+
+ limit_y_1 =ParametricFunction(
+ lambda u : np.array([
+ u,
+ 1,
+ 1/2
+ ]),color=BLUE_D,t_min=-3,t_max=3,
+ )
+
+ limit_y_x_2 =ParametricFunction(
+ lambda u : np.array([
+ u,
+ u*u,
+ (u - u*u)/2*(u - 1)
+ ]),color=RED_D,t_min=-3,t_max=3,
+ )
+
+ limit_y_2_x =ParametricFunction(
+ lambda u : np.array([
+ u,
+ 2 - u,
+ 1
+ ]),color=YELLOW_D,t_min=-3,t_max=3,
+ )
+
+ plane_y_x = Polygon(np.array([-3,-3,-3]),np.array([3,3,-3]),np.array([3,3,3]),np.array([-3,-3,3]),np.array([-3,-3,-3]), color = GREEN_C, fill_color = GREEN_C, fill_opacity = 0.1)
+ plane_y_x_text = TextMobject(r"$y = x$", color = GREEN_C).move_to(np.array([5,0,3]))
+
+ plane_y_1 = Polygon(np.array([-3,1,-3]),np.array([3,1,-3]),np.array([3,1,3]),np.array([-3,1,3]),np.array([-3,1,-3]), color = BLUE_C, fill_color = BLUE_C, fill_opacity = 0.1)
+ plane_y_1_text = TextMobject(r"$y = 1$", color = BLUE_C).move_to(np.array([5,0,2.5]))
+
+
+ #Creating plane y = x^2
+ ######
+ y_x_2 = []
+ y_x_2.append(np.array([2, 4, -3]))
+ y_x_2.append(np.array([2, 4, 3]))
+ y_x_2_1 = [np.array([i, i*i, 3]) for i in np.arange(1.9,-2.1, -0.1)]
+
+ y_x_2 = y_x_2 + y_x_2_1
+
+ y_x_2.append(np.array([-2, 4, 3]))
+ y_x_2.append(np.array([-2, 4, -3]))
+
+ y_x_2_2 = [np.array([i, i*i, -3]) for i in np.arange(-2,2.1, 0.1)]
+
+ y_x_2 = y_x_2 + y_x_2_2
+ #y_x_2.append(np.array([-3, 9, 0]))
+
+ plane_y_x_2 = Polygon(*y_x_2, color = RED_C, fill_color = RED_C, fill_opacity = 0.1)
+ plane_y_x_2_text = TextMobject(r"$y = x^2$", color = RED_C).move_to(np.array([5,0,2]))
+
+ ######
+
+ plane_y_2_x = Polygon(np.array([-3,5,-3]),np.array([3,-1,-3]),np.array([3,-1,3]),np.array([-3,5,3]),np.array([-3,5,-3]), color = YELLOW_C, fill_color = YELLOW_C, fill_opacity = 0.1)
+ plane_y_2_x_text = TextMobject(r"$y = 2 - x$", color = YELLOW_C).move_to(np.array([5,0,1.5]))
+
+ line_1_1 = Line(np.array([1,1,-3]), np.array([1,1,3]), color = PINK)
+
+ point = Polygon(*[np.array([0.05*np.cos(i*DEGREES),0,0.05*np.sin(i*DEGREES)]) for i in range(361)], color = "#000080", fill_color = "#000080", fill_opacity = 1).move_to(np.array([1,1,0]))
+ point_text = TextMobject(r"$(1,1,0)$", color = WHITE).scale(0.7).move_to(np.array([1.8,1,0]))
+
+
+
+
+ self.set_camera_orientation(phi=70 * DEGREES, theta = -95*DEGREES)
+
+
+ self.add(axes)
+
+ axis = TextMobject(r"X",r"Y",r"Z")
+ axis[0].move_to(6*RIGHT)
+ axis[1].move_to(6*UP)
+ axis[2].move_to(3.7*UP)
+
+ self.add_fixed_in_frame_mobjects(axis[2])
+ self.add_fixed_orientation_mobjects(axis[0])
+ self.add_fixed_orientation_mobjects(axis[1])
+
+ self.play(ShowCreation(limit_func))
+ self.wait(2)
+
+ self.play(ShowCreation(plane_y_x))
+ self.add_fixed_orientation_mobjects(plane_y_x_text)
+ self.play(ShowCreation(limit_y_x))
+ self.wait()
+
+ self.play(ShowCreation(plane_y_1))
+ self.add_fixed_orientation_mobjects(plane_y_1_text)
+ self.play(ShowCreation(limit_y_1))
+ self.wait()
+
+ self.play(ShowCreation(plane_y_x_2))
+ self.add_fixed_orientation_mobjects(plane_y_x_2_text)
+ self.play(ShowCreation(limit_y_x_2))
+ self.wait()
+
+ self.play(ShowCreation(plane_y_2_x))
+ self.add_fixed_orientation_mobjects(plane_y_2_x_text)
+ self.play(ShowCreation(limit_y_2_x))
+ self.wait()
+
+ self.play(ShowCreation(line_1_1))
+ self.wait()
+
+ self.play(ShowCreation(point))
+ self.add_fixed_orientation_mobjects(point_text)
+ self.wait()
+
+ self.play(FadeOut(plane_y_x_text), FadeOut(plane_y_1_text), FadeOut(plane_y_x_2_text), FadeOut(plane_y_2_x_text))
+
+ self.move_camera(phi=0* DEGREES,theta=-95*DEGREES)
+ self.wait(2)
+ self.play(FadeOut(plane_y_x), FadeOut(plane_y_1), FadeOut(plane_y_x_2), FadeOut(plane_y_2_x))
+ self.wait(3)
+
+ self.move_camera(phi=75* DEGREES,theta=-95*DEGREES)
+ self.wait(3)
+
+
+
\ No newline at end of file diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file4_limit_different_point.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file4_limit_different_point.py new file mode 100644 index 0000000..0a43def --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file4_limit_different_point.py @@ -0,0 +1,115 @@ +from manimlib.imports import *
+
+class DifferentPoint(ThreeDScene):
+ def construct(self):
+ axes = ThreeDAxes()
+
+ text3d = TextMobject(r"$f(x,y) = \frac{x^2 - y^2}{x^2 + y^2}$")
+ self.add_fixed_in_frame_mobjects(text3d)
+
+ text3d.to_corner(UL)
+
+ text3d.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
+
+ self.play(Write(text3d))
+ self.wait(1)
+
+ limit_func = ParametricSurface(
+ lambda u, v: np.array([
+ 3*np.sin(u)*np.cos(v),
+ 3*np.sin(u)*np.sin(v),
+ (np.cos(v)*np.cos(v) - np.sin(v)*np.sin(v))
+ ]),u_min=0,u_max=PI,v_min=0,v_max=2*PI,checkerboard_colors=[YELLOW_C, YELLOW_E],
+ resolution=(15, 32)).scale(1)
+
+ limit_func_copy1 = limit_func.copy()
+ limit_func_copy2 = limit_func.copy()
+
+ limit_func_x = ParametricSurface(
+ lambda u, v: np.array([
+ 3*np.sin(u)*np.cos(v),
+ 3*np.sin(u)*np.sin(v),
+ (np.cos(v)*np.cos(v) - np.sin(v)*np.sin(v))
+ ]),u_min=0,u_max=PI,v_min=PI,v_max=2*PI,checkerboard_colors=[YELLOW_C, YELLOW_E],
+ resolution=(15, 32)).scale(1)
+
+ limit_func_y = ParametricSurface(
+ lambda u, v: np.array([
+ 3*np.sin(u)*np.cos(v),
+ 3*np.sin(u)*np.sin(v),
+ (np.cos(v)*np.cos(v) - np.sin(v)*np.sin(v))
+ ]),u_min=0,u_max=PI,v_min=PI/2,v_max=3*PI/2,checkerboard_colors=[YELLOW_C, YELLOW_E],
+ resolution=(15, 32)).scale(1)
+
+ limit_x =ParametricFunction(
+ lambda u : np.array([
+ u,
+ 0,
+ 1
+ ]),color="#006400",t_min=-3,t_max=3,
+ )
+
+ limit_y =ParametricFunction(
+ lambda u : np.array([
+ 0,
+ u,
+ -1
+ ]),color="#000080",t_min=-3,t_max=3,
+ )
+
+ plane_x = Polygon(np.array([-3,0,-2]),np.array([3,0,-2]),np.array([3,0,2]),np.array([-3,0,2]),np.array([-3,0,-2]), color = GREEN, fill_color = GREEN, fill_opacity = 0.2)
+ plane_x_text = TextMobject(r"$y = 0$", color = GREEN_C).move_to(1.7*UP + 3.8*RIGHT)
+
+ plane_y = Polygon(np.array([0,-3,-2]),np.array([0,3,-2]),np.array([0,3,2]),np.array([0,-3,2]),np.array([0,-3,-2]), color = BLUE, fill_color = BLUE, fill_opacity = 0.2)
+ plane_y_text = TextMobject(r"$x = 0$", color = BLUE_C).move_to(1.7*UP + 3.8*RIGHT)
+
+ origin_x = Polygon(*[np.array([0.05*np.cos(i*DEGREES),0,0.05*np.sin(i*DEGREES)]) for i in range(361)], color = "#000080", fill_color = "#000080", fill_opacity = 1).move_to(np.array([0,0,0]))
+ origin_x_text = TextMobject(r"$(0,0,0)$", color = RED_C).scale(0.7).move_to(np.array([-0.6,0,-0.5]))
+
+ origin_y = Polygon(*[np.array([0,0.05*np.cos(i*DEGREES),0.05*np.sin(i*DEGREES)]) for i in range(361)], color = "#000080", fill_color = "#000080", fill_opacity = 1).move_to(np.array([0,0,0]))
+ origin_y_text = TextMobject(r"$(0,0,0)$", color = RED_C).scale(0.7).move_to(np.array([0,-0.6,-0.5]))
+
+ self.set_camera_orientation(phi=80 * DEGREES, theta = 0*DEGREES)
+
+
+ self.add(axes)
+
+ axis = TextMobject(r"X",r"Y",r"Z")
+ axis[0].move_to(6*RIGHT)
+ axis[1].move_to(6*UP)
+ axis[2].move_to(3.7*UP)
+
+ self.add_fixed_in_frame_mobjects(axis[2])
+ self.add_fixed_orientation_mobjects(axis[0])
+ self.add_fixed_orientation_mobjects(axis[1])
+
+ self.play(ShowCreation(limit_func))
+
+ self.move_camera(phi=80* DEGREES,theta=105*DEGREES)
+
+ self.play(ShowCreation(plane_x))
+ self.add_fixed_in_frame_mobjects(plane_x_text)
+ self.wait()
+ self.play(ReplacementTransform(limit_func, limit_func_x))
+ self.play(FadeOut(plane_x), FadeOut(plane_x_text), ShowCreation(origin_x))
+ self.add_fixed_orientation_mobjects(origin_x_text)
+ self.play(ShowCreation(limit_x))
+
+ self.move_camera(phi=80* DEGREES,theta=15*DEGREES)
+ self.wait(3)
+
+ self.play(FadeOut(origin_x), FadeOut(origin_x_text), FadeOut(limit_x), ReplacementTransform(limit_func_x, limit_func_copy1))
+ self.play(ShowCreation(plane_y))
+ self.add_fixed_in_frame_mobjects(plane_y_text)
+ self.wait()
+ self.play(ReplacementTransform(limit_func_copy1, limit_func_y))
+ self.play(FadeOut(plane_y), FadeOut(plane_y_text), ShowCreation(origin_y))
+ self.add_fixed_orientation_mobjects(origin_y_text)
+ self.play(ShowCreation(limit_y))
+
+ self.move_camera(phi=80* DEGREES,theta=75*DEGREES)
+ self.wait(3)
+
+ self.play(FadeOut(origin_y), FadeOut(origin_y_text), FadeOut(limit_y), ReplacementTransform(limit_func_y, limit_func_copy2))
+ self.wait(2)
+
\ No newline at end of file diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file5_continuity_func.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file5_continuity_func.py new file mode 100644 index 0000000..99159a4 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file5_continuity_func.py @@ -0,0 +1,115 @@ +from manimlib.imports import *
+
+class Continuity(ThreeDScene):
+ def construct(self):
+ axes = ThreeDAxes()
+
+ text3d = TextMobject(r"$f(x,y) = \frac{3x^2y}{x^2 + y^2}$")
+ self.add_fixed_in_frame_mobjects(text3d)
+
+ text3d.to_corner(UL)
+
+ text3d.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
+
+ self.play(Write(text3d))
+ self.wait(1)
+
+
+ continuity_func = ParametricSurface(
+ lambda u, v: np.array([
+ 3*np.sin(u)*np.cos(v),
+ 3*np.sin(u)*np.sin(v),
+ 9*np.sin(u)*np.cos(v)*np.cos(v)*np.sin(v)
+ ]),u_min=0,u_max=PI,v_min=0,v_max=2*PI,checkerboard_colors=[YELLOW_C, YELLOW_E],
+ resolution=(15, 32)).scale(1)
+
+ continuity_func_copy1 = continuity_func.copy()
+ continuity_func_copy2 = continuity_func.copy()
+
+ continuity_func_x = ParametricSurface(
+ lambda u, v: np.array([
+ 3*np.sin(u)*np.cos(v),
+ 3*np.sin(u)*np.sin(v),
+ 9*np.sin(u)*np.cos(v)*np.cos(v)*np.sin(v)
+ ]),u_min=0,u_max=PI,v_min=PI,v_max=2*PI,checkerboard_colors=[YELLOW_C, YELLOW_E],
+ resolution=(15, 32)).scale(1)
+
+ continuity_func_y = ParametricSurface(
+ lambda u, v: np.array([
+ 3*np.sin(u)*np.cos(v),
+ 3*np.sin(u)*np.sin(v),
+ 9*np.sin(u)*np.cos(v)*np.cos(v)*np.sin(v)
+ ]),u_min=0,u_max=PI,v_min=PI/2,v_max=3*PI/2,checkerboard_colors=[YELLOW_C, YELLOW_E],
+ resolution=(15, 32)).scale(1)
+
+ continuity_x =ParametricFunction(
+ lambda u : np.array([
+ u,
+ 0,
+ 0
+ ]),color="#006400",t_min=-3,t_max=3,
+ )
+
+ continuity_y =ParametricFunction(
+ lambda u : np.array([
+ 0,
+ u,
+ 0
+ ]),color="#000080",t_min=-3,t_max=3,
+ )
+
+ plane_x = Polygon(np.array([-3,0,-3]),np.array([3,0,-3]),np.array([3,0,3]),np.array([-3,0,3]),np.array([-3,0,-3]), color = GREEN, fill_color = GREEN, fill_opacity = 0.2)
+ plane_x_text = TextMobject(r"$y = 0$", color = GREEN_C).move_to(1.7*UP + 3.8*RIGHT)
+
+ plane_y = Polygon(np.array([0,-3,-3]),np.array([0,3,-3]),np.array([0,3,3]),np.array([0,-3,3]),np.array([0,-3,-3]), color = BLUE, fill_color = BLUE, fill_opacity = 0.2)
+ plane_y_text = TextMobject(r"$x = 0$", color = BLUE_C).move_to(1.7*UP + 3.8*RIGHT)
+
+ origin_x = Polygon(*[np.array([0.05*np.cos(i*DEGREES),0,0.05*np.sin(i*DEGREES)]) for i in range(361)], color = "#000080", fill_color = "#000080", fill_opacity = 1).move_to(np.array([0,0,0]))
+ origin_x_text = TextMobject(r"$(0,0,0)$", color = RED_C).scale(0.7).move_to(np.array([-0.6,0,-0.5]))
+
+ origin_y = Polygon(*[np.array([0,0.05*np.cos(i*DEGREES),0.05*np.sin(i*DEGREES)]) for i in range(361)], color = "#006400", fill_color = "#006400", fill_opacity = 1).move_to(np.array([0,0,0]))
+ origin_y_text = TextMobject(r"$(0,0,0)$", color = RED_C).scale(0.7).move_to(np.array([0,-0.6,-0.5]))
+
+ self.set_camera_orientation(phi=80 * DEGREES, theta = 0*DEGREES)
+
+
+ self.add(axes)
+
+ axis = TextMobject(r"X",r"Y",r"Z")
+ axis[0].move_to(6*RIGHT)
+ axis[1].move_to(6*UP)
+ axis[2].move_to(3.7*UP)
+
+ self.add_fixed_in_frame_mobjects(axis[2])
+ self.add_fixed_orientation_mobjects(axis[0])
+ self.add_fixed_orientation_mobjects(axis[1])
+
+ self.play(ShowCreation(continuity_func))
+
+ self.move_camera(phi=80* DEGREES,theta=105*DEGREES)
+
+ self.play(ShowCreation(plane_x))
+ self.add_fixed_in_frame_mobjects(plane_x_text)
+ self.wait()
+ self.play(ReplacementTransform(continuity_func, continuity_func_x))
+ self.play(FadeOut(plane_x), FadeOut(plane_x_text))
+ self.play(ShowCreation(continuity_x), ShowCreation(origin_x))
+ self.add_fixed_orientation_mobjects(origin_x_text)
+
+ self.move_camera(phi=80* DEGREES,theta=15*DEGREES)
+ self.wait(3)
+
+ self.play(FadeOut(origin_x), FadeOut(origin_x_text), FadeOut(continuity_x), ReplacementTransform(continuity_func_x, continuity_func_copy1))
+ self.play(ShowCreation(plane_y))
+ self.add_fixed_in_frame_mobjects(plane_y_text)
+ self.wait()
+ self.play(ReplacementTransform(continuity_func_copy1, continuity_func_y))
+ self.play(FadeOut(plane_y), FadeOut(plane_y_text))
+ self.play(ShowCreation(continuity_y), ShowCreation(origin_y))
+ self.add_fixed_orientation_mobjects(origin_y_text)
+
+ self.move_camera(phi=80* DEGREES,theta=75*DEGREES)
+ self.wait(3)
+
+ self.play(FadeOut(origin_y), FadeOut(origin_y_text), FadeOut(continuity_y), ReplacementTransform(continuity_func_y, continuity_func_copy2))
+ self.wait(2)
\ No newline at end of file diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/gifs/file1_epsilon_delta_defn.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/gifs/file1_epsilon_delta_defn.gif Binary files differnew file mode 100644 index 0000000..2378bcf --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/gifs/file1_epsilon_delta_defn.gif diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/gifs/file2_limit_approach_point.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/gifs/file2_limit_approach_point.gif Binary files differnew file mode 100644 index 0000000..3abd596 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/gifs/file2_limit_approach_point.gif diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/gifs/file3_limit_approach_point_3d.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/gifs/file3_limit_approach_point_3d.gif Binary files differnew file mode 100644 index 0000000..3e87cdd --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/gifs/file3_limit_approach_point_3d.gif diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/gifs/file4_limit_different_point.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/gifs/file4_limit_different_point.gif Binary files differnew file mode 100644 index 0000000..9a831e4 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/gifs/file4_limit_different_point.gif diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/gifs/file5_continuity_func.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/gifs/file5_continuity_func.gif Binary files differnew file mode 100644 index 0000000..2a0a61f --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/gifs/file5_continuity_func.gif diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/README.md b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/README.md new file mode 100644 index 0000000..c62dd51 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/README.md @@ -0,0 +1,23 @@ +**file1_partial_deriv_gas_law** + + +**file2_partial_deriv_hill** + + +**file3_partial_deriv_defn** + + +**file4_partial_deriv_example** + + +**file5_partial_deriv_func_2maximas** + + +**file6_clariant_rule** + + +**file7_partial_deriv_clariant_rule** + + +**file8_chain_rule** + diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file1_partial_deriv_gas_law.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file1_partial_deriv_gas_law.py new file mode 100644 index 0000000..3d35c97 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file1_partial_deriv_gas_law.py @@ -0,0 +1,88 @@ +from manimlib.imports import *
+
+class GasLaw(Scene):
+ def construct(self):
+ gas_law = TextMobject(r"$P$", r"$V$", r"=", r"$n$", r"$R$", r"$T$").scale(1.5)
+ gas_law[0].set_color(BLUE_C)
+ gas_law[1].set_color(GREEN_C)
+ gas_law[3].set_color(RED_C)
+ gas_law[4].set_color(ORANGE)
+ gas_law[5].set_color(YELLOW_C)
+
+ gas_law_trans = TexMobject("V", "=", "{n", "R", "T", "\\over", "P}").scale(1.5)
+ gas_law_trans[0].set_color(GREEN_C)
+ gas_law_trans[2].set_color(RED_C)
+ gas_law_trans[3].set_color(ORANGE)
+ gas_law_trans[4].set_color(YELLOW_C)
+ gas_law_trans[6].set_color(BLUE_C)
+
+ gas_law_func = TexMobject("V", "=", "f(", "n", ",", "T", ",", "P", ")").scale(1.5)
+ gas_law_func[0].set_color(GREEN_C)
+ gas_law_func[2].set_color(ORANGE)
+ gas_law_func[3].set_color(RED_C)
+ gas_law_func[5].set_color(YELLOW_C)
+ gas_law_func[7].set_color(BLUE_C)
+ gas_law_func[8].set_color(ORANGE)
+
+ partial_gas_law_func = TexMobject("{\\partial", "V","\\over", "\\partial", "P}", r"=", "{\\partial", "\\over", "\\partial", "P}", "f(", r"n", ",", r"T", ",", r"P", r")").scale(1.5)
+ partial_gas_law_func.set_color_by_tex("\\partial", PINK)
+ partial_gas_law_func.set_color_by_tex("P}", BLUE_C)
+
+ partial_gas_law_func[1].set_color(GREEN_C)
+ partial_gas_law_func[10].set_color(ORANGE)
+ partial_gas_law_func[11].set_color(RED_C)
+ partial_gas_law_func[13].set_color(YELLOW_C)
+ partial_gas_law_func[15].set_color(BLUE_C)
+ partial_gas_law_func[16].set_color(ORANGE)
+
+ partial_gas_law_trans = TexMobject("{\\partial", "V","\\over", "\\partial", "P}", r"=", "{\\partial", "\\over", "\\partial", "P}", "{n", "R", "T", "\\over", "P}").scale(1.5)
+ partial_gas_law_trans.set_color_by_tex("\\partial", PINK)
+ partial_gas_law_trans.set_color_by_tex("P}", BLUE_C)
+
+ partial_gas_law_trans[1].set_color(GREEN_C)
+ partial_gas_law_trans[10].set_color(RED_C)
+ partial_gas_law_trans[11].set_color(ORANGE)
+ partial_gas_law_trans[12].set_color(YELLOW_C)
+
+ partial_gas_law_trans2 = TexMobject("{\\partial", "V","\\over", "\\partial", "P}", r"=", "n", "R", "T", "{\\partial", "\\over", "\\partial", "P}", "P^{-1}",).scale(1.5)
+ partial_gas_law_trans2.set_color_by_tex("\\partial", PINK)
+ partial_gas_law_trans2.set_color_by_tex("P}", BLUE_C)
+
+ partial_gas_law_trans2[1].set_color(GREEN_C)
+ partial_gas_law_trans2[6].set_color(RED_C)
+ partial_gas_law_trans2[7].set_color(ORANGE)
+ partial_gas_law_trans2[8].set_color(YELLOW_C)
+ partial_gas_law_trans2[-1].set_color(BLUE_C)
+
+ partial_gas_law_trans3 = TexMobject("{\\partial", "V","\\over", "\\partial", "P}", r"=", "n", "R", "T", "P^{-2}",).scale(1.5)
+ partial_gas_law_trans3.set_color_by_tex("\\partial", PINK)
+ partial_gas_law_trans3.set_color_by_tex("P}", BLUE_C)
+
+ partial_gas_law_trans3[1].set_color(GREEN_C)
+ partial_gas_law_trans3[6].set_color(RED_C)
+ partial_gas_law_trans3[7].set_color(ORANGE)
+ partial_gas_law_trans3[8].set_color(YELLOW_C)
+ partial_gas_law_trans3[9].set_color(BLUE_C)
+
+ framebox = SurroundingRectangle(partial_gas_law_trans3, color = PURPLE, buff = 0.3)
+
+
+
+ self.play(Write(gas_law))
+ self.wait()
+ self.play(Transform(gas_law, gas_law_trans))
+ self.wait()
+ self.play(Transform(gas_law, gas_law_func))
+ self.wait()
+ self.play(Transform(gas_law, gas_law_trans))
+ self.wait()
+ self.play(Transform(gas_law, partial_gas_law_func))
+ self.wait()
+ self.play(Transform(gas_law, partial_gas_law_trans))
+ self.wait()
+ self.play(Transform(gas_law, partial_gas_law_trans2))
+ self.wait()
+ self.play(Transform(gas_law, partial_gas_law_trans3))
+ self.wait()
+ self.play(ShowCreation(framebox))
+ self.wait()
\ No newline at end of file diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file2_partial_deriv_hill.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file2_partial_deriv_hill.py new file mode 100644 index 0000000..bfb7687 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file2_partial_deriv_hill.py @@ -0,0 +1,122 @@ +from manimlib.imports import *
+
+class Hill(ThreeDScene):
+ def construct(self):
+ axes = ThreeDAxes()
+
+ function = ParametricSurface(
+ lambda u, v: np.array([
+ 1.2*np.sin(u)*np.cos(v),
+ 1.2*np.sin(u)*np.sin(v),
+ -1.2*1.2*np.sin(u)*np.sin(u)*(1+0.5*np.sin(v)*np.sin(v))+2
+ ]),u_min=0,u_max=PI/2,v_min=0,v_max=2*PI,checkerboard_colors=[GREEN_C, GREEN_E],
+ resolution=(15, 32)).scale(1)
+
+ func_x =ParametricFunction(
+ lambda u : np.array([
+ u,
+ 0,
+ 2 - u*u
+ ]),color=RED_E,t_min=-1.2,t_max=1.2,
+ )
+
+ func_y =ParametricFunction(
+ lambda u : np.array([
+ 0,
+ u,
+ 2 - 1.5*u*u
+ ]),color=PINK,t_min=-1.2,t_max=1.2,
+ )
+
+ self.set_camera_orientation(phi=60 * DEGREES, theta = 0*DEGREES)
+ #self.set_camera_orientation(phi=45 * DEGREES, theta = -20*DEGREES)
+
+ self.add(axes)
+ axis = TextMobject(r"X",r"Y",r"Z")
+ axis[0].move_to(6*RIGHT)
+ axis[1].move_to(6*UP)
+ axis[2].move_to(np.array([0,0,3.7]))
+
+ self.add_fixed_orientation_mobjects(axis[2])
+ self.add_fixed_orientation_mobjects(axis[0])
+ self.add_fixed_orientation_mobjects(axis[1])
+
+ self.play(ShowCreation(function))
+ self.wait()
+
+ self.move_camera(phi=60 * DEGREES, theta = 45*DEGREES)
+ #self.play(ShowCreation(func_x))
+
+ text_x = TextMobject("Slope of the hill along", r"$x$", "axis", color = YELLOW_C).scale(0.6).move_to(2.7*UP + 3.5*RIGHT)
+ text_x[1].set_color(PINK)
+
+
+ slope_text_x = TexMobject("Slope =", "{\\partial", "f", "\\over", "\\partial", "x}").scale(0.6).move_to(2*UP + 3.5*RIGHT)
+ slope_text_x[0].set_color(BLUE_E)
+ slope_text_x.set_color_by_tex("\\partial",YELLOW_C)
+ slope_text_x.set_color_by_tex("f",RED_E)
+ slope_text_x[5].set_color(PINK)
+
+ self.add_fixed_in_frame_mobjects(text_x, slope_text_x)
+
+ dot_x = Dot().rotate(PI/2).set_color(YELLOW_E)
+ alpha_x = ValueTracker(0)
+ vector_x = self.get_tangent_vector(alpha_x.get_value(),func_x,scale=1.5)
+ dot_x.add_updater(lambda m: m.move_to(vector_x.get_center()))
+ self.play(
+ ShowCreation(func_x),
+ GrowFromCenter(dot_x),
+ GrowArrow(vector_x)
+ )
+ vector_x.add_updater(
+ lambda m: m.become(
+ self.get_tangent_vector(alpha_x.get_value()%1,func_x,scale=1.5)
+ )
+ )
+
+ self.add(vector_x,dot_x)
+
+ self.play(alpha_x.increment_value, 1, run_time=10, rate_func=linear)
+
+ #self.move_camera(phi=60 * DEGREES, theta = 0*DEGREES)
+ self.play(FadeOut(vector_x), FadeOut(dot_x), FadeOut(func_x), FadeOut(text_x), FadeOut(slope_text_x))
+
+ text_y = TextMobject("Slope of the hill along", r"$y$", "axis", color = YELLOW_C).scale(0.6).move_to(2.7*UP + 3.5*RIGHT)
+ text_y[1].set_color(RED_C)
+
+
+ slope_text_y = TexMobject("Slope =", "{\\partial", "f", "\\over", "\\partial", "x}").scale(0.6).move_to(2*UP + 3.5*RIGHT)
+ slope_text_y[0].set_color(BLUE_E)
+ slope_text_y.set_color_by_tex("\\partial",YELLOW_C)
+ slope_text_y.set_color_by_tex("f",PINK)
+ slope_text_y[5].set_color(RED_C)
+
+ self.add_fixed_in_frame_mobjects(text_y, slope_text_y)
+
+ dot_y = Dot().rotate(PI/2).set_color(BLUE_E)
+ alpha_y = ValueTracker(0)
+ vector_y = self.get_tangent_vector(alpha_y.get_value(),func_y,scale=1.5)
+ dot_y.add_updater(lambda m: m.move_to(vector_y.get_center()))
+ self.play(
+ ShowCreation(func_y),
+ GrowFromCenter(dot_y),
+ GrowArrow(vector_y)
+ )
+ vector_y.add_updater(
+ lambda m: m.become(
+ self.get_tangent_vector(alpha_y.get_value()%1,func_y,scale=1.5)
+ )
+ )
+
+ self.add(vector_y,dot_y)
+ self.play(alpha_y.increment_value, 1, run_time=10, rate_func=linear)
+ self.play(FadeOut(vector_y), FadeOut(dot_y), FadeOut(func_y), FadeOut(text_y), FadeOut(slope_text_y))
+ self.wait(2)
+
+ def get_tangent_vector(self, proportion, curve, dx=0.001, scale=1):
+ coord_i = curve.point_from_proportion(proportion)
+ coord_f = curve.point_from_proportion(proportion + dx)
+ reference_line = Line(coord_i,coord_f)
+ unit_vector = reference_line.get_unit_vector() * scale
+ vector = Line(coord_i - unit_vector, coord_i + unit_vector, color = ORANGE, buff=0)
+ return vector
\ No newline at end of file diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file3_partial_deriv_defn.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file3_partial_deriv_defn.py new file mode 100644 index 0000000..a25ca56 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file3_partial_deriv_defn.py @@ -0,0 +1,218 @@ +from manimlib.imports import *
+
+class PartialDeriv(ThreeDScene):
+ def construct(self):
+ axes = ThreeDAxes()
+
+ paraboloid = ParametricSurface(
+ lambda u, v: np.array([
+ 2*np.sin(u)*np.cos(v),
+ 2*np.sin(u)*np.sin(v),
+ -2*2*np.sin(u)*np.sin(u)+2
+ ]),u_min=0,u_max=PI/2,v_min=0,v_max=2*PI,checkerboard_colors=[PINK, PURPLE],
+ resolution=(15, 32)).scale(1)
+
+ paraboloid_copy1 = paraboloid.copy()
+ paraboloid_copy2 = paraboloid.copy()
+
+ paraboloid_x = ParametricSurface(
+ lambda u, v: np.array([
+ 2*np.sin(u)*np.cos(v),
+ 2*np.sin(u)*np.sin(v),
+ -2*2*np.sin(u)*np.sin(u)+2
+ ]),u_min=0,u_max=PI/2,v_min=PI,v_max=2*PI,checkerboard_colors=[PINK, PURPLE],
+ resolution=(15, 32)).scale(1)
+
+ paraboloid_x_copy = paraboloid_x.copy()
+
+ paraboloid_y = ParametricSurface(
+ lambda u, v: np.array([
+ 2*np.sin(u)*np.cos(v),
+ 2*np.sin(u)*np.sin(v),
+ -2*2*np.sin(u)*np.sin(u)+2
+ ]),u_min=0,u_max=PI/2,v_min=PI/2,v_max=3*PI/2,checkerboard_colors=[PINK, PURPLE],
+ resolution=(15, 32)).scale(1)
+
+ parabola1 =ParametricFunction(
+ lambda u : np.array([
+ u,
+ 0,
+ -(u*u) + 2
+ ]),color="#006400",t_min=-2,t_max=2,
+ )
+ parabola2 =ParametricFunction(
+ lambda u : np.array([
+ 0,
+ u,
+ -(u*u) + 2
+ ]),color=BLUE_C,t_min=-2,t_max=2,
+ )
+
+ plane1 = Polygon(np.array([-2.2,0,-2.5]),np.array([2.2,0,-2.5]),np.array([2.2,0,2.5]),np.array([-2.2,0,2.5]),np.array([-2.2,0,-2.5]), color = GREEN, fill_color = GREEN, fill_opacity = 0.2)
+ plane1_text = TextMobject(r"$y = 0$", color = GREEN_C).move_to(2*UP + 3.3*RIGHT)
+
+ plane2 = Polygon(np.array([0,-2.2,-2.5]),np.array([0,2.2,-2.5]),np.array([0,2.2,2.5]),np.array([0,-2.2,2.5]),np.array([0,-2.2,-2.5]), color = BLUE, fill_color = BLUE, fill_opacity = 0.2)
+ plane2_text = TextMobject(r"$x = 0$", color = BLUE_C).move_to(2*UP + 3.2*RIGHT)
+
+ surface_eqn = TextMobject("Surface", r"$z = 2- x^2 -y^2$", color = YELLOW_C).scale(0.6).move_to(np.array([3*LEFT +3*UP]))
+ surface_eqn[0].set_color(PINK)
+
+ dot1 =Sphere(radius=0.08).move_to(np.array([-1,0,1]))
+ dot1.set_fill(RED)
+ line1 = Line(np.array([-1.55, 0,0]), np.array([-0.4, 0,2.2]), color = RED)
+ lab_x = TextMobject(r"$f(x_0,y_0)$", color = RED).scale(0.7)
+ para_lab_x = TextMobject(r"$f(x,y_0)$", color = "#006400").scale(0.7)
+ tangent_line_x = TextMobject("Tangent Line", color = RED_C, buff = 0.4).scale(0.6).move_to(np.array([1.7*RIGHT +1.8*UP]))
+
+
+ text1 = TextMobject(r"$\frac{\partial f}{\partial x}\vert_{(x_0,y_0)} = \frac{d}{dx}$", r"$f(x,y_0)$", r"$\vert_{x=x_0}$").scale(0.6)
+ brace1 = Brace(text1[1], DOWN, buff = SMALL_BUFF, color = GREEN)
+ t1 = brace1.get_text("Just depends on x")
+ t1.scale(0.6)
+ t1.set_color(GREEN)
+
+
+ dot2 =Sphere(radius=0.08).move_to(np.array([0,1,1]))
+ dot2.set_fill(RED)
+ line2 = Line(np.array([0, 1.55,0]), np.array([0, 0.4,2.2]), color = RED)
+ lab_y = TextMobject(r"$f(x_0,y_0)$", color = RED).scale(0.7)
+ para_lab_y = TextMobject(r"$f(x_0,y)$", color = BLUE_C).scale(0.7)
+ tangent_line_y = TextMobject("Tangent Line", color = RED_C, buff = 0.4).scale(0.6).move_to(np.array([1.7*RIGHT +1.8*UP]))
+
+ text2 = TextMobject(r"$\frac{\partial f}{\partial y}\vert_{(x_0,y_0)} = \frac{d}{dy}$", r"$f(x_0,y)$", r"$\vert_{y=y_0}$").scale(0.6)
+ brace2 = Brace(text2[1], DOWN, buff = SMALL_BUFF, color = GREEN)
+ t2 = brace2.get_text("Just depends on y")
+ t2.scale(0.6)
+ t2.set_color(GREEN)
+
+ text3 = TextMobject(r"$= \lim_{h \to 0} \frac{f(x_0+h,y_0) - f(x_0,y_0)}{h}$").scale(0.6)
+
+ dot3 =Sphere(radius=0.08).move_to(np.array([-1.22,0,0.5]))
+ dot3.set_fill(YELLOW_C)
+ line3 = Line(np.array([-1.44,0,0]), np.array([-0.6,0,2.2]), color = YELLOW_C)
+ lab_line3 = TextMobject(r"$f(x_0+h,y_0)$", color = YELLOW_C).scale(0.7)
+
+
+ self.set_camera_orientation(phi=80 * DEGREES, theta = 0*DEGREES)
+ #self.set_camera_orientation(phi=80 * DEGREES, theta = 20*DEGREES)
+ #self.begin_ambient_camera_rotation(rate=0.3)
+
+
+ self.add(axes)
+
+ axis = TextMobject(r"X",r"Y",r"Z")
+ axis[0].move_to(6*RIGHT)
+ axis[1].move_to(6*UP)
+ axis[2].move_to(3.7*UP)
+
+ self.add_fixed_in_frame_mobjects(axis[2])
+ #self.add_fixed_orientation_mobjects(axis[2])
+
+ self.play(Write(paraboloid))
+
+ self.add_fixed_in_frame_mobjects(surface_eqn)
+ #self.move_camera(phi=80* DEGREES,theta=110*DEGREES)
+ self.move_camera(phi=80* DEGREES,theta=45*DEGREES)
+
+ self.add_fixed_orientation_mobjects(axis[0])
+ self.add_fixed_orientation_mobjects(axis[1])
+ self.play(ShowCreation(plane1))
+ self.add_fixed_in_frame_mobjects(plane1_text)
+ self.wait()
+ self.play(ReplacementTransform(paraboloid, paraboloid_x))
+
+ lab_x.move_to(np.array([1.8*RIGHT +1.15*UP]))
+ para_lab_x.move_to(np.array([1.3*LEFT +1.6*UP]))
+ self.wait()
+ self.play(FadeOut(plane1), FadeOut(plane1_text))
+ self.play(ShowCreation(parabola1))
+ self.add_fixed_in_frame_mobjects(para_lab_x)
+ self.play(ShowCreation(dot1))
+ self.add_fixed_in_frame_mobjects(lab_x)
+ #self.play(ShowCreation(dot1))
+ self.wait()
+ self.play(ShowCreation(line1))
+ self.add_fixed_in_frame_mobjects(tangent_line_x)
+ self.wait()
+
+ self.add_fixed_in_frame_mobjects(text1, brace1, t1)
+ grp1 = VGroup(text1, brace1, t1)
+ grp1.move_to(3*UP+3*RIGHT)
+ self.play(Write(text1),GrowFromCenter(brace1), FadeIn(t1))
+ self.wait()
+ self.play(FadeOut(parabola1), FadeOut(line1), FadeOut(lab_x), FadeOut(para_lab_x), FadeOut(dot1), FadeOut(tangent_line_x),FadeOut(grp1))
+
+
+
+
+ #self.move_camera(phi=80* DEGREES,theta=20*DEGREES)
+
+ self.play(ReplacementTransform(paraboloid_x, paraboloid_copy1))
+ self.wait()
+ self.play(ShowCreation(plane2))
+ self.add_fixed_in_frame_mobjects(plane2_text)
+ self.wait()
+ self.play(ReplacementTransform(paraboloid_copy1, paraboloid_y))
+
+ lab_y.move_to(np.array([1.8*RIGHT +1.15*UP]))
+ para_lab_y.move_to(np.array([1.3*LEFT +1.6*UP]))
+ self.wait()
+ self.play(FadeOut(plane2), FadeOut(plane2_text))
+ self.play(ShowCreation(parabola2))
+ self.add_fixed_in_frame_mobjects(para_lab_y)
+ self.play(ShowCreation(dot2))
+ self.add_fixed_in_frame_mobjects(lab_y)
+ self.wait()
+ self.play(ShowCreation(line2))
+ self.add_fixed_in_frame_mobjects(tangent_line_y)
+ self.wait()
+
+ self.add_fixed_in_frame_mobjects(text2, brace2, t2)
+ grp2 = VGroup(text2, brace2, t2)
+ grp2.move_to(3*UP+3*RIGHT)
+ self.play(Write(text2),GrowFromCenter(brace2), FadeIn(t2))
+ self.wait()
+ self.play(FadeOut(parabola2), FadeOut(line2), FadeOut(lab_y), FadeOut(para_lab_y), FadeOut(dot2), FadeOut(tangent_line_y), FadeOut(grp2))
+ self.wait()
+
+
+ #self.move_camera(phi=80* DEGREES,theta=105*DEGREES)
+ self.play(ReplacementTransform(paraboloid_y, paraboloid_copy2))
+ self.wait()
+
+
+ self.play(ShowCreation(plane1))
+ self.add_fixed_in_frame_mobjects(plane1_text)
+ self.wait()
+ self.play(ReplacementTransform(paraboloid_copy2, paraboloid_x_copy))
+
+ lab_x.move_to(np.array([1.8*RIGHT +1.15*UP]))
+ para_lab_x.move_to(np.array([1.3*LEFT +1.6*UP]))
+ lab_line3.move_to(np.array([2.4*RIGHT +0.5*UP]))
+ self.wait()
+ self.play(FadeOut(plane1), FadeOut(plane1_text))
+ self.play(ShowCreation(parabola1))
+ self.add_fixed_in_frame_mobjects(para_lab_x)
+ self.play(ShowCreation(dot1))
+ self.add_fixed_in_frame_mobjects(lab_x)
+ self.play(ShowCreation(dot3))
+ self.add_fixed_in_frame_mobjects(lab_line3)
+ self.wait()
+ self.play(ShowCreation(line1))
+ self.add_fixed_in_frame_mobjects(tangent_line_x)
+ self.play(ShowCreation(line3))
+ self.wait()
+
+
+ self.add_fixed_in_frame_mobjects(text1,text3)
+ text1.move_to(3*UP+3*RIGHT)
+ text3.next_to(text1, DOWN)
+ self.play(Write(text1),Write(text3))
+ self.wait()
+ self.play(FadeOut(parabola1), FadeOut(line1), FadeOut(lab_x), FadeOut(line3), FadeOut(lab_line3), FadeOut(para_lab_x), FadeOut(dot1), FadeOut(dot3), FadeOut(tangent_line_x), FadeOut(text1), FadeOut(text3))
+ self.wait()
+
+
+
+
+
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file4_partial_deriv_example.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file4_partial_deriv_example.py new file mode 100644 index 0000000..5712a62 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file4_partial_deriv_example.py @@ -0,0 +1,246 @@ +from manimlib.imports import *
+
+class PartialDerivX(ThreeDScene):
+ def construct(self):
+ axes = ThreeDAxes()
+
+ paraboloid = ParametricSurface(
+ lambda u, v: np.array([
+ 2*np.sin(u)*np.cos(v),
+ 2*np.sin(u)*np.sin(v),
+ -2*2*np.sin(u)*np.sin(u)+2
+ ]),u_min=0,u_max=PI/2,v_min=0,v_max=2*PI,checkerboard_colors=[PINK, PURPLE],
+ resolution=(15, 32)).scale(1)
+
+ paraboloid_copy = paraboloid.copy()
+
+
+ paraboloid_x = ParametricSurface(
+ lambda u, v: np.array([
+ 2*np.sin(u)*np.cos(v),
+ 2*np.sin(u)*np.sin(v),
+ -2*2*np.sin(u)*np.sin(u)+2
+ ]),u_min=0,u_max=PI/2,v_min=PI,v_max=2*PI,checkerboard_colors=[PINK, PURPLE],
+ resolution=(15, 32)).scale(1)
+
+
+ parabola =ParametricFunction(
+ lambda u : np.array([
+ u,
+ 0,
+ -(u*u) + 2
+ ]),color="#006400",t_min=-2,t_max=2,
+ )
+
+ plane = Polygon(np.array([-2.2,0,-2.5]),np.array([2.2,0,-2.5]),np.array([2.2,0,2.5]),np.array([-2.2,0,2.5]),np.array([-2.2,0,-2.5]), color = GREEN, fill_color = GREEN, fill_opacity = 0.2)
+ plane_text = TextMobject(r"$y = 0$", color = GREEN_C).move_to(2*UP + 3*RIGHT)
+
+ surface_eqn = TextMobject("Surface", r"$z = 2- x^2 -y^2$", color = PINK).scale(0.6).move_to(np.array([3*LEFT +3*UP]))
+ surface_eqn[0].set_color(BLUE_C)
+
+ line = Line(np.array([-2,0,0]), np.array([2,0,0]), color = RED_C)
+
+
+ self.add(axes)
+
+ axis = TextMobject(r"X",r"Y",r"Z")
+ axis[0].move_to(6*RIGHT)
+ axis[1].move_to(6*UP)
+ axis[2].move_to(3.7*UP)
+
+ self.add_fixed_in_frame_mobjects(axis[2])
+ self.add_fixed_orientation_mobjects(axis[0])
+ self.add_fixed_orientation_mobjects(axis[1])
+
+
+ self.set_camera_orientation(phi=80 * DEGREES, theta = 0*DEGREES)
+
+ self.play(Write(paraboloid))
+
+ self.add_fixed_in_frame_mobjects(surface_eqn)
+ #self.move_camera(phi=80* DEGREES,theta=95*DEGREES)
+ self.move_camera(phi=80* DEGREES,theta=45*DEGREES)
+ self.play(ShowCreation(plane))
+ self.add_fixed_in_frame_mobjects(plane_text)
+ self.wait()
+ self.play(ReplacementTransform(paraboloid, paraboloid_x))
+ self.play(FadeOut(plane), FadeOut(plane_text))
+ self.play(ShowCreation(parabola), ShowCreation(line))
+
+ text1 = TextMobject("Moving small", r"$dx$", r"steps").scale(0.6).move_to(3*UP + 3.5*RIGHT).set_color_by_gradient(RED, ORANGE, YELLOW, BLUE, PURPLE)
+
+ text2 = TextMobject("Observing change in function, keeping", r"$y$", r"constant").scale(0.6).move_to(2.6*UP + 3.5*RIGHT).set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
+
+ slope_text = TexMobject("Slope =", "{\\partial", "f", "\\over", "\\partial", "x}").scale(0.6).move_to(2*UP + 3.5*RIGHT)
+ slope_text[0].set_color(BLUE_E)
+ slope_text.set_color_by_tex("\\partial",PINK)
+ slope_text.set_color_by_tex("f","#006400")
+ slope_text[5].set_color(RED_C)
+
+ self.add_fixed_in_frame_mobjects(text1, text2)
+ self.wait()
+ self.add_fixed_in_frame_mobjects(slope_text)
+ #add_fixed_orientation_mobjects
+
+
+ dot = Dot().rotate(PI/2).set_color(RED_C)
+ alpha = ValueTracker(0)
+ vector = self.get_tangent_vector(alpha.get_value(),parabola,scale=1.5)
+ dot.add_updater(lambda m: m.move_to(vector.get_center()))
+ self.play(
+ ShowCreation(parabola),
+ GrowFromCenter(dot),
+ GrowArrow(vector)
+ )
+ vector.add_updater(
+ lambda m: m.become(
+ self.get_tangent_vector(alpha.get_value()%1,parabola,scale=1.5)
+ )
+ )
+ self.add(vector,dot)
+ self.play(alpha.increment_value, 1, run_time=10, rate_func=linear)
+ self.wait()
+
+
+ '''
+ for i in np.arange(-2,2,0.2):
+ self.play(ReplacementTransform(Line(np.array([i,0,0]), np.array([i,0,-i*i + 2]), color = GREEN_C), Line(np.array([i+0.2,0,0]), np.array([i+0.2,0,-(i+0.2)**2 + 2]), color = GREEN_C)))
+ #self.wait()
+ '''
+
+ self.wait()
+ self.play(FadeOut(parabola), FadeOut(line), FadeOut(vector), FadeOut(dot), FadeOut(text1), FadeOut(text2), FadeOut(slope_text),FadeOut(surface_eqn))
+
+ #self.move_camera(phi=80* DEGREES,theta= 0*DEGREES)
+ self.play(ReplacementTransform(paraboloid_x, paraboloid_copy))
+ self.wait()
+
+
+ def get_tangent_vector(self, proportion, curve, dx=0.001, scale=1):
+ coord_i = curve.point_from_proportion(proportion)
+ coord_f = curve.point_from_proportion(proportion + dx)
+ reference_line = Line(coord_i,coord_f)
+ unit_vector = reference_line.get_unit_vector() * scale
+ vector = Line(coord_i - unit_vector, coord_i + unit_vector, color = BLUE_E, buff=0)
+ return vector
+
+
+class PartialDerivY(ThreeDScene):
+ def construct(self):
+ axes = ThreeDAxes()
+
+ paraboloid = ParametricSurface(
+ lambda u, v: np.array([
+ 2*np.sin(u)*np.cos(v),
+ 2*np.sin(u)*np.sin(v),
+ -2*2*np.sin(u)*np.sin(u)+2
+ ]),u_min=0,u_max=PI/2,v_min=0,v_max=2*PI,checkerboard_colors=[PINK, PURPLE],
+ resolution=(15, 32)).scale(1)
+
+ paraboloid_copy = paraboloid.copy()
+
+
+ paraboloid_y = ParametricSurface(
+ lambda u, v: np.array([
+ 2*np.sin(u)*np.cos(v),
+ 2*np.sin(u)*np.sin(v),
+ -2*2*np.sin(u)*np.sin(u)+2
+ ]),u_min=0,u_max=PI/2,v_min=PI/2,v_max=3*PI/2,checkerboard_colors=[PINK, PURPLE],
+ resolution=(15, 32)).scale(1)
+
+
+ parabola =ParametricFunction(
+ lambda u : np.array([
+ 0,
+ u,
+ -(u*u) + 2
+ ]),color=YELLOW_C,t_min=-2,t_max=2,
+ )
+
+ plane = Polygon(np.array([0,-2.2,-2.5]),np.array([0,2.2,-2.5]),np.array([0,2.2,2.5]),np.array([0,-2.2,2.5]),np.array([0,-2.2,-2.5]), color = BLUE, fill_color = BLUE, fill_opacity = 0.2)
+ plane_text = TextMobject(r"$x = 0$", color = BLUE_C).move_to(2*UP + 3*RIGHT)
+
+ surface_eqn = TextMobject("Surface", r"$z = 2- x^2 -y^2$", color = PINK).scale(0.6).move_to(np.array([3*LEFT +3*UP]))
+ surface_eqn[0].set_color(BLUE_C)
+
+ line = Line(np.array([0,-2,0]), np.array([0,2,0]), color = RED_C)
+
+ self.add(axes)
+
+ axis = TextMobject(r"X",r"Y",r"Z")
+ axis[0].move_to(6*RIGHT)
+ axis[1].move_to(6*UP)
+ axis[2].move_to(3.7*UP)
+
+ self.add_fixed_in_frame_mobjects(axis[2])
+ self.add_fixed_orientation_mobjects(axis[0])
+ self.add_fixed_orientation_mobjects(axis[1])
+
+ self.set_camera_orientation(phi=80 * DEGREES, theta = 45*DEGREES)
+
+ self.play(Write(paraboloid))
+
+ self.add_fixed_in_frame_mobjects(surface_eqn)
+ #self.move_camera(phi=80* DEGREES,theta=5*DEGREES)
+ self.play(ShowCreation(plane))
+ self.add_fixed_in_frame_mobjects(plane_text)
+ self.wait()
+ self.play(ReplacementTransform(paraboloid, paraboloid_y))
+ self.play(FadeOut(plane), FadeOut(plane_text))
+ self.play(ShowCreation(parabola), ShowCreation(line))
+
+ text1 = TextMobject("Moving small", r"$dy$", r"steps").scale(0.6).move_to(3*UP + 3.5*RIGHT).set_color_by_gradient(RED, ORANGE, YELLOW, BLUE, PURPLE)
+
+ text2 = TextMobject("Observing change in function, keeping", r"$x$", r"constant").scale(0.6).move_to(2.6*UP + 3.5*RIGHT).set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
+
+ slope_text = TexMobject("Slope =", "{\\partial", "f", "\\over", "\\partial", "y}").scale(0.6).move_to(2*UP + 3.5*RIGHT)
+ slope_text[0].set_color("#006400")
+ slope_text.set_color_by_tex("\\partial",PINK)
+ slope_text.set_color_by_tex("f",YELLOW_C)
+ slope_text[5].set_color(RED_C)
+
+ self.add_fixed_in_frame_mobjects(text1, text2)
+ self.wait()
+ self.add_fixed_in_frame_mobjects(slope_text)
+
+ dot = Dot().rotate(PI/2).set_color(RED_C)
+ alpha = ValueTracker(0)
+ vector = self.get_tangent_vector(alpha.get_value(),parabola,scale=1.5)
+ dot.add_updater(lambda m: m.move_to(vector.get_center()))
+ self.play(
+ ShowCreation(parabola),
+ GrowFromCenter(dot),
+ GrowArrow(vector)
+ )
+ vector.add_updater(
+ lambda m: m.become(
+ self.get_tangent_vector(alpha.get_value()%1,parabola,scale=1.5)
+ )
+ )
+ self.add(vector,dot)
+ self.play(alpha.increment_value, 1, run_time=10, rate_func=linear)
+ self.wait()
+
+ '''
+ for i in np.arange(-2,2,0.2):
+ self.play(ReplacementTransform(Line(np.array([0,i,0]), np.array([0,i,-i*i + 2]), color = BLUE_C), Line(np.array([0,i+0.2,0]), np.array([0,i+0.2,-(i+0.2)**2 + 2]), color = BLUE_C)))
+ #self.wait()
+ '''
+
+
+ self.wait()
+ self.play(FadeOut(parabola), FadeOut(line), FadeOut(vector), FadeOut(dot), FadeOut(text1), FadeOut(text2), FadeOut(slope_text),FadeOut(surface_eqn))
+
+ #self.move_camera(phi=80* DEGREES,theta= 90*DEGREES)
+ self.play(ReplacementTransform(paraboloid_y, paraboloid_copy))
+ self.wait()
+
+ def get_tangent_vector(self, proportion, curve, dx=0.001, scale=1):
+ coord_i = curve.point_from_proportion(proportion)
+ coord_f = curve.point_from_proportion(proportion + dx)
+ reference_line = Line(coord_i,coord_f)
+ unit_vector = reference_line.get_unit_vector() * scale
+ vector = Line(coord_i - unit_vector, coord_i + unit_vector, color = "#006400", buff=0)
+ return vector
+
+
\ No newline at end of file diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file5_partial_deriv_func_2maximas.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file5_partial_deriv_func_2maximas.py new file mode 100644 index 0000000..7bbb9a7 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file5_partial_deriv_func_2maximas.py @@ -0,0 +1,227 @@ +from manimlib.imports import *
+
+class MaximaMinima(ThreeDScene):
+ def construct(self):
+ axes = ThreeDAxes()
+
+ paraboloid = ParametricSurface(
+ lambda u, v: np.array([
+ 3.5*np.sin(u)*np.cos(v),
+ 3.5*np.sin(u)*np.sin(v),
+ 3.5*3.5*np.sin(u)*np.sin(u)*(1+2*np.sin(v)*np.sin(v))*np.exp(1 - 3.5*3.5*np.sin(u)*np.sin(u) )
+ ]),u_min=0,u_max=PI,v_min=0,v_max=2*PI, color = BLUE_C, fill_color = BLUE_C, fill_opacity = 0.1,
+ resolution=(15, 32)).scale(1)
+
+ paraboloid_copy1 = paraboloid.copy()
+ paraboloid_copy2 = paraboloid.copy()
+
+ paraboloid_x = ParametricSurface(
+ lambda u, v: np.array([
+ 3.5*np.sin(u)*np.cos(v),
+ 3.5*np.sin(u)*np.sin(v),
+ 3.5*3.5*np.sin(u)*np.sin(u)*(1+2*np.sin(v)*np.sin(v))*np.exp(1 - 3.5*3.5*np.sin(u)*np.sin(u) )
+ ]),u_min=0,u_max=PI,v_min=PI,v_max=2*PI, color = BLUE_C, fill_color = BLUE_C, fill_opacity = 0.1,
+ resolution=(15, 32)).scale(1)
+
+ paraboloid_y = ParametricSurface(
+ lambda u, v: np.array([
+ 3.5*np.sin(u)*np.cos(v),
+ 3.5*np.sin(u)*np.sin(v),
+ 3.5*3.5*np.sin(u)*np.sin(u)*(1+2*np.sin(v)*np.sin(v))*np.exp(1 - 3.5*3.5*np.sin(u)*np.sin(u) )
+ ]),u_min=0,u_max=PI,v_min=PI/2,v_max=3*PI/2, color = BLUE_C, fill_color = BLUE_C, fill_opacity = 0.1,
+ resolution=(15, 32)).scale(1)
+
+ parabola_x_out =ParametricFunction(
+ lambda u : np.array([
+ u,
+ 0,
+ (u*u )*np.exp(1-u*u)
+ ]),color=RED_E,t_min=-3.5,t_max=3.5,
+ )
+
+ parabola_y_out =ParametricFunction(
+ lambda u : np.array([
+ 0,
+ u,
+ (3*u*u)*np.exp(1-u*u)
+ ]),color=PINK,t_min=-3.5,t_max=3.5,
+ )
+
+ plane1 = Polygon(np.array([-3.5,0,-3]),np.array([3.5,0,-3]),np.array([3.5,0,3]),np.array([-3.5,0,3]),np.array([-3.5,0,-3]), color = RED_C, fill_color = RED_C, fill_opacity = 0.2)
+ plane_text_x = TextMobject(r"$y = 0$", color = RED_C).move_to(2*UP + 4.5*RIGHT)
+
+ plane2 = Polygon(np.array([0,-3.5,-3]),np.array([0,3.5,-3]),np.array([0,3.5,3]),np.array([0,-3.5,3]),np.array([0,-3.5,-3]), color = PINK, fill_color = PINK, fill_opacity = 0.2)
+ plane_text_y = TextMobject(r"$x = 0$", color = PINK).move_to(2*UP + 4.5*RIGHT)
+
+ surface_eqn = TextMobject("Surface", r"$z = (x^2 + 3y^2)e^{(1 - x^2 - y^2)}$", color = YELLOW_C).scale(0.6).move_to(np.array([3.5*LEFT +3.5*UP]))
+ surface_eqn[0].set_color(BLUE_C)
+
+ self.set_camera_orientation(phi=60 * DEGREES, theta = 45*DEGREES)
+
+ self.add(axes)
+ axis = TextMobject(r"X",r"Y",r"Z")
+ axis[0].move_to(6*RIGHT)
+ axis[1].move_to(6*UP)
+ axis[2].move_to(np.array([0,0,3.7]))
+
+ self.add_fixed_orientation_mobjects(axis[2])
+ self.add_fixed_orientation_mobjects(axis[0])
+ self.add_fixed_orientation_mobjects(axis[1])
+
+ self.play(ShowCreation(paraboloid))
+
+
+ #self.move_camera(phi=60 * DEGREES, theta = 45*DEGREES,run_time=3)
+
+
+ plane_x = Polygon(np.array([-3.5,2,-3]),np.array([3.5,2,-3]),np.array([3.5,2,3]),np.array([-3.5,2,3]),np.array([-3.5,2,-3]), color = YELLOW_C, fill_color = YELLOW_A, fill_opacity = 0.2)
+
+ plane_y = Polygon(np.array([2,-3.5,-3]),np.array([2,3.5,-3]),np.array([2,3.5,3]),np.array([2,-3.5,3]),np.array([2,-3.5,-3]), color = GREEN_C, fill_color = GREEN_A, fill_opacity = 0.2)
+
+ text_x = TextMobject(r"$x$", "is fixed on this" ,"plane").scale(0.7).to_corner(UL)
+ text_y = TextMobject(r"$y$", "is fixed on this" ,"plane").scale(0.7).to_corner(UR)
+
+ text_x[0].set_color(RED_C)
+ text_y[0].set_color(PINK)
+ text_x[1].set_color(BLUE_C)
+ text_y[1].set_color(BLUE_C)
+ text_x[2].set_color(GREEN_C)
+ text_y[2].set_color(YELLOW_C)
+
+ self.add_fixed_in_frame_mobjects(text_x, text_y)
+
+ for i in range(2,-4,-1):
+
+ parabola_x =ParametricFunction(lambda u : np.array([u,i,(u*u + 3*i*i)*np.exp(1- u*u - i*i)]),color=RED_C,t_min=-3.5,t_max=3.5,)
+
+ parabola_y =ParametricFunction(lambda u : np.array([i,u,(i*i + 3*u*u)*np.exp(1- u*u - i*i)]),color=PINK,t_min=-3.5,t_max=3.5,)
+
+ if(i==2):
+ self.play(ShowCreation(plane_x), ShowCreation(plane_y))
+ parabola_copy_x = parabola_x.copy()
+ parabola_copy_y = parabola_y.copy()
+
+
+ self.play(ShowCreation(parabola_copy_x), ShowCreation(parabola_copy_y))
+ self.wait()
+ self.play(FadeOut(parabola_copy_x), FadeOut(parabola_copy_y))
+
+ else:
+ self.play(ApplyMethod(plane_x.move_to, np.array([0,i,0])),ReplacementTransform(parabola_copy_x, parabola_x),ApplyMethod(plane_y.move_to, np.array([i,0,0])),ReplacementTransform(parabola_copy_y, parabola_y))
+ self.play(FadeOut(parabola_x), FadeOut(parabola_y))
+ self.wait()
+
+ parabola_copy_x = parabola_x.copy()
+ parabola_copy_y = parabola_y.copy()
+
+ self.play(FadeOut(plane_x), FadeOut(plane_y), FadeOut(text_x), FadeOut(text_y))
+
+
+ self.add_fixed_in_frame_mobjects(surface_eqn)
+
+ self.move_camera(phi=80 * DEGREES, theta = 95*DEGREES)
+
+ self.play(ShowCreation(plane1))
+ self.add_fixed_in_frame_mobjects(plane_text_x)
+ self.wait()
+ self.play(ReplacementTransform(paraboloid, paraboloid_x))
+ self.play(FadeOut(plane1), FadeOut(plane_text_x))
+
+ line_x = Line(np.array([-3.5,0,0]), np.array([3.5,0,0]), color = YELLOW_E)
+
+ self.play(ShowCreation(parabola_x_out), ShowCreation(line_x))
+
+ slope_text_x = TexMobject("Slope =", "{\\partial", "f", "\\over", "\\partial", "x}").scale(0.6).move_to(2*UP + 3.5*RIGHT)
+ slope_text_x[0].set_color(ORANGE)
+ slope_text_x.set_color_by_tex("\\partial",GREEN_E)
+ slope_text_x.set_color_by_tex("f",RED_E)
+ slope_text_x[5].set_color(YELLOW_E)
+
+ self.add_fixed_in_frame_mobjects(slope_text_x)
+
+
+ dot_x = Dot().rotate(PI/2).set_color(YELLOW_E)
+ alpha_x = ValueTracker(0)
+ vector_x = self.get_tangent_vector(alpha_x.get_value(),parabola_x_out,scale=1.5)
+ dot_x.add_updater(lambda m: m.move_to(vector_x.get_center()))
+ self.play(
+ ShowCreation(parabola_x_out),
+ GrowFromCenter(dot_x),
+ GrowArrow(vector_x)
+ )
+ vector_x.add_updater(
+ lambda m: m.become(
+ self.get_tangent_vector(alpha_x.get_value()%1,parabola_x_out,scale=1.5)
+ )
+ )
+ self.add(vector_x,dot_x)
+ self.play(alpha_x.increment_value, 1, run_time=10, rate_func=linear)
+
+ self.wait(2)
+ self.play(FadeOut(parabola_x_out), FadeOut(line_x), FadeOut(vector_x), FadeOut(dot_x), FadeOut(slope_text_x))
+
+ self.move_camera(phi=80* DEGREES,theta= 5*DEGREES)
+ self.play(ReplacementTransform(paraboloid_x, paraboloid_copy1))
+ self.wait()
+
+
+
+ self.play(ShowCreation(plane2))
+ self.add_fixed_in_frame_mobjects(plane_text_y)
+ self.wait()
+ self.play(ReplacementTransform(paraboloid_copy1, paraboloid_y))
+ self.play(FadeOut(plane2), FadeOut(plane_text_y))
+
+ line_y = Line(np.array([0,-3.5,0]), np.array([0,3.5,0]), color = GREEN_E)
+
+ self.play(ShowCreation(parabola_y_out), ShowCreation(line_y))
+
+ slope_text_y = TexMobject("Slope =", "{\\partial", "f", "\\over", "\\partial", "y}").scale(0.6).move_to(2*UP + 3.5*RIGHT)
+ slope_text_y[0].set_color(ORANGE)
+ slope_text_y.set_color_by_tex("\\partial",YELLOW_E)
+ slope_text_y.set_color_by_tex("f",PINK)
+ slope_text_y[5].set_color(GREEN_E)
+
+ self.add_fixed_in_frame_mobjects(slope_text_y)
+
+
+ dot_y = Dot().rotate(PI/2).set_color(GREEN_E)
+ alpha_y = ValueTracker(0)
+ vector_y = self.get_tangent_vector(alpha_y.get_value(),parabola_y_out,scale=1.5)
+ dot_y.add_updater(lambda m: m.move_to(vector_y.get_center()))
+ self.play(
+ ShowCreation(parabola_y_out),
+ GrowFromCenter(dot_y),
+ GrowArrow(vector_y)
+ )
+ vector_y.add_updater(
+ lambda m: m.become(
+ self.get_tangent_vector(alpha_y.get_value()%1,parabola_y_out,scale=1.5)
+ )
+ )
+ self.add(vector_y,dot_y)
+ self.play(alpha_y.increment_value, 1, run_time=10, rate_func=linear)
+
+ self.wait(2)
+ self.play(FadeOut(parabola_y_out), FadeOut(line_y), FadeOut(vector_y), FadeOut(dot_y), FadeOut(slope_text_y))
+
+ self.move_camera(phi=60* DEGREES,theta= 45*DEGREES)
+ self.play(ReplacementTransform(paraboloid_y, paraboloid_copy2))
+ self.wait()
+
+
+
+
+
+
+
+
+
+ def get_tangent_vector(self, proportion, curve, dx=0.001, scale=1):
+ coord_i = curve.point_from_proportion(proportion)
+ coord_f = curve.point_from_proportion(proportion + dx)
+ reference_line = Line(coord_i,coord_f)
+ unit_vector = reference_line.get_unit_vector() * scale
+ vector = Line(coord_i - unit_vector , coord_i + unit_vector, color = ORANGE, buff=0)
+ return vector
+
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file6_clariant_rule.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file6_clariant_rule.py new file mode 100644 index 0000000..b79f77c --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file6_clariant_rule.py @@ -0,0 +1,64 @@ +from manimlib.imports import *
+
+class ClariantRule(Scene):
+ def construct(self):
+ derivatives = TextMobject(r"$cos(x)y^3$",r"$-sin(x)y^3$", r"$3cos(x)y^2$", r"$-cos(x)y^3$", r"$-3sin(x)y^2$", r"$-3sin(x)y^2$", r"$6cos(x)y$")
+
+ partial_derivatives = TextMobject(r"$\frac{\partial}{\partial x}$", r"$\frac{\partial}{\partial y}$")
+
+
+ derivatives[0].move_to(2*UP).set_color(PURPLE)
+ derivatives[1].move_to(3*LEFT).set_color(YELLOW_C)
+ derivatives[2].move_to(3*RIGHT).set_color(BLUE_C)
+
+ arrrow_1 = Arrow(derivatives[0].get_bottom(), derivatives[1].get_top())
+ arrrow_1_lab = partial_derivatives[0].copy().scale(0.7)
+ arrrow_1_lab.move_to(2.5*LEFT+ 1.3*UP)
+
+ arrrow_2 = Arrow(derivatives[0].get_bottom(), derivatives[2].get_top())
+ arrrow_2_lab = partial_derivatives[1].copy().scale(0.7)
+ arrrow_2_lab.move_to(2.5*RIGHT+ 1.3*UP)
+
+ self.play(Write(derivatives[0]))
+ self.play(GrowArrow(arrrow_1), GrowArrow(arrrow_2), Write(arrrow_1_lab), Write(arrrow_2_lab))
+
+ self.play(Write(derivatives[1]))
+ self.play(Write(derivatives[2]))
+
+ derivatives[3].move_to(2*DOWN + 4.5*LEFT).set_color(GREEN_C)
+ derivatives[4].move_to(2*DOWN + 1.5*LEFT).set_color(PINK)
+ derivatives[5].move_to(2*DOWN + 1.5*RIGHT).set_color(PINK)
+ derivatives[6].move_to(2*DOWN + 4.5*RIGHT).set_color(ORANGE)
+
+ arrrow_3 = Arrow(derivatives[1].get_bottom(), derivatives[3].get_top())
+ arrrow_3_lab = partial_derivatives[0].copy().scale(0.7)
+ arrrow_3_lab.move_to(4.3*LEFT+ 0.8*DOWN)
+
+ arrrow_4 = Arrow(derivatives[1].get_bottom(), derivatives[4].get_top())
+ arrrow_4_lab = partial_derivatives[1].copy().scale(0.7)
+ arrrow_4_lab.move_to(1.6*LEFT+ 0.8*DOWN)
+
+ arrrow_5 = Arrow(derivatives[2].get_bottom(), derivatives[5].get_top())
+ arrrow_5_lab = partial_derivatives[0].copy().scale(0.7)
+ arrrow_5_lab.move_to(1.6*RIGHT+ 0.8*DOWN)
+
+ arrrow_6 = Arrow(derivatives[2].get_bottom(), derivatives[6].get_top())
+ arrrow_6_lab = partial_derivatives[1].copy().scale(0.7)
+ arrrow_6_lab.move_to(4.3*RIGHT+ 0.8*DOWN)
+
+ self.play(GrowArrow(arrrow_3), GrowArrow(arrrow_4), Write(arrrow_3_lab), Write(arrrow_4_lab))
+ self.play(Write(derivatives[3]), Write(derivatives[4]))
+
+ self.play(GrowArrow(arrrow_5), GrowArrow(arrrow_6), Write(arrrow_5_lab), Write(arrrow_6_lab))
+ self.play(Write(derivatives[5]), Write(derivatives[6]))
+
+ brace1 = Brace(derivatives[4:6], DOWN, buff = SMALL_BUFF, color = RED_C)
+ brace_t1 = brace1.get_text("Mixed partial derivatives are the same!")
+ brace_t1.set_color(RED_C)
+
+ self.play(GrowFromCenter(brace1), FadeIn(brace_t1))
+
+ self.wait()
+
+
+
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file7_partial_deriv_clariant_rule.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file7_partial_deriv_clariant_rule.py new file mode 100644 index 0000000..313c6cd --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file7_partial_deriv_clariant_rule.py @@ -0,0 +1,108 @@ +from manimlib.imports import *
+
+class ClariantRule(ThreeDScene):
+ def construct(self):
+ axes = ThreeDAxes()
+
+ function = ParametricSurface(
+ lambda u, v: np.array([
+ 3.5*np.sin(u)*np.cos(v),
+ 3.5*np.sin(u)*np.sin(v),
+ 3.5*3.5*np.sin(u)*np.sin(u)*(1+2*np.sin(v)*np.sin(v))*np.exp(1 - 3.5*3.5*np.sin(u)*np.sin(u) )
+ ]),u_min=0,u_max=PI,v_min=0,v_max=2*PI, color = BLUE_C, fill_color = BLUE_C, fill_opacity = 0.1,
+ resolution=(15, 32)).scale(1)
+
+
+ function_copy1 = function.copy()
+ function_copy2 = function.copy()
+
+ func_x =ParametricFunction(
+ lambda u : np.array([
+ u,
+ -1,
+ (u*u )*np.exp(1-u*u)
+ ]),color=RED_E,t_min=-3.5,t_max=3.5,
+ )
+
+ func_y =ParametricFunction(
+ lambda u : np.array([
+ 0,
+ u,
+ (3*u*u)*np.exp(1-u*u)
+ ]),color=PINK,t_min=-3.5,t_max=3.5,
+ )
+
+ plane_x = Polygon(np.array([-3.5,-1,-3]),np.array([3.5,-1,-3]),np.array([3.5,-1,3]),np.array([-3.5,-1,3]),np.array([-3.5,-1,-3]), color = YELLOW_E, fill_color = YELLOW_B, fill_opacity = 0.1)
+ plane_text_x = TextMobject(r"$y = -1$", color = YELLOW_C).move_to(np.array([5,0,2.7])).scale(0.7)
+
+ plane_y = Polygon(np.array([0,-3.5,-3]),np.array([0,3.5,-3]),np.array([0,3.5,3]),np.array([0,-3.5,3]),np.array([0,-3.5,-3]), color = GREEN_E, fill_color = GREEN_B, fill_opacity = 0.1)
+ plane_text_y = TextMobject(r"$x = 0$", color = GREEN_C).move_to(np.array([0,4,2.7])).scale(0.7)
+
+ surface_eqn = TextMobject("Surface", r"$z = (x^2 + 3y^2)e^{(1 - x^2 - y^2)}$", color = YELLOW_C).scale(0.6).move_to(np.array([4.6*LEFT+3.5*UP]))
+ surface_eqn[0].set_color(BLUE_C)
+
+ self.set_camera_orientation(phi=60 * DEGREES, theta = 45*DEGREES)
+
+ self.add(axes)
+ axis = TextMobject(r"X",r"Y",r"Z")
+ axis[0].move_to(6*RIGHT)
+ axis[1].move_to(6*UP)
+ axis[2].move_to(np.array([0,0,3.7]))
+
+ self.add_fixed_orientation_mobjects(axis[2])
+ self.add_fixed_orientation_mobjects(axis[0])
+ self.add_fixed_orientation_mobjects(axis[1])
+
+ self.play(ShowCreation(function))
+
+ self.add_fixed_in_frame_mobjects(surface_eqn)
+
+ self.play(ShowCreation(plane_x), ShowCreation(plane_y))
+ self.add_fixed_orientation_mobjects(plane_text_x, plane_text_y)
+
+ self.play(ShowCreation(func_x), ShowCreation(func_y))
+
+ dot_x = Dot().rotate(PI/2).set_color(YELLOW_E)
+ alpha_x = ValueTracker(0)
+ vector_x = self.get_tangent_vector(alpha_x.get_value(),func_x,scale=1.5)
+ dot_x.add_updater(lambda m: m.move_to(vector_x.get_center()))
+ self.play(
+ ShowCreation(func_x),
+ GrowFromCenter(dot_x),
+ GrowArrow(vector_x)
+ )
+ vector_x.add_updater(
+ lambda m: m.become(
+ self.get_tangent_vector(alpha_x.get_value()%1,func_x,scale=1.5)
+ )
+ )
+ dot_y = Dot().rotate(PI/2).set_color(GREEN_E)
+ alpha_y = ValueTracker(0)
+ vector_y = self.get_tangent_vector(alpha_y.get_value(),func_y,scale=1.5)
+ dot_y.add_updater(lambda m: m.move_to(vector_y.get_center()))
+ self.play(
+ ShowCreation(func_y),
+ GrowFromCenter(dot_y),
+ GrowArrow(vector_y)
+ )
+ vector_y.add_updater(
+ lambda m: m.become(
+ self.get_tangent_vector(alpha_y.get_value()%1,func_y,scale=1.5)
+ )
+ )
+ self.add(vector_x,dot_x)
+
+ self.play(alpha_x.increment_value, 1, run_time=10, rate_func=linear)
+
+ self.add(vector_y,dot_y)
+ self.play(alpha_y.increment_value, 1, run_time=10, rate_func=linear)
+
+ self.wait(2)
+
+
+
+
+
+
+
+
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file8_chain_rule.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file8_chain_rule.py new file mode 100644 index 0000000..f50d2d1 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file8_chain_rule.py @@ -0,0 +1,60 @@ +from manimlib.imports import *
+
+class ChainRule(Scene):
+ def construct(self):
+
+ chain_rule = TextMobject(r"$\frac{dw}{dt}$", r"=", r"$\frac{\partial w}{\partial x}$", r"$\frac{dx}{dt}$", r"+", r"$\frac{\partial w}{\partial y}$", r"$\frac{dy}{dt}$").move_to(4*RIGHT).scale(0.8)
+
+ chain_rule[0].set_color(ORANGE)
+ chain_rule[2].set_color(GREEN_C)
+ chain_rule[3].set_color(RED_C)
+ chain_rule[5].set_color(YELLOW_C)
+ chain_rule[6].set_color(BLUE_C)
+
+ functions = TextMobject(r"$w =f(x,y)$",r"$x$", r"$y$", r"$t$")
+
+ functions[0].move_to(3.3*UP+1*LEFT).set_color(ORANGE)
+ functions[1].move_to(3.3*LEFT).set_color(PURPLE)
+ functions[2].move_to(1.3*RIGHT).set_color(PURPLE)
+ functions[3].move_to(3.3*DOWN+1*LEFT).set_color(WHITE)
+
+ partial_derivatives = TextMobject(r"$\frac{\partial w}{\partial x}$", r"$\frac{\partial w}{\partial y}$")
+
+ partial_derivatives[0].move_to(1.5*UP+3*LEFT).set_color(GREEN_C)
+ partial_derivatives[1].move_to(1.5*UP+1*RIGHT).set_color(YELLOW_C)
+
+ derivatives = TextMobject(r"$\frac{dx}{dt}$", r"$\frac{dy}{dt}$")
+
+ derivatives[0].move_to(1.5*DOWN+3*LEFT).set_color(RED_C)
+ derivatives[1].move_to(1.5*DOWN+1*RIGHT).set_color(BLUE_C)
+
+ line_f_x = Line(np.array([-1,3,0]), np.array([-3,0,0]), color = BLUE_C)
+ line_f_y = Line(np.array([-1,3,0]), np.array([1,0,0]), color = BLUE_C)
+ line_x_t = Line(np.array([-3,0,0]), np.array([-1,-3,0]), color = BLUE_C)
+ line_y_t = Line(np.array([1,0,0]), np.array([-1,-3,0]), color = BLUE_C)
+
+ dot_f = Dot().shift(np.array([-1,3,0])).set_color(BLUE_C)
+ dot_x = Dot().shift(np.array([-3,0,0])).set_color(BLUE_C)
+ dot_y = Dot().shift(np.array([1,0,0])).set_color(BLUE_C)
+ dot_t = Dot().shift(np.array([-1,-3,0])).set_color(BLUE_C)
+
+ variables = TextMobject("Dependent Variable","Intermediate Variables", "Dependent Variable").set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE).scale(0.7)
+ variables[0].move_to(3.3*UP+3.5*RIGHT)
+ variables[1].move_to(3.5*RIGHT)
+ variables[2].move_to(3.3*DOWN+3.5*RIGHT)
+
+ self.play(ShowCreation(dot_f), Write(functions[0]))
+ self.play(ShowCreation(dot_x), ShowCreation(line_f_x), Write(functions[1]), ShowCreation(dot_y), ShowCreation(line_f_y), Write(functions[2]))
+ self.play(Write(partial_derivatives[0]), Write(partial_derivatives[1]))
+ self.wait()
+
+ self.play(ShowCreation(dot_t), ShowCreation(line_x_t), ShowCreation(line_y_t), Write(functions[3]))
+ self.play(Write(derivatives[0]), Write(derivatives[1]))
+ self.wait()
+
+ self.play(Write(variables[0]), Write(variables[1]), Write(variables[2]))
+
+ self.play(FadeOut(variables))
+ self.play(Write(chain_rule))
+ self.wait()
+
\ No newline at end of file diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file1_partial_deriv_gas_law.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file1_partial_deriv_gas_law.gif Binary files differnew file mode 100644 index 0000000..8fdb80f --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file1_partial_deriv_gas_law.gif diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file2_partial_deriv_hill.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file2_partial_deriv_hill.gif Binary files differnew file mode 100644 index 0000000..3c758ff --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file2_partial_deriv_hill.gif diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file3_partial_deriv_defn.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file3_partial_deriv_defn.gif Binary files differnew file mode 100644 index 0000000..c66b3fa --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file3_partial_deriv_defn.gif diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file4_partial_deriv_example.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file4_partial_deriv_example.gif Binary files differnew file mode 100644 index 0000000..d2bf541 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file4_partial_deriv_example.gif diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file5_partial_deriv_func_2maximas.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file5_partial_deriv_func_2maximas.gif Binary files differnew file mode 100644 index 0000000..db7f4f8 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file5_partial_deriv_func_2maximas.gif diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file6_clariant_rule.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file6_clariant_rule.gif Binary files differnew file mode 100644 index 0000000..8377827 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file6_clariant_rule.gif diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file7_partial_deriv_clariant_rule.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file7_partial_deriv_clariant_rule.gif Binary files differnew file mode 100644 index 0000000..32d5e92 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file7_partial_deriv_clariant_rule.gif diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file8_chain_rule.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file8_chain_rule.gif Binary files differnew file mode 100644 index 0000000..596b08d --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file8_chain_rule.gif diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/README.md b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/README.md new file mode 100644 index 0000000..4339c30 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/README.md @@ -0,0 +1,20 @@ +**file1_scalar_function** + + +**file2_domain_range** + + +**file3_parabola_example** + + +**file4_level_curves** + + +**file5_level_surface** + + +**file6_scalar_function_application** + + +**file7_neural_nets** + diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file1_scalar_functions.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file1_scalar_functions.py new file mode 100644 index 0000000..1a6f4ed --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file1_scalar_functions.py @@ -0,0 +1,50 @@ +from manimlib.imports import *
+
+class ScalarFunction(Scene):
+ def construct(self):
+ circle = Circle(radius = 1.5, color = BLUE_E, fill_color = BLUE_C, fill_opacity = 0.1).move_to(2*LEFT)
+ dot_circle = Dot().shift(np.array([-1.5,0,0])).set_color(BLUE_E)
+ dot_circle_lab = TextMobject(r"$a$", color = BLUE_E).next_to(dot_circle, DOWN)
+
+ arrow = Arrow(np.array([3,-3,0]),np.array([3,3,0]))
+ line = Line(np.array([3,-1.5,0]),np.array([3,1.5,0]), color = RED_C)
+
+ dot0 = Dot().shift(np.array([3,0,0])).set_color(RED_E)
+ dot0_lab = TextMobject(r"$f(a)$", color = RED_E).scale(0.8).next_to(dot0, RIGHT)
+
+ dot1 = Dot().shift(np.array([3,-1.5,0])).set_color(RED_C)
+
+ dot2 = Dot().shift(np.array([3,1.5,0])).set_color(RED_C)
+ dot2_lab = TextMobject(r"$f(A)$", color = RED_C).scale(0.8).next_to(dot2, RIGHT)
+
+ arrow_f = Arrow(np.array([-1.5,0,0]),np.array([3,0,0]), color = YELLOW_C, buff = 0.1)
+
+ R = TextMobject(r"$\mathbb{R}$", color = WHITE).move_to(np.array([3,-3.3,0]))
+
+ A = TextMobject(r"$A$", color = BLUE_E).move_to(np.array([-2.5,-3.3,0]))
+
+ F = TextMobject(r"$f$", color = GREY).move_to(np.array([0,-2.9,0]))
+
+ F_center = TextMobject(r"$f$", color = YELLOW_C).move_to(np.array([0.8,0.5,0]))
+
+ arrow_R_A = Arrow(np.array([-2.3,-3.3,0]),np.array([2.7,-3.3,0]), color = GREY, buff = 0.1)
+
+ scalar_function = TextMobject(r"Scalar Valued Function", r"$f: A \rightarrow \mathbb{R}$", color = PURPLE).move_to(np.array([0,3.5,0]))
+ scalar_function[1].set_color(GREEN_C)
+
+
+
+ self.play(ShowCreation(circle))
+ self.play(ShowCreation(arrow))
+
+
+ self.play(ShowCreation(dot1), ShowCreation(dot2))
+ self.play(ShowCreation(dot_circle))
+ self.play(ShowCreation(dot_circle_lab), ShowCreation(dot2_lab))
+ self.play(ShowCreation(A), ShowCreation(R))
+ self.play(GrowArrow(arrow_f), ShowCreation(dot0), ShowCreation(dot0_lab), ShowCreation(F_center), GrowArrow(arrow_R_A), ShowCreation(F), Transform(circle.copy(), line.copy()))
+
+ self.play(Write(scalar_function))
+
+
+ self.wait(2)
\ No newline at end of file diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file1_domain_range.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file2_domain_range.py index 9b1ca7b..1b54cb6 100644 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file1_domain_range.py +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file2_domain_range.py @@ -20,6 +20,11 @@ class PlotGraphs(GraphScene): self.play(FadeOut(topic))
self.wait(1)
+ scalar_func_R = TextMobject(r"Scalar Valued Functions in $R$").scale(1.5).set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
+ self.play(Write(scalar_func_R))
+ self.play(FadeOut(scalar_func_R))
+ self.wait(1)
+
XTD = self.x_axis_width/(self.x_max- self.x_min)
YTD = self.y_axis_height/(self.y_max- self.y_min)
@@ -40,8 +45,8 @@ class PlotGraphs(GraphScene): rangeMsg.scale(0.5)
rangeMsg.set_color(YELLOW)
- domainline1 = Line(self.graph_origin+0.6*YTD*DOWN+1.2*XTD*LEFT, self.graph_origin+0.6*YTD*DOWN + 4*XTD*LEFT)
- domainline2 = Arrow(self.graph_origin+0.6*YTD*DOWN+1.1*XTD*RIGHT, self.graph_origin+0.6*YTD*DOWN + 5.3*XTD*RIGHT)
+ domainline1 = Arrow(self.graph_origin+0.6*YTD*DOWN+1.2*XTD*LEFT, self.graph_origin+0.6*YTD*DOWN + 4*XTD*LEFT, buff = 0.1)
+ domainline2 = Arrow(self.graph_origin+0.6*YTD*DOWN+1.1*XTD*RIGHT, self.graph_origin+0.6*YTD*DOWN + 5.3*XTD*RIGHT, buff = 0.1)
domainline1.set_color(PINK)
domainline2.set_color(PINK)
@@ -128,5 +133,58 @@ class PlotSineGraphs(GraphScene): self.play(Write(domainMsg))
self.wait(3)
+
+
+
+class Paraboloid(ThreeDScene):
+ def construct(self):
+
+ scalar_func_R2 = TextMobject(r"Scalar Valued Functions in $R^2$").scale(1.5).set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
+ self.play(Write(scalar_func_R2))
+ self.play(FadeOut(scalar_func_R2))
+ self.wait(1)
+
+ axes = ThreeDAxes()
+
+ paraboloid = ParametricSurface(
+ lambda u, v: np.array([
+ 2*np.sin(u)*np.cos(v),
+ 2*np.sin(u)*np.sin(v),
+ 2*2*np.sin(u)*np.sin(u)
+ ]),u_min=0,u_max=PI/2,v_min=0,v_max=2*PI,checkerboard_colors=[GREEN_C, GREEN_E],
+ resolution=(15, 32)).scale(1)
+
+ domain = Polygon(np.array([-5,-5,0]),np.array([5,-5,0]),np.array([5,5,0]),np.array([-5,5,0]),np.array([-5,-5,0]), color = BLUE_C, fill_color = BLUE_C, fill_opacity = 0.2)
+ domain_lab = TextMobject(r"$Domain: R^2$", color = YELLOW_C).scale(0.7).move_to(1*DOWN + 2*LEFT)
+
+ rangef = Line(np.array([0, 0,0]), np.array([0, 0,5]), color = RED_C)
+ rangef_lab = TextMobject(r"$Range: z \geq 0$", color = RED_C).scale(0.7).move_to(2*UP + 1.5*RIGHT)
+
+ func = TextMobject(r"$z = f(x,y) = x^2+y^2$").scale(0.7).move_to(3*UP + 4*LEFT).set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
+
+ self.set_camera_orientation(phi=60 * DEGREES, theta = 0*DEGREES)
+ self.begin_ambient_camera_rotation(rate=0.3)
+
+ self.add(axes)
+
+ axis = TextMobject(r"X",r"Y",r"Z")
+ axis[0].move_to(6*RIGHT)
+ axis[1].move_to(6*UP)
+ axis[2].move_to(np.array([0,0,3.7]))
+
+ self.add_fixed_orientation_mobjects(axis[2])
+ self.add_fixed_orientation_mobjects(axis[0])
+ self.add_fixed_orientation_mobjects(axis[1])
+
+
+
+ self.add_fixed_in_frame_mobjects(func)
+ self.play(Write(paraboloid))
+ self.play(ShowCreation(domain))
+ self.add_fixed_in_frame_mobjects(domain_lab)
+ self.wait()
+ self.play(ShowCreation(rangef))
+ self.add_fixed_in_frame_mobjects(rangef_lab)
+ self.wait(5)
\ No newline at end of file diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file3_parabola_example.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file3_parabola_example.py index 74dc063..63c16b3 100644 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file3_parabola_example.py +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file3_parabola_example.py @@ -9,11 +9,10 @@ class Parabola(ThreeDScene): 2*np.cosh(u)*np.cos(v),
2*np.cosh(u)*np.sin(v),
2*np.sinh(u)
- ]),v_min=0,v_max=TAU,u_min=0,u_max=2,checkerboard_colors=[YELLOW_D, YELLOW_E],
+ ]),v_min=0,v_max=TAU,u_min=0,u_max=2,checkerboard_colors=[YELLOW_D, YELLOW_E],#
resolution=(15, 32))
- text3d = TextMobject(r"Plot of $f: \mathbb{R}^2 \rightarrow \mathbb{R}$", "z = f(x,y)")
- self.add_fixed_in_frame_mobjects(text3d)
+ text3d = TextMobject(r"Plot of $f: \mathbb{R}^2 \rightarrow \mathbb{R}$", r"$z = f(x,y) = \sqrt{x^2 + y^2 - 4}$")
text3d[0].move_to(4*LEFT+2*DOWN)
text3d[1].next_to(text3d[0], DOWN)
text3d[0].set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
@@ -21,8 +20,21 @@ class Parabola(ThreeDScene): #self.set_camera_orientation(phi=0 * DEGREES,theta=270*DEGREES)
self.move_camera(phi=110* DEGREES,theta=45*DEGREES)
+
self.add(axes)
+
+ axis = TextMobject(r"X",r"Y",r"Z")
+ axis[0].move_to(6*RIGHT)
+ axis[1].move_to(6*UP)
+ axis[2].move_to(np.array([0,0,3.7]))
+
+ self.add_fixed_orientation_mobjects(axis[2])
+ self.add_fixed_orientation_mobjects(axis[0])
+ self.add_fixed_orientation_mobjects(axis[1])
+
+
self.play(ShowCreation(paraboloid))
+ self.add_fixed_in_frame_mobjects(text3d)
self.play(Write(text3d[0]))
self.play(Write(text3d[1]))
self.begin_ambient_camera_rotation(rate=0.2)
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file4_level_curves.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file4_level_curves.py new file mode 100644 index 0000000..2b6f719 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file4_level_curves.py @@ -0,0 +1,118 @@ +from manimlib.imports import *
+
+class LevelCurves(ThreeDScene):
+ def construct(self):
+ axes = ThreeDAxes()
+
+ paraboloid = ParametricSurface(
+ lambda u, v: np.array([
+ u*np.cos(v),
+ u*np.sin(v),
+ -u*u+2
+ ]),u_min=-1.414,u_max=1.414,v_min=0,v_max=2*PI, color = BLUE_C, fill_color = BLUE_C, fill_opacity = 0.1,
+ resolution=(15, 32)).scale(1)
+
+ plane_0 = Polygon(np.array([2,-2,0]),np.array([2,2,0]),np.array([-2,2,0]),np.array([-2,-2,0]),np.array([2,-2,0]), color = BLUE_E, fill_color = BLUE_E, fill_opacity = 0.3)
+ plane_0_lab = TextMobject("C = 0").move_to(0.4*UP+3.2*RIGHT).set_color(BLUE_E).scale(0.6)
+ circle_0 = Circle(radius = 1.414 , color = BLUE_E)
+ circle_0_lab = TextMobject("0").move_to(1.1*DOWN+1.1*RIGHT).set_color(BLUE_E).scale(0.6)
+
+ plane_0_5 = Polygon(np.array([2,-2,0.5]),np.array([2,2,0.5]),np.array([-2,2,0.5]),np.array([-2,-2,0.5]),np.array([2,-2,0.5]), color = GREEN_C, fill_color = GREEN_C, fill_opacity = 0.3)
+ plane_0_5_lab = TextMobject("C = 0.5").move_to(0.8*UP+3.4*RIGHT).set_color(GREEN_C).scale(0.6)
+ circle_0_5 = Circle(radius = 1.224 , color = GREEN_C)
+ circle_0_5_lab = TextMobject("0.5").move_to(0.9*DOWN+0.9*RIGHT).set_color(GREEN_C).scale(0.6)
+ circle_0_5_copy = circle_0_5.copy().move_to(np.array([0,0,0.5]))
+
+ plane_1 = Polygon(np.array([2,-2,1]),np.array([2,2,1]),np.array([-2,2,1]),np.array([-2,-2,1]),np.array([2,-2,1]), color = YELLOW_C, fill_color = YELLOW_C, fill_opacity = 0.3)
+ plane_1_lab = TextMobject("C = 1").move_to(1.2*UP+3.3*RIGHT).set_color(YELLOW_C).scale(0.6)
+ circle_1 = Circle(radius = 1 , color = YELLOW_C)
+ circle_1_lab = TextMobject("1").move_to(0.7*DOWN+0.7*RIGHT).set_color(YELLOW_C).scale(0.6)
+ circle_1_copy = circle_1.copy().move_to(np.array([0,0,1]))
+
+ plane_1_5 = Polygon(np.array([2,-2,1.5]),np.array([2,2,1.5]),np.array([-2,2,1.5]),np.array([-2,-2,1.5]),np.array([2,-2,1.5]), color = ORANGE, fill_color = ORANGE, fill_opacity = 0.3)
+ plane_1_5_lab = TextMobject("C = 1.5").move_to(1.7*UP+3.4*RIGHT).set_color(ORANGE).scale(0.6)
+ circle_1_5 = Circle(radius = 0.707 , color = ORANGE)
+ circle_1_5_lab = TextMobject("1.5").move_to(0.5*DOWN+0.5*RIGHT).set_color(ORANGE).scale(0.6)
+ circle_1_5_copy = circle_1_5.copy().move_to(np.array([0,0,1.5]))
+
+ plane_2 = Polygon(np.array([2,-2,2]),np.array([2,2,2]),np.array([-2,2,2]),np.array([-2,-2,2]),np.array([2,-2,2]), color = RED_C, fill_color = RED_C, fill_opacity = 0.3)
+ plane_2_lab = TextMobject("C = 2").move_to(2.1*UP+3.3*RIGHT).set_color(RED_C).scale(0.6)
+ dot_2 = Dot().set_fill(RED_C)
+ circle_2_lab = TextMobject("2").move_to(0.2*DOWN+0.2*RIGHT).set_color(RED_C).scale(0.6)
+ dot_2_copy = dot_2.copy().move_to(np.array([0,0,2]))
+
+ level_curves_line1 = DashedLine(np.array([0,-1.414,0]),np.array([0,-2,1]), color = WHITE)
+ level_curves_line2 = DashedLine(np.array([0,-1.224,0.5]),np.array([0,-2,1]), color = WHITE)
+ level_curves_line3 = DashedLine(np.array([0,-1,1]),np.array([0,-2,1]), color = WHITE)
+ level_curves_line4 = DashedLine(np.array([0,-0.707,1.5]),np.array([0,-2,1]), color = WHITE)
+ level_curves_line5 = DashedLine(np.array([0,0,2]),np.array([0,-2,1]), color = WHITE)
+
+ level_curves = TextMobject("Level Curves").move_to(1.4*UP+3*LEFT).set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE).scale(0.8)
+
+
+ contour_line1 = DashedLine(np.array([0,-1.414,0]),np.array([0,-2,1]), color = WHITE)
+ contour_line2 = DashedLine(np.array([0,-1.224,0]),np.array([0,-2,1]), color = WHITE)
+ contour_line3 = DashedLine(np.array([0,-1,0]),np.array([0,-2,1]), color = WHITE)
+ contour_line4 = DashedLine(np.array([0,-0.707,0]),np.array([0,-2,1]), color = WHITE)
+ contour_line5 = DashedLine(np.array([0,0,0]),np.array([0,-2,1]), color = WHITE)
+
+ contours = TextMobject("Contours").move_to(1.4*UP+2.7*LEFT).set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE).scale(0.8)
+
+
+ topic = TextMobject("Contour Plot").move_to(3*UP+3*LEFT).set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE).scale(0.8)
+
+ self.set_camera_orientation(phi=80 * DEGREES, theta = 0*DEGREES)
+ #self.set_camera_orientation(phi=0 * DEGREES, theta = 0*DEGREES)
+
+ self.add(axes)
+
+ axis = TextMobject(r"X",r"Y",r"Z")
+ axis[0].move_to(6*RIGHT)
+ axis[1].move_to(6*UP)
+ axis[2].move_to(np.array([0,0,3.7]))
+
+ self.add_fixed_orientation_mobjects(axis[2])
+ self.add_fixed_orientation_mobjects(axis[0])
+ self.add_fixed_orientation_mobjects(axis[1])
+
+ self.play(Write(paraboloid))
+ self.wait()
+ self.play(ShowCreation(plane_0), ShowCreation(circle_0))
+ self.add_fixed_in_frame_mobjects(plane_0_lab)
+ self.wait()
+ self.play(ShowCreation(plane_0_5), ShowCreation(circle_0_5_copy), ShowCreation(circle_0_5))
+ self.add_fixed_in_frame_mobjects(plane_0_5_lab)
+ self.wait()
+ self.play(ShowCreation(plane_1), ShowCreation(circle_1_copy), ShowCreation(circle_1))
+ self.add_fixed_in_frame_mobjects(plane_1_lab)
+ self.wait()
+ self.play(ShowCreation(plane_1_5), ShowCreation(circle_1_5_copy), ShowCreation(circle_1_5))
+ self.add_fixed_in_frame_mobjects(plane_1_5_lab)
+ self.wait()
+ self.play(ShowCreation(plane_2), ShowCreation(dot_2_copy), ShowCreation(dot_2))
+ self.add_fixed_in_frame_mobjects(plane_2_lab)
+ self.wait()
+
+ self.move_camera(phi=60 * DEGREES, theta = 30*DEGREES,run_time=3)
+ self.play(FadeOut(plane_0), FadeOut(plane_0_lab), FadeOut(plane_0_5), FadeOut(plane_0_5_lab), FadeOut(plane_1), FadeOut(plane_1_lab), FadeOut(plane_1_5), FadeOut(plane_1_5_lab), FadeOut(plane_2), FadeOut(plane_2_lab))
+
+ self.play(GrowArrow(level_curves_line1), GrowArrow(level_curves_line2), GrowArrow(level_curves_line3), GrowArrow(level_curves_line4), GrowArrow(level_curves_line5))
+ self.add_fixed_in_frame_mobjects(level_curves)
+ self.wait()
+ self.play(FadeOut(level_curves_line1), FadeOut(level_curves_line2), FadeOut(level_curves_line3), FadeOut(level_curves_line4), FadeOut(level_curves_line5), FadeOut(level_curves))
+ self.play(FadeOut(circle_0_5_copy), FadeOut(circle_1_copy), FadeOut(circle_1_5_copy), FadeOut(dot_2_copy))
+ self.wait()
+
+ self.play(GrowArrow(contour_line1), GrowArrow(contour_line2), GrowArrow(contour_line3), GrowArrow(contour_line4), GrowArrow(contour_line5))
+ self.add_fixed_in_frame_mobjects(contours)
+ self.wait()
+ self.play(FadeOut(contour_line1), FadeOut(contour_line2), FadeOut(contour_line3), FadeOut(contour_line4), FadeOut(contour_line5), FadeOut(contours))
+
+
+ self.move_camera(phi=0 * DEGREES, theta = 0*DEGREES,run_time=3)
+ self.play(FadeOut(paraboloid))
+ self.wait()
+
+ self.add_fixed_in_frame_mobjects(circle_0_lab, circle_0_5_lab, circle_1_lab, circle_1_5_lab,circle_2_lab)
+ self.add_fixed_in_frame_mobjects(topic)
+ self.wait(3)
\ No newline at end of file diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file5_level_surface.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file5_level_surface.py new file mode 100644 index 0000000..8052676 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file5_level_surface.py @@ -0,0 +1,78 @@ +from manimlib.imports import *
+
+class LevelSurface(ThreeDScene):
+ def construct(self):
+ axes = ThreeDAxes()
+
+ surface_0 = ParametricSurface(
+ lambda u, v: np.array([
+ u*np.cos(v),
+ u*np.sin(v),
+ (u*u*np.cos(v)*np.cos(v))-(u*np.sin(v)/5)+0
+ ]),u_min=-1,u_max=1,v_min=0,v_max=2*PI,checkerboard_colors=[RED_C, RED_E],
+ resolution=(15, 32)).scale(1)
+
+ k_0 = TextMobject("K = 0", color = RED_C).scale(0.7)
+
+ surface_1 = ParametricSurface(
+ lambda u, v: np.array([
+ u*np.cos(v),
+ u*np.sin(v),
+ (u*u*np.cos(v)*np.cos(v))-(u*np.sin(v)/5)+1
+ ]),u_min=-1,u_max=1,v_min=0,v_max=2*PI,checkerboard_colors=[GREEN_C, GREEN_E],
+ resolution=(15, 32)).scale(1)
+
+ k_1 = TextMobject("K = 1", color = GREEN_C).scale(0.7)
+
+ surface_2 = ParametricSurface(
+ lambda u, v: np.array([
+ u*np.cos(v),
+ u*np.sin(v),
+ (u*u*np.cos(v)*np.cos(v))-(u*np.sin(v)/5)+2
+ ]),u_min=-1,u_max=1,v_min=0,v_max=2*PI,checkerboard_colors=[YELLOW_C, YELLOW_E],
+ resolution=(15, 32)).scale(1)
+
+ k_2 = TextMobject("K = 2", color = YELLOW_C).scale(0.7)
+
+ func = TextMobject(r"$w = g(x,y,z)$", r"$= z - f(x,y)$", r"$z-x^2+y/5 = K$")
+ func.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
+
+ self.set_camera_orientation(phi=90 * DEGREES, theta = 90*DEGREES)
+ self.begin_ambient_camera_rotation(rate=0.3)
+
+
+ self.add(axes)
+
+ axis = TextMobject(r"X",r"Y",r"Z")
+ axis[0].move_to(6*RIGHT)
+ axis[1].move_to(6*UP)
+ axis[2].move_to(3.7*UP)
+
+ self.add_fixed_in_frame_mobjects(axis[2])
+ self.add_fixed_orientation_mobjects(axis[0])
+ self.add_fixed_orientation_mobjects(axis[1])
+
+ self.play(Write(surface_0))
+ self.add_fixed_in_frame_mobjects(k_0)
+ k_0.move_to(np.array([1.4*RIGHT ]))
+
+ self.play(Write(surface_1))
+ self.add_fixed_in_frame_mobjects(k_1)
+ k_1.move_to(np.array([1.4*RIGHT + 1*UP]))
+
+ self.play(Write(surface_2))
+ self.add_fixed_in_frame_mobjects(k_2)
+ k_2.move_to(np.array([1.4*RIGHT + 2*UP]))
+ self.wait()
+
+ self.add_fixed_in_frame_mobjects(func)
+ func[0].move_to(np.array([4.5*LEFT + 3*UP]))
+ func[1].move_to(np.array([4.5*LEFT + 2.5*UP]))
+ func[2].move_to(np.array([4.5*LEFT + 2*UP]))
+
+ self.wait(3)
+ self.move_camera(phi=60 * DEGREES,run_time=3)
+ self.wait(2)
+
+
+
\ No newline at end of file diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file2_scalar_function_application.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file6_scalar_function_application.py index 56b3e53..3ccfad6 100644 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file2_scalar_function_application.py +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file6_scalar_function_application.py @@ -3,12 +3,23 @@ from manimlib.imports import * class ScalarApplication(ThreeDScene):
def construct(self):
axes = ThreeDAxes() # creates a 3D Axis
+
+ self.add(axes)
+
+ axis = TextMobject(r"X",r"Y",r"Z")
+ axis[0].move_to(6*RIGHT)
+ axis[1].move_to(6*UP)
+ axis[2].move_to(np.array([0,0,3.7]))
+
+ self.add_fixed_orientation_mobjects(axis[2])
+ self.add_fixed_orientation_mobjects(axis[0])
+ self.add_fixed_orientation_mobjects(axis[1])
cube = Cube()
- cube.set_fill(YELLOW_E, opacity = 0.1)
+ cube.set_fill(YELLOW_C, opacity = 0.2)
cube.scale(2)
self.set_camera_orientation(phi=0 * DEGREES,theta=270*DEGREES)
- self.play(ShowCreation(cube),ShowCreation(axes))
+ self.play(ShowCreation(cube))
dot = Sphere()
dot.scale(0.1)
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file4_neural_nets.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file7_neural_nets.py index eb6bf45..eb6bf45 100644 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file4_neural_nets.py +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file7_neural_nets.py diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file1_domain_range.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file1_domain_range.gif Binary files differdeleted file mode 100644 index d0351e5..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file1_domain_range.gif +++ /dev/null diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file1_scalar_functions.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file1_scalar_functions.gif Binary files differnew file mode 100644 index 0000000..bea9c7b --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file1_scalar_functions.gif diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file2_domain_range.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file2_domain_range.gif Binary files differnew file mode 100644 index 0000000..6801e4f --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file2_domain_range.gif diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file2_scalar_function_application.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file2_scalar_function_application.gif Binary files differdeleted file mode 100644 index 831ec8e..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file2_scalar_function_application.gif +++ /dev/null diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file3_parabola_example.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file3_parabola_example.gif Binary files differindex 3fdecf4..9576b4a 100644 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file3_parabola_example.gif +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file3_parabola_example.gif diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file4_level_curves.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file4_level_curves.gif Binary files differnew file mode 100644 index 0000000..b4ac106 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file4_level_curves.gif diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file4_neural_nets.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file4_neural_nets.gif Binary files differdeleted file mode 100644 index 9d24688..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file4_neural_nets.gif +++ /dev/null diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file5_level_surface.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file5_level_surface.gif Binary files differnew file mode 100644 index 0000000..e4dc80d --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file5_level_surface.gif diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file6_scalar_function_application.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file6_scalar_function_application.gif Binary files differnew file mode 100644 index 0000000..8bb176a --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file6_scalar_function_application.gif diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file7_neural_nets.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file7_neural_nets.gif Binary files differnew file mode 100644 index 0000000..a22f1b8 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file7_neural_nets.gif diff --git a/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file1_introduction.py b/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file1_introduction.py new file mode 100644 index 0000000..ccd23c9 --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file1_introduction.py @@ -0,0 +1,33 @@ +from manimlib.imports import * + +class Orthonormal(Scene): + def construct(self): + Centre = DOWN + arrow_1 = Arrow(start = Centre+ORIGIN,end = Centre+1.414*(UP+RIGHT)) + arrow_2 = Arrow(start = Centre+ORIGIN,end = Centre+2*UP) + arrow_1.scale(1.35) + arrow_2.scale(1.35) + text = TextMobject("This is a set of linearly independent vectors") + text.scale(0.75) + text.move_to(3*UP+3*LEFT) + text.set_color(PURPLE_E) + arrow_1.set_color(PURPLE_E) + arrow_2.set_color(PURPLE_E) + self.play(Write(text)) + self.play(ShowCreation(arrow_1), ShowCreation(arrow_2)) + self.wait(2) + text1 = TextMobject("After we apply Gram-Schmidt Orthogonalization Process to set of linearly independent vectors") + text1.scale(0.6) + text1.move_to(3*UP+2*LEFT) + text1.set_color(GREEN) + arrow_a = Arrow(start = Centre+ORIGIN,end = Centre+0.707*(UP+RIGHT)) + arrow_a.set_color(GREEN) + arrow_a.scale(2) + self.play(Transform(text,text1)) + self.wait(2) + self.play(Transform(arrow_1,arrow_a)) + arrow_b = Arrow(start = Centre+ORIGIN,end = Centre+0.707*(UP+LEFT)) + arrow_b.set_color(GREEN) + arrow_b.scale(2) + self.play(Transform(arrow_2,arrow_b)) + self.wait(2)
\ No newline at end of file diff --git a/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file2_projections.py b/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file2_projections.py new file mode 100755 index 0000000..dd4b8d4 --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file2_projections.py @@ -0,0 +1,79 @@ +from manimlib.imports import * + +class Projections(GraphScene): + CONFIG = { + "x_min": -6, + "x_max": 6, + "y_min": -4, + "y_max": 4, + "graph_origin" : ORIGIN , + } + def construct(self): + + self.setup_axes(animate=True) + + XTD = self.x_axis_width/(self.x_max-self.x_min) + YTD = self.y_axis_height/(self.y_max-self.y_min) + + arrow_a = Arrow(start = ORIGIN, end = 4*XTD*RIGHT) + arrow_a.scale(1.2) + arrow_a.set_color(DARK_BLUE) + arrow_b = Arrow(start = ORIGIN, end = 2*YTD*UP+2*XTD*RIGHT) + arrow_b.scale(1.3) + arrow_b.set_color(DARK_BLUE) + self.play(ShowCreation(arrow_a), ShowCreation(arrow_b)) + + text = TextMobject(r"Consider 2 linearly independent vectors $a$ and $b$") + text.set_color(DARK_BLUE) + text.scale(0.6) + text.move_to(3*YTD*UP+5*XTD*LEFT) + text_a = TextMobject("a") + text_a.move_to(0.4*YTD*DOWN+3*XTD*RIGHT) + text_a.set_color(DARK_BLUE) + text_b = TextMobject("b") + text_b.move_to(1.5*YTD*UP+RIGHT*XTD) + text_b.set_color(DARK_BLUE) + + self.play(Write(text),Write(text_a), Write(text_b)) + self.wait() + + arrow_b_copy = Arrow(start = ORIGIN, end = 2*YTD*UP+2*XTD*RIGHT) + arrow_b_copy.scale(1.25) + + arrow_p = Arrow(start = ORIGIN, end = 2*XTD*RIGHT) + arrow_p.scale(1.5) + arrow_p.set_color(GOLD_E) + + text_p = TextMobject("p") + text_p.move_to(0.25*DOWN+RIGHT) + text_p.set_color(GOLD_E) + + self.play(FadeOut(text), Transform(arrow_b_copy,arrow_p), FadeOut(text_a), FadeOut(text_b)) + text = TextMobject(r"$p$ is the projection of $b$ on $a$") + text.set_color(GOLD_E) + text.move_to(3*UP+4*LEFT) + text.scale(0.8) + self.play(Write(text),Write(text_p)) + self.wait() + + self.play(FadeIn(text_a), FadeIn(text_b)) + + arrow_o = Arrow(start = 2*XTD*RIGHT, end = 2*YTD*UP+2*XTD*RIGHT) + arrow_o.scale(1.5) + arrow_o.set_color(GREEN_E) + + text_o = TextMobject("b-p") + text_o.move_to(UP*YTD+2.7*XTD*RIGHT) + text_o.set_color(GREEN_E) + + self.play(ShowCreation(arrow_o)) + self.play(FadeOut(text),Write(text_o)) + + text = TextMobject(r"Observe, ($b-p$) is orthogonal to $a$") + text.set_color(GREEN_E) + text.move_to(2*DOWN+4*LEFT) + text.scale(0.8) + self.play(Write(text)) + self.wait(2) + + self.play(FadeOut(self.axes), FadeOut(arrow_a), FadeOut(arrow_b), FadeOut(arrow_b_copy), FadeOut(arrow_o), FadeOut(text_a), FadeOut(text_b), FadeOut(text_o), FadeOut(text_p), FadeOut(text))
\ No newline at end of file diff --git a/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file3_orthonormal.py b/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file3_orthonormal.py new file mode 100644 index 0000000..af51fc6 --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file3_orthonormal.py @@ -0,0 +1,333 @@ +from manimlib.imports import * + +class Algo(ThreeDScene): + def construct(self): + + 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.set_color(GREEN) + text.scale(0.6) + text.move_to(3*UP+5*LEFT) + self.play(Write(text)) + + arrow_a = Arrow(start = ORIGIN, end = 4*RIGHT) + arrow_a.set_color(GREEN) + arrow_a.scale(1.15) + self.play(ShowCreation(arrow_a)) + + text_a = TextMobject(r"$\beta_1$") + text_a.move_to(0.4*DOWN+3*RIGHT) + text_a.set_color(GREEN) + text_a.scale(0.75) + self.play(Write(text_a)) + self.wait() + self.play(FadeOut(text)) + + text = TextMobject(r"Normalize $\beta_1$ to get $\alpha_1$") + text.set_color(DARK_BLUE) + text.scale(0.75) + text.move_to(3*UP+5*LEFT) + self.play(Write(text)) + + alpha_1 = Arrow(start = ORIGIN,end = RIGHT) + alpha_1.scale(1.9) + alpha_1.set_color(DARK_BLUE) + text_alpha_1 = TextMobject(r"$\alpha_1$") + text_alpha_1.move_to(0.4*DOWN+RIGHT) + text_alpha_1.set_color(DARK_BLUE) + text_alpha_1.scale(0.75) + self.play(Transform(text_a,text_alpha_1), Transform(arrow_a,alpha_1)) + self.wait() + self.play(FadeOut(text)) + + 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) + text.scale(0.6) + text1.scale(0.6) + text.move_to(3*UP+4*LEFT) + text1.move_to(2*UP+4*LEFT) + self.play(Write(text)) + self.play(Write(text1)) + + arrow_b = Arrow(start = ORIGIN, end = 2*UP+2*RIGHT) + arrow_b.scale(1.2) + arrow_b.set_color(GREEN) + text_b = TextMobject(r"$\beta_2$") + text_b.move_to(1.5*UP+RIGHT) + text_b.set_color(GREEN) + text_b.scale(0.75) + + self.play(ShowCreation(arrow_b), Write(text_b)) + self.wait() + + arrow_b_copy = Arrow(start = ORIGIN, end = 2*UP+2*RIGHT) + arrow_b_copy.scale(1.2) + + arrow_p = Arrow(start = ORIGIN, end = 2*RIGHT) + arrow_p.scale(1.35) + arrow_p.set_color(GOLD_E) + + text_p = TextMobject("p") + text_p.move_to(0.25*DOWN+RIGHT) + text_p.set_color(GOLD_E) + + self.play(FadeOut(text), FadeOut(text1), Transform(arrow_b_copy,arrow_p), FadeOut(text_a), FadeOut(text_b)) + text = TextMobject(r"$p$ is the projection of $\beta_2$ on $\alpha_1$") + text.set_color(GOLD_E) + text.move_to(3*UP+4*LEFT) + text.scale(0.8) + self.play(Write(text),Write(text_p)) + self.wait() + + self.play(FadeIn(text_b)) + + arrow_o = Arrow(start = 2*RIGHT, end = 2*UP+2*RIGHT) + arrow_o.scale(1.35) + arrow_o.set_color(PURPLE_E) + + text_o = TextMobject(r"$\beta_2-p$") + text_o.move_to(UP+2.7*RIGHT) + text_o.scale(0.75) + text_o.set_color(PURPLE_E) + + self.play(ShowCreation(arrow_o)) + self.play(FadeOut(text),Write(text_o)) + + text = TextMobject(r"$\beta_2-p$ is orthogonal to p") + text1 = TextMobject(r"(and hence orthogonal to $\alpha_1$ also)") + text.set_color(PURPLE_E) + text1.set_color(PURPLE_E) + text.scale(0.7) + text1.scale(0.7) + text.move_to(3*UP+4*LEFT) + text1.move_to(2.5*UP+4*LEFT) + self.play(Write(text)) + self.play(Write(text1)) + self.wait(2) + + self.play(FadeOut(text_p), FadeIn(arrow_a), FadeOut(text), FadeOut(text1), FadeOut(arrow_b_copy), FadeOut(arrow_p), FadeOut(text_b), FadeOut(arrow_b)) + self.play(ApplyMethod(arrow_o.move_to,UP), ApplyMethod(text_o.move_to,RIGHT+UP)) + + text = TextMobject(r"Now, Normalize $\beta_2-p$") + text.set_color(DARK_BLUE) + text.scale(0.6) + text.move_to(3*UP+4*LEFT) + self.play(Write(text)) + + alpha_2 = Arrow(start = ORIGIN,end = UP) + alpha_2.scale(1.9) + alpha_2.set_color(DARK_BLUE) + text_alpha_2 = TextMobject(r"$\alpha_2$") + text_alpha_2.move_to(0.4*LEFT+UP) + text_alpha_2.set_color(DARK_BLUE) + text_alpha_2.scale(0.75) + self.play(Transform(text_o,text_alpha_2), Transform(arrow_o,alpha_2), FadeIn(text_a)) + self.wait() + self.play(FadeOut(text),FadeOut(text_a),FadeOut(text_o)) + + self.add(axes) + ############################################################################# + axis = TextMobject(r"$\alpha_1$",r"$\alpha_2$",r"$\alpha_3$",r"$\beta_3$",r"$\alpha_3$",r"$\alpha_3$",r"$\alpha_3$",r"$\alpha_3$") + axis.scale(0.5) + axis[0].move_to(0.5*RIGHT+[0,0,-0.5]) + axis[1].move_to(0.5*UP+[0,0,-0.5]) + axis[2].move_to(np.array([0,0,0.5])) + axis[3].move_to(np.array([1,1,1.5])) + self.add_fixed_orientation_mobjects(axis[0]) + 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=60*DEGREES,theta=45*DEGREES,run_time=3) + self.begin_ambient_camera_rotation(rate=0.3) + + line1 = Line(start = ORIGIN,end = 1*RIGHT) + line1.set_color(DARK_BLUE) + tip1 = Polygon(RIGHT,0.8*RIGHT-0.2*DOWN,0.8*RIGHT-0.2*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,0.8*UP-0.2*RIGHT,0.8*UP-0.2*LEFT) + tip2.set_opacity(1) + tip2.set_fill(DARK_BLUE) + tip2.set_color(DARK_BLUE) + arrow2.set_color(DARK_BLUE) + + self.play(ShowCreation(line1), ShowCreation(tip1), ShowCreation(arrow2), ShowCreation(tip2), FadeOut(arrow_a), FadeOut(arrow_o)) + self.wait() + + a_line = Line(start = ORIGIN,end = 2*UP+2*RIGHT+[0,0,2]) + a_line.set_color(GOLD_E) + a_tip = Polygon(2*UP+2*RIGHT+[0,0,2],2*UP+1.6*RIGHT+[0,0,1.8],1.6*UP+2*RIGHT+[0,0,1.8]) + a_tip.set_opacity(1) + a_tip.set_fill(GOLD_E) + a_tip.set_color(GOLD_E) + + a_line_c1 = Line(start = ORIGIN,end = 2*UP+2*RIGHT+[0,0,2]) + a_line_c1.set_color(GOLD_E) + a_tip_c1 = Polygon(2*UP+2*RIGHT+[0,0,2],2*UP+1.6*RIGHT+[0,0,1.8],1.6*UP+2*RIGHT+[0,0,1.8]) + a_tip_c1.set_opacity(1) + 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)) + + 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) + self.add_fixed_orientation_mobjects(axis[3]) + text.move_to(3*(DOWN+RIGHT)) + self.play(Write(text)) + self.wait() + self.play(FadeOut(text)) + + 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.set_opacity(1) + p_tip1.set_fill(GOLD_E) + p_tip1.set_color(GOLD_E) + + self.play(Transform(a_line_c1,p_line1),Transform(a_tip_c1,p_tip1)) + + text = TextMobject(r"Take projection of $\beta_3$ on $\alpha_1$") + text.scale(0.6) + text.set_color(GOLD_E) + self.add_fixed_in_frame_mobjects(text) + text.move_to(3*(DOWN+RIGHT)) + self.play(Write(text)) + self.wait() + self.play(FadeOut(text)) + + o_line1 = Line(start = 2*RIGHT,end = 2*UP+2*RIGHT+[0,0,2]) + o_line1.set_color(GREEN_E) + o_tip1 = Polygon(2*UP+2*RIGHT+[0,0,2],1.8*UP+2*RIGHT+[0,0,1.8]+0.2*RIGHT,1.8*UP+2*RIGHT+[0,0,1.8]-0.2*RIGHT) + o_tip1.set_opacity(1) + o_tip1.set_fill(GREEN_E) + o_tip1.set_color(GREEN_E) + + a_line1 = Line(start = ORIGIN,end = 2*UP+[0,0,2]) + a_line1.set_color(GREEN_E) + a_tip1 = Polygon(2*UP+[0,0,2],1.8*UP+[0,0,1.8]+0.2*RIGHT,1.8*UP+[0,0,1.8]-0.2*RIGHT) + a_tip1.set_opacity(1) + a_tip1.set_fill(GREEN_E) + a_tip1.set_color(GREEN_E) + + a_line1_c1 = Line(start = ORIGIN,end = 2*UP+[0,0,2]) + a_line1_c1.set_color(GREEN_E) + a_tip1_c1 = Polygon(2*UP+[0,0,2],1.8*UP+[0,0,1.8]+0.2*RIGHT,1.8*UP+[0,0,1.8]-0.2*RIGHT) + a_tip1_c1.set_opacity(1) + a_tip1_c1.set_fill(GREEN_E) + a_tip1_c1.set_color(GREEN_E) + + text = TextMobject(r"$\beta_3$-(projection of $\beta_3$ on $\alpha_1$)") + text.set_color(GREEN_E) + text.scale(0.6) + 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), + FadeOut(a_line), FadeOut(a_tip), FadeOut(axis[3]), + Transform(o_line1,a_line1), Transform(o_tip1,a_tip1)) + + self.wait() + self.play(FadeOut(text)) + + p_arrow2 = Line(start = ORIGIN,end = 2*UP) + p_arrow2.set_color(GOLD_E) + p_tip2 = Polygon(2*UP,1.8*UP+0.2*RIGHT,1.8*UP+0.2*LEFT) + p_tip2.set_opacity(1) + p_tip2.set_fill(GOLD_E) + p_tip2.set_color(GOLD_E) + p_arrow2.set_color(GOLD_E) + + last_a = Line(start = 2*UP,end = [0,2,2]) + last_a.set_color(PURPLE_E) + last_a_tip = Polygon([0,0,2],[0,0,1.8]+0.2*RIGHT,[0,0,1.8]+0.2*LEFT) + last_a_tip.move_to([0,2,2]) + last_a_tip.set_opacity(1) + last_a_tip.set_fill(PURPLE_E) + last_a_tip.set_color(PURPLE_E) + + self.wait() + text = TextMobject(r"Take projection on $\alpha_2$") + text.scale(0.6) + text.set_color(GOLD_E) + self.add_fixed_in_frame_mobjects(text) + text.move_to(3*(DOWN+RIGHT)) + self.play(Write(text)) + self.play(Transform(a_line1_c1,p_arrow2),Transform(a_tip1_c1,p_tip2)) + self.wait() + self.play(FadeOut(text)) + + text = TextMobject(r"$\beta_3$-(projection of $\beta_3$ on $\alpha_1$ + projection of $\beta_3$ on $\alpha_2$)") + text.set_color(PURPLE_E) + text.scale(0.6) + 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.wait(2) + self.play(ShowCreation(last_a_tip), ShowCreation(last_a)) + self.wait() + self.play(FadeOut(text)) + + larrow3 = Line(start = ORIGIN,end = [0,0,2]) + larrow3.set_color(PURPLE_E) + ltip3 = Polygon([0,0,2],[0,0,1.8]+0.2*RIGHT,[0,0,1.8]+0.2*LEFT) + ltip3.set_opacity(1) + ltip3.set_fill(PURPLE_E) + ltip3.set_color(PURPLE_E) + self.wait() + 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 $\alpha_2$") + text.set_color(PURPLE_E) + text1.set_color(PURPLE_E) + text.scale(0.6) + text1.scale(0.6) + 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) + self.play(Write(text)) + self.play(Write(text1)) + + arrow3 = Line(start = ORIGIN,end = [0,0,1]) + arrow3.set_color(DARK_BLUE) + tip3 = Polygon([0,0,1],[0,0,0.8]-0.2*RIGHT,[0,0,0.8]-0.2*LEFT) + tip3.set_opacity(1) + tip3.set_fill(DARK_BLUE) + tip3.set_color(DARK_BLUE) + self.play(Transform(last_a,arrow3), Transform(last_a_tip,tip3)) + self.add_fixed_orientation_mobjects(axis[2]) + + self.wait() + self.play(FadeOut(text),FadeOut(text1)) + + text = TextMobject(r"These are the three orthonormal vectors $\alpha_1, \alpha_2, \alpha_3$") + 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(3)
\ No newline at end of file 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..6410a2c --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file4_Non_Standard_Basis.py @@ -0,0 +1,51 @@ +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/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)/file2_before_matrix.py b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file2_before_matrix.py new file mode 100755 index 0000000..96e456d --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file2_before_matrix.py @@ -0,0 +1,232 @@ +from manimlib.imports import * + +class Linear(GraphScene): + + CONFIG = { + "x_min": -5, + "x_max": 5, + "y_min": -5, + "y_max": 5, + "graph_origin": ORIGIN, + "x_labeled_nums": list(range(-5, 6)), + "y_labeled_nums": list(range(-5, 6)), + "x_axis_width": 7, + "y_axis_height": 7, + } + + 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(animate = True) + heading = TextMobject(r"$T(x,y) = T(x+2y,x-y)$") + heading.move_to(UP*3+LEFT*4) + heading.scale(0.7) + self.play(Write(heading)) + self.wait() + + before = TextMobject("Before Linear Transformation") + before.set_color(ORANGE) + before.move_to(3*UP+4*RIGHT) + before.scale(0.75) + dot1 = Dot().shift(self.graph_origin+1*XTD*RIGHT+1*YTD*UP) + dot2 = Dot().shift(self.graph_origin+2*XTD*RIGHT+1*YTD*UP) + dot1.set_color(ORANGE) + dot2.set_color(ORANGE) + p1 = TextMobject(r"$P_1$") + p1.scale(0.75) + p1.set_color(ORANGE) + p1.move_to(self.graph_origin+1*XTD*RIGHT+1.5*YTD*UP) + p2 = TextMobject(r"$P_2$") + p2.set_color(ORANGE) + p2.scale(0.75) + p2.move_to(self.graph_origin+2*XTD*RIGHT+1.5*YTD*UP) + + after = TextMobject("After applying Linear Transformation") + after.set_color(YELLOW) + after.move_to(3*UP+4.5*RIGHT) + after.scale(0.5) + dot3 = Dot().shift(self.graph_origin+3*XTD*RIGHT+0*YTD*UP) + dot4 = Dot().shift(self.graph_origin+4*XTD*RIGHT+1*YTD*UP) + dot3.set_color(YELLOW) + dot4.set_color(YELLOW) + p3 = TextMobject(r"$T(P_1)$") + p3.scale(0.7) + p3.set_color(YELLOW) + p3.move_to(self.graph_origin+3*XTD*RIGHT-1.1*YTD*UP) + p4 = TextMobject(r"$T(P_2)$") + p4.scale(0.7) + p4.set_color(YELLOW) + p4.move_to(self.graph_origin+4*XTD*RIGHT+1.5*YTD*UP) + + self.play(Write(before), ShowCreation(dot1), ShowCreation(dot2),Write(p1), Write(p2)) + self.wait(3) + self.play(Transform(before,after), Transform(dot1,dot3), Transform(dot2,dot4), Transform(p2,p4), Transform(p1,p3)) + self.wait(3) + + +class withgrid(LinearTransformationScene): + def construct(self): + + heading = TextMobject(r"Now, Imagine this happening for all the vectors") + heading.scale(0.5) + heading.move_to(UP*2.5+LEFT*4) + self.play(Write(heading)) + self.wait() + + before = TextMobject("Before Linear Transformation") + before.set_color(ORANGE) + before.move_to(3.5*UP+4*RIGHT) + before.scale(0.75) + dot1 = Dot().shift(1*RIGHT+1*UP) + dot2 = Dot().shift(2*RIGHT+1*UP) + dot1.set_color(ORANGE) + dot2.set_color(ORANGE) + + dot1_c = Dot(radius = 0.05).shift(1*RIGHT+1*UP) + dot2_c = Dot(radius = 0.05).shift(2*RIGHT+1*UP) + dot1_c.set_color(YELLOW) + dot2_c.set_color(YELLOW) + self.add_transformable_mobject(dot1_c) + self.add_transformable_mobject(dot2_c) + + p1 = TextMobject(r"$P_1$") + p1.scale(0.75) + p1.set_color(ORANGE) + p1.move_to(1*RIGHT+1.5*UP) + p2 = TextMobject(r"$P_2$") + p2.scale(0.75) + p2.set_color(ORANGE) + p2.move_to(2*RIGHT+1.5*UP) + + after = TextMobject("After applying Linear Transformation") + after.set_color(YELLOW) + after.move_to(3.5*UP+3.5*RIGHT) + after.scale(0.75) + dot3 = Dot().shift(3*RIGHT+0*UP) + dot4 = Dot().shift(4*RIGHT+1*UP) + dot3.set_color(YELLOW) + dot4.set_color(YELLOW) + p3 = TextMobject(r"$T(P_1)$") + p3.scale(0.75) + p3.set_color(YELLOW) + p3.move_to(3*RIGHT-0.6*UP) + p4 = TextMobject(r"$T(P_2)$") + p4.scale(0.75) + p4.set_color(YELLOW) + p4.move_to(4*RIGHT+1.5*UP) + + self.play(Write(before), ShowCreation(dot1), ShowCreation(dot2),Write(p1), Write(p2)) + self.wait(3) + matrix = [[1,2],[1,-1]] + dot1.set_color(GREY) + dot2.set_color(GREY) + self.play(FadeIn(dot1),FadeIn(dot2)) + self.apply_matrix(matrix) + self.play(Transform(before,after), Transform(p2,p4), Transform(p1,p3)) + self.play(Transform(before,after)) + self.wait(3) + + ending = TextMobject(r"$T(\left[\begin{array}{c}x \\ y\end{array}\right]) = \left[\begin{array}{c} x+2y \\ x-y\end{array}\right]$") + ending.move_to(UP*2+LEFT*4) + self.play(Transform(heading,ending)) + self.wait() + +from manimlib.imports import * +class ThreeDExplanation(ThreeDScene): + + def construct(self): + + text = TextMobject(r"$T(x,y) = (x+y,x-y,x+2y)$") + text.scale(0.75) + text.move_to(UP*2.5+LEFT*4) + self.add_fixed_in_frame_mobjects(text) + self.play(Write(text)) + self.wait() + + before = TextMobject("Before Linear Transformation") + self.add_fixed_in_frame_mobjects(before) + before.set_color(ORANGE) + before.move_to(3.5*UP+4*RIGHT) + before.scale(0.75) + + p1 = TextMobject(r"$P_1$") + p2 = TextMobject(r"$P_2$") + p3 = TextMobject(r"$P_3$") + p1.scale(0.75) + p2.scale(0.75) + p3.scale(0.75) + dot1 = Dot().shift(1*RIGHT+1*UP) + dot2 = Dot().shift(2*RIGHT+1*UP) + dot3 = Dot().shift(1*RIGHT+1*DOWN) + dot1.set_color(ORANGE) + dot2.set_color(ORANGE) + dot3.set_color(ORANGE) + self.play(ShowCreation(before)) + + p1.move_to(1*RIGHT+1*UP+[0,0,0.5]) + p2.move_to(2*RIGHT+1*UP+[0,0,0.5]) + p3.move_to(1*RIGHT-1*UP+[0,0,0.5]) + + dot1_c = Dot(radius = 0.05).shift(1*RIGHT+1*UP) + dot2_c = Dot(radius = 0.05).shift(0*RIGHT+2*UP) + dot3_c = Dot(radius = 0.05).shift(1*RIGHT-1*UP) + dot1_c.set_color(YELLOW) + dot2_c.set_color(YELLOW) + dot3_c.set_color(YELLOW) + + axes = ThreeDAxes(x_min = -7,x_max=7,y_min=-4,y_max=4,z_min=-4,z_max=4) + 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) + self.wait(1) + self.stop_ambient_camera_rotation() + + plane = NumberPlane() + self.add_fixed_orientation_mobjects(p1) + self.add_fixed_orientation_mobjects(p2) + self.add_fixed_orientation_mobjects(p3) + self.play(ShowCreation(dot1),ShowCreation(dot3),ShowCreation(dot2),ShowCreation(plane)) + + self.play(FadeOut(before)) + after = TextMobject("After applying Linear Transformation") + self.add_fixed_in_frame_mobjects(after) + after.set_color(YELLOW) + after.move_to(3.5*UP+3.5*RIGHT) + after.scale(0.75) + + self.play(FadeOut(p1),FadeOut(p2),FadeOut(p3)) + matrix = [[1,1],[1,-1],[2,1]] + self.play(FadeOut(dot1),FadeOut(dot2),FadeOut(dot3),ApplyMethod(plane.apply_matrix,matrix),ApplyMethod(dot1_c.apply_matrix,matrix),ApplyMethod(dot3_c.apply_matrix,matrix),ApplyMethod(dot2_c.apply_matrix,matrix)) + + p4 = TextMobject(r"$T(P_1)$") + p5 = TextMobject(r"$T(P_2)$") + p6 = TextMobject(r"$T(P_3)$") + p4.scale(0.75) + p5.scale(0.75) + p6.scale(0.75) + p4.move_to(2*RIGHT+0*UP+[0,0,3.5]) + p5.move_to(2*RIGHT-2*UP+[0,0,2.5]) + p6.move_to(0*RIGHT+2*UP+[0,0,1.5]) + self.add_fixed_orientation_mobjects(p5) + self.add_fixed_orientation_mobjects(p4) + self.add_fixed_orientation_mobjects(p6) + + self.begin_ambient_camera_rotation(rate=0.3) + 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.scale(0.75) + ending.move_to(-UP*2+LEFT*4) + self.play(Transform(text,ending)) + self.add_fixed_in_frame_mobjects(ending) + + self.play(FadeOut(plane)) + self.wait(3) + + self.begin_ambient_camera_rotation(rate=0.5) + self.wait(5) + self.stop_ambient_camera_rotation() diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file3_square.py b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file3_square.py new file mode 100644 index 0000000..e828de4 --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file3_square.py @@ -0,0 +1,246 @@ +from manimlib.imports import * + +class Linear(GraphScene): + CONFIG = { + "x_min": -5, + "x_max": 5, + "y_min": -5, + "y_max": 5, + "graph_origin": ORIGIN, + "x_labeled_nums": list(range(-5, 6)), + "y_labeled_nums": list(range(-5, 6)), + "x_axis_width": 7, + "y_axis_height": 7, + } + def construct(self): + + text = TextMobject("T(x,y) = T(x+y,y)") + text.scale(0.75) + text.set_color(PURPLE) + text.move_to(3*UP+5*LEFT) + self.play(Write(text)) + + 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(animate = True) + + text1 = TextMobject("Before Linear Transformation") + text1.scale(0.6) + text1.move_to(UP*3+3*RIGHT) + + a = TextMobject("(1,1)") + b = TextMobject("(3,1)") + c = TextMobject("(3,2)") + d = TextMobject("(1,2)") + a.scale(0.5) + b.scale(0.5) + c.scale(0.5) + d.scale(0.5) + a.move_to(self.graph_origin+0.6*UP+0.6*RIGHT) + b.move_to(self.graph_origin+0.6*UP+3.4*RIGHT) + c.move_to(self.graph_origin+2.4*UP+3.4*RIGHT) + d.move_to(self.graph_origin+2.6*UP+0.6*RIGHT) + + square = Polygon(self.graph_origin+UP+RIGHT,self.graph_origin+UP+3*RIGHT,self.graph_origin+2*UP+3*RIGHT,self.graph_origin+2*UP+RIGHT) + + self.play(Write(text1), Write(a), Write(b), Write(c), Write(d), ShowCreation(square)) + self.wait(2) + self.play(FadeOut(text1), FadeOut(a), FadeOut(b), FadeOut(c), FadeOut(d), ApplyMethod(square.apply_matrix,[[1,1],[0,1]])) + + a = TextMobject("(2,1)") + b = TextMobject("(4,1)") + c = TextMobject("(3,2)") + d = TextMobject("(5,2)") + a.scale(0.5) + b.scale(0.5) + c.scale(0.5) + d.scale(0.5) + a.move_to(self.graph_origin+0.6*UP+1.6*RIGHT) + b.move_to(self.graph_origin+0.6*UP+4.4*RIGHT) + d.move_to(self.graph_origin+2.4*UP+5.4*RIGHT) + c.move_to(self.graph_origin+2.4*UP+2.6*RIGHT) + + text1 = TextMobject("After Linear Transformation") + text1.scale(0.6) + text1.move_to(UP*3+3*RIGHT) + + self.play(Write(text1), Write(a), Write(b), Write(c), Write(d)) + + self.wait(2) + +class grid(LinearTransformationScene): + def construct(self): + + text = TextMobject("Now, consider all the vectors.") + text.scale(0.75) + text.set_color(PURPLE) + text.move_to(2.5*UP+3*LEFT) + self.play(Write(text)) + + text1 = TextMobject("Before Linear Transformation") + text1.scale(0.6) + text1.move_to(UP*3.5+3.5*RIGHT) + + square = Polygon(UP+RIGHT,UP+3*RIGHT,2*UP+3*RIGHT,2*UP+RIGHT) + square.set_color(YELLOW) + + self.play(Write(text1), ShowCreation(square)) + self.wait(2) + self.play(FadeOut(text1)) + self.add_transformable_mobject(square) + + text1 = TextMobject("After Linear Transformation") + text1.scale(0.6) + text1.move_to(UP*3.5+3.5*RIGHT) + + matrix = [[1,1],[0,1]] + + self.apply_matrix(matrix) + self.play(Write(text1)) + + self.wait() + +class grid2(LinearTransformationScene): + CONFIG = { + "include_background_plane": True, + "include_foreground_plane": False, + "show_coordinates": True, + "show_basis_vectors": True, + "basis_vector_stroke_width": 3, + "i_hat_color": X_COLOR, + "j_hat_color": Y_COLOR, + "leave_ghost_vectors": True, + } + + def construct(self): + + text = TextMobject("Now, let us focus only on the standard basis") + text.scale(0.7) + text.set_color(PURPLE) + text.move_to(2.5*UP+3.5*LEFT) + self.play(Write(text)) + + text1 = TextMobject("Before Linear Transformation") + text1.scale(0.6) + text1.move_to(UP*3.5+3.5*RIGHT) + + square = Polygon(UP+RIGHT,UP+3*RIGHT,2*UP+3*RIGHT,2*UP+RIGHT) + square.set_color(YELLOW) + + self.play(Write(text1), ShowCreation(square)) + self.wait(2) + self.play(FadeOut(text1)) + self.add_transformable_mobject(square) + + text1 = TextMobject("After Linear Transformation") + text1.scale(0.6) + text1.move_to(UP*3.5+3.5*RIGHT) + + matrix = [[1,1],[0,1]] + + self.apply_matrix(matrix) + self.play(Write(text1)) + + self.play(FadeOut(square), FadeOut(text1)) + + cor_x = TextMobject("(1,0)") + cor_y = TextMobject("(1,1)") + cor_x.scale(0.65) + cor_y.scale(0.65) + cor_y.move_to(1.25*RIGHT+1.5*UP) + cor_x.move_to(0.75*RIGHT-0.5*UP) + cor_x.set_color(GREEN) + cor_y.set_color(RED) + + x_cor = TextMobject(r"$\left[\begin{array}{c} 1\\0\end{array}\right]$") + x_cor.set_color(GREEN) + x_cor.scale(0.5) + y_cor = TextMobject(r"$\left[\begin{array}{c} 1\\1\end{array}\right]$") + x_cor.move_to(0.75*RIGHT-0.5*UP) + y_cor.move_to(1.25*RIGHT+1.5*UP) + y_cor.set_color(RED) + y_cor.scale(0.5) + + text1 = TextMobject(r"$T(\left[\begin{array}{c} x\\y \end{array}\right]) = $",r"$\left[\begin{array}{c} x+y\\y \end{array}\right]$") + text1.scale(0.7) + text1.set_color(PURPLE) + text1.move_to(1.5*UP+3*LEFT) + + text = TextMobject(r"$T(x,y) = (x+y,y)$") + text.scale(0.6) + text.set_color(PURPLE) + text.move_to(1.5*UP+3*LEFT) + + self.play(FadeIn(text),FadeIn(cor_x), FadeIn(cor_y)) + self.wait() + + self.play(Transform(text,text1), Transform(cor_x,x_cor), Transform(cor_y,y_cor)) + + text3 = TextMobject(r"$\left[\begin{array}{c} x+y\\y \end{array}\right]$") + text3.scale(0.7) + text3.set_color(PURPLE) + text3.move_to(1.5*DOWN+5*LEFT) + + equal = TextMobject("=") + equal.move_to(1.5*DOWN+3.5*LEFT) + + text3 = TextMobject("[") + text4 = TextMobject(r"$\begin{array}{c} (1)x\\(0)x \end{array}$") + text5 = TextMobject(r"$\begin{array}{c} + \\ + \end{array}$") + text6 = TextMobject(r"$\begin{array}{c} (1)y\\(1)y \end{array}$") + text7 = TextMobject("]") + text3.scale(2) + text4.scale(0.7) + text5.scale(0.7) + text6.scale(0.7) + text7.scale(2) + text4.set_color(GREEN) + text5.set_color(PURPLE) + text6.set_color(RED) + text3.move_to(1.5*DOWN+3*LEFT) + text4.move_to(1.5*DOWN+2.5*LEFT) + text5.move_to(1.5*DOWN+2*LEFT) + text6.move_to(1.5*DOWN+1.5*LEFT) + text7.move_to(1.5*DOWN+1*LEFT) + + text1[1].scale(1.2) + self.play(FadeOut(text1[0]), ApplyMethod(text1[1].move_to,1.5*DOWN+5*LEFT), FadeIn(text3), FadeIn(equal), FadeIn(text4), FadeIn(text5), FadeIn(text6), FadeIn(text7)) + + self.wait() + self.play(FadeOut(text1[1])) + + self.play(ApplyMethod(text3.move_to,1.5*DOWN+6*LEFT), + ApplyMethod(text4.move_to,1.5*DOWN+5.5*LEFT), + ApplyMethod(text5.move_to,1.5*DOWN+5*LEFT), + ApplyMethod(text6.move_to,1.5*DOWN+4.5*LEFT), + ApplyMethod(text7.move_to,1.5*DOWN+4*LEFT)) + + text10 = TextMobject("[") + text11 = TextMobject(r"$\begin{array}{c} 1\\0 \end{array}$") + text13 = TextMobject(r"$\begin{array}{c} 1\\1 \end{array}$") + text14 = TextMobject("]") + text10.scale(2) + text11.scale(0.7) + text13.scale(0.7) + text14.scale(2) + text11.set_color(GREEN) + text13.set_color(RED) + text10.move_to(1.5*DOWN+3*LEFT) + text11.move_to(1.5*DOWN+2.75*LEFT) + text13.move_to(1.5*DOWN+2.25*LEFT) + text14.move_to(1.5*DOWN+2*LEFT) + + self.play(FadeIn(text10), Transform(x_cor,text11), Transform(y_cor,text13), FadeIn(text14)) + + text15 = TextMobject(r"$\left[\begin{array}{c} x\\y \end{array}\right]$") + text15.scale(0.7) + text15.set_color(PURPLE) + text15.move_to(1.5*DOWN+1.5*LEFT) + + self.play(FadeIn(text15)) + self.play(FadeOut(text3), FadeOut(text4), FadeOut(text5), FadeOut(text7), FadeOut(text6)) + + text1[0].scale(1.2) + self.play(ApplyMethod(text1[0].move_to,1.5*DOWN+4.5*LEFT), FadeOut(equal)) + self.wait(2)
\ No newline at end of file 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/Orthonormal Basis/file1_orthogonal.py b/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file1_orthogonal.py index b400f93..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 @@ -4,31 +4,37 @@ class Orthogonal(ThreeDScene): def construct(self):
axes = ThreeDAxes()
self.play(ShowCreation(axes))
- self.move_camera(phi=30*DEGREES,theta=-45*DEGREES,run_time=3)
- line1 = Line(start = ORIGIN,end = -3*LEFT)
+ self.move_camera(phi=60*DEGREES,theta=45*DEGREES,run_time=3)
+
+ text = TextMobject(r"$\hat{i}$",r"$\hat{j}$",r"$\hat{k}$")
+ text[0].move_to(0.7*DOWN+0.8*LEFT)
+ text[1].move_to(0.75*DOWN+0.7*RIGHT)
+ text[2].move_to(0.75*UP+0.4*RIGHT)
+ self.add_fixed_in_frame_mobjects(text)
+ self.play(Write(text))
+
+ line1 = Line(start = ORIGIN,end = RIGHT)
line1.set_color(DARK_BLUE)
- tip1 = Polygon(-LEFT,-0.8*LEFT-0.2*DOWN,-0.8*LEFT-0.2*UP)
- tip1.move_to(-3*LEFT)
+ tip1 = Polygon(-0.95*LEFT,-0.8*LEFT-0.1*DOWN,-0.8*LEFT-0.1*UP)
tip1.set_opacity(1)
tip1.set_fill(DARK_BLUE)
tip1.set_color(DARK_BLUE)
- arrow2 = Line(start = ORIGIN,end = -3*UP)
+ arrow2 = Line(start = ORIGIN,end = UP)
arrow2.set_color(DARK_BLUE)
- tip2 = Polygon(DOWN,0.8*DOWN-0.2*RIGHT,0.8*DOWN-0.2*LEFT)
- tip2.move_to(3*DOWN)
+ tip2 = Polygon(0.95*UP,0.8*UP-0.1*RIGHT,0.8*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 = [0,0,3])
+ arrow3 = Line(start = ORIGIN,end = [0,0,1])
arrow3.set_color(DARK_BLUE)
- tip3 = Polygon([0,0,3],[0,0,2.8]-0.2*RIGHT,[0,0,2.8]-0.2*LEFT)
+ tip3 = Polygon([0,0,0.95],[0,0,0.8]-0.1*RIGHT,[0,0,0.8]-0.1*LEFT)
tip3.set_opacity(1)
tip3.set_fill(DARK_BLUE)
tip3.set_color(DARK_BLUE)
self.play(ShowCreation(line1), ShowCreation(tip1), ShowCreation(arrow2), ShowCreation(tip2), ShowCreation(arrow3), ShowCreation(tip3))
- self.wait()
\ No newline at end of file + self.wait()
diff --git a/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file2_OrthonormalBasis.py b/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file2_OrthonormalBasis.py deleted file mode 100644 index 0a28f22..0000000 --- a/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file2_OrthonormalBasis.py +++ /dev/null @@ -1,82 +0,0 @@ -from manimlib.imports import * -class OrthonormalBasis(GraphScene): - CONFIG = { - "x_min" : -6, - "x_max" : 6, - "y_min" : -4, - "y_max" : 4, - "graph_origin" : ORIGIN , -} - - def construct(self): - self.setup_axes(animate=True) - - XTD = self.x_axis_width/(self.x_max-self.x_min) - YTD = self.y_axis_height/(self.y_max-self.y_min) - - arrow1 = Arrow(start = ORIGIN,end = 0.707*YTD*UP+0.707*XTD*RIGHT) - arrow1.scale(2.25) - arrow1.set_color(DARK_BLUE) - - arrow2 = Arrow(start = ORIGIN,end = 0.707*YTD*UP+0.707*XTD*LEFT) - arrow2.scale(2.25) - arrow2.set_color(DARK_BLUE) - - square = Polygon(UP*0.4*YTD,0.2*(YTD*UP+XTD*RIGHT),ORIGIN,0.2*(YTD*UP+XTD*LEFT)) - square.set_color(DARK_BLUE) - self.play(ShowCreation(arrow2), ShowCreation(arrow1), ShowCreation(square)) - - ortho = TextMobject("Orthonormal Vectors") - ortho.scale(0.75) - ortho.move_to(DOWN+3*RIGHT) - self.play(Write(ortho)) - self.wait() - self.play(FadeOut(ortho)) - - arrow3 = Arrow(start = ORIGIN,end = YTD*3*UP+XTD*LEFT) - arrow3.scale(1.25) - arrow3.set_color(GOLD_E) - self.play(ShowCreation(arrow3)) - - arrow4 = Arrow(start = ORIGIN,end = YTD*UP+XTD*RIGHT) - arrow4.scale(1.8) - arrow4.set_color(GOLD_A) - - arrow5 = Arrow(start = ORIGIN,end = 2*YTD*UP-2*XTD*RIGHT) - arrow5.scale(1.3) - arrow5.set_color(GOLD_A) - - self.play(ShowCreation(arrow5), ShowCreation(arrow4)) - - self.wait() - - self.play(FadeOut(arrow1), FadeOut(arrow2), FadeOut(square)) - - self.wait() - - text1 = TextMobject(r"$<v,v_1> v_1$") - text1.move_to(UP+2*RIGHT) - text1.scale(0.75) - text2 = TextMobject(r"$<v,v_2> v_2$") - text2.move_to(UP+3*LEFT) - text2.scale(0.75) - - text3 = TextMobject("v") - text3.move_to(YTD*3.5*UP+XTD*1.5*LEFT) - - self.play(Write(text1), Write(text2), Write(text3)) - self.wait() - - line1 = DashedLine(start = YTD*UP+XTD*RIGHT, end = YTD*3*UP+XTD*1*LEFT) - line2 = DashedLine(start = YTD*2*UP+XTD*2*LEFT, end = YTD*3*UP+XTD*1*LEFT) - self.play(ShowCreation(line1),ShowCreation(line2)) - - self.wait() - - text = TextMobject(r"$v$ is the sum of projections","on the orthonormal vectors") - text[0].move_to(DOWN+3.2*RIGHT) - text[1].move_to(1.5*DOWN+3.2*RIGHT) - self.play(Write(text)) - self.wait(2) - self.play(FadeOut(arrow3), FadeOut(arrow4), FadeOut(arrow5), FadeOut(text1), FadeOut(text2), FadeOut(text3), FadeOut(self.axes), FadeOut(line1), FadeOut(line2)) - self.play(FadeOut(text)) 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 new file mode 100755 index 0000000..81a0888 --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file2_sum_of_projections_part1.py @@ -0,0 +1,133 @@ +from manimlib.imports import *
+class LinearTrans(LinearTransformationScene):
+ CONFIG = {
+ "show_basis_vectors": True,
+ "basis_vector_stroke_width": 1,
+ "leave_ghost_vectors": False,
+ "show_coordinates": True,
+ }
+
+ def construct(self):
+
+ self.setup()
+
+ matrix = [[0.6,-0.8],[0.8,0.6]]
+ self.apply_matrix(matrix)
+
+ self.wait(2)
+ orthonormal = TextMobject(r"These are 2 orthonormal vectors($v_1$ and $v_2$)")
+ orthonormal.scale(0.7)
+ orthonormal.move_to(DOWN+LEFT*3.5)
+ orthonormal.add_background_rectangle()
+ v1 = TextMobject(r"$v_1$")
+ v1.scale(0.75)
+ v1.set_color(X_COLOR)
+ v1.move_to(0.75*UP+RIGHT)
+ v1.add_background_rectangle()
+ v2 = TextMobject(r"$v_2$")
+ v2.scale(0.75)
+ v2.set_color(Y_COLOR)
+ v2.move_to(0.75*UP+LEFT*1.25)
+ v2.add_background_rectangle()
+ self.play(Write(orthonormal))
+ self.play(Write(v1),Write(v2))
+ self.wait()
+ self.play(FadeOut(orthonormal), FadeOut(v1), FadeOut(v2))
+
+ arrow = Arrow(start = ORIGIN,end = 3*RIGHT+UP)
+ arrow.scale(1.2)
+ arrow.set_color(BLUE)
+ arrow.apply_matrix(matrix)
+ text3 = TextMobject("v")
+ text3.move_to(3.2*UP+1.2*RIGHT)
+ text3.add_background_rectangle()
+ self.play(ShowCreation(arrow),Write(text3))
+ self.wait()
+ 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)
+ v_cor.add_background_rectangle()
+ self.play(Transform(text3,v_cor))
+
+ line1 = DashedLine(start = 1*UP+3*RIGHT, end = 3*RIGHT)
+ line2 = DashedLine(start = 1*UP+3*RIGHT, end = UP)
+ line1.apply_matrix(matrix)
+ line2.apply_matrix(matrix)
+ self.play(ShowCreation(line1),ShowCreation(line2),run_time = 2)
+
+ v1 = Arrow(start = ORIGIN,end = 3*RIGHT+UP)
+ v1.scale(1.2)
+ v1.set_color(BLUE)
+ v1.apply_matrix(matrix)
+ arrow1 = Arrow(start = ORIGIN,end = 3*RIGHT)
+ arrow1.scale(1.2)
+ arrow1.set_color("#6B8E23")
+ arrow1.apply_matrix(matrix)
+ self.play(Transform(v1,arrow1))
+ v1_cor = TextMobject(r"$<v,v_1> v_1$")
+ v1_cor.move_to(2.5*UP+3*RIGHT)
+ v1_cor.scale(0.75)
+ v1_cor.add_background_rectangle()
+ self.play(Write(v1_cor))
+ self.wait(0.5)
+ text1 = TextMobject(r"(1.8,2.4)")
+ text1.move_to(2.1*UP+2.5*RIGHT)
+ text1.scale(0.75)
+ text1.set_color("#6B8E23")
+ text1.add_background_rectangle()
+ self.play(Transform(v1_cor,text1))
+
+ v2 = Arrow(start = ORIGIN,end = 3*RIGHT+UP)
+ v2.scale(1.2)
+ v2.set_color("#8b0000")
+ v2.apply_matrix(matrix)
+ arrow2 = Arrow(start = ORIGIN,end = UP)
+ arrow2.scale(2.1)
+ arrow2.set_color("#8b0000")
+ arrow2.apply_matrix(matrix)
+ self.wait(0.5)
+ self.play(Transform(v2,arrow2))
+ self.wait(0.5)
+ v2_cor = TextMobject(r"$<v,v_2> v_2$")
+ v2_cor.move_to(0.75*UP+2.5*LEFT)
+ v2_cor.scale(0.75)
+ v2_cor.add_background_rectangle()
+ self.play(Write(v2_cor))
+ self.wait(0.5)
+ text2 = TextMobject(r"(-0.8,0.6)")
+ text2.move_to(0.75*UP+1.75*LEFT)
+ text2.scale(0.75)
+ text2.set_color("#8b0000")
+ text2.add_background_rectangle()
+ self.play(Transform(v2_cor,text2))
+
+ self.wait()
+
+ self.play(ApplyMethod(v2.move_to,1.4*RIGHT+2.7*UP),FadeOut(v1_cor),FadeOut(v2_cor),FadeOut(v_cor))
+
+ self.wait()
+
+ ending = TextMobject(r"$v = <v,v_1> v_1 + <v,v_2> v_2$")
+ ending.scale(0.7)
+ ending.move_to(DOWN)
+ ending.add_background_rectangle()
+ self.play(Write(ending))
+ self.wait()
+ self.play(FadeOut(ending))
+
+ ending = TextMobject(r"$\left[ \begin{array} {c} 1\\ 3 \end{array}\right] = \left[ \begin{array} {c}1.8 \\ 2.4 \end{array}\right] + \left[ \begin{array} {c} -0.8\\ 0.6 \end{array}\right]$")
+ ending.scale(0.7)
+ ending.move_to(DOWN)
+ ending.add_background_rectangle()
+ self.play(Write(ending))
+ self.wait()
+ self.play(FadeOut(ending))
+
+ ending = TextMobject(r"$v$ is the sum of projections on the orthonormal vectors")
+ ending.scale(0.7)
+ ending.move_to(DOWN)
+ ending.add_background_rectangle()
+ self.play(Write(ending))
+ self.wait()
+ self.play(FadeOut(ending))
\ No newline at end of file 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 new file mode 100644 index 0000000..9d25192 --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file3_sum_of_projections_part2.py @@ -0,0 +1,173 @@ +from manimlib.imports import * +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) + self.play(Write(basis)) + v = TextMobject(r"$v_1$",r"$v_2$",r"$v_3$") + v[0].move_to(UP*0.5+RIGHT*0.75) + v[1].move_to(UP*0.5+RIGHT*2.5) + v[2].move_to(UP*0.5+RIGHT*4) + eq = TextMobject(r"$v = \left(\begin{array}{c}3\\4\\5\end{array}\right)$") + eq1 = TextMobject(r"$<v,v_1> = \frac{3}{\sqrt{2}} + \frac{4}{\sqrt{2}} + 0 = \frac{7}{\sqrt{2}}$") + eq2 = TextMobject(r"$<v,v_2> = \frac{-3}{\sqrt{2}} + \frac{4}{\sqrt{2}} + 0 =\frac{1}{\sqrt{2}}$") + eq3 = TextMobject(r"$<v,v_3> = 0 + 0 + 5 =5$") + eq.move_to(4*LEFT+DOWN) + eq1.move_to(0.5*DOWN+2*RIGHT) + eq2.move_to(1.5*DOWN+2*RIGHT) + eq3.move_to(2.5*DOWN+2*RIGHT) + self.play(Write(v)) + self.play(Write(eq)) + self.play(Write(eq1)) + 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.wait() + + text = TextMobject("These are the 3 mutually orthonormal basis of the set(", r"$v_1$, ", r"$v_2$, ", r"$v_3$",")") + text[1].set_color(DARK_BLUE) + text[2].set_color(RED) + text[3].set_color(YELLOW) + text.scale(0.75) + self.add_fixed_in_frame_mobjects(text) + text.move_to(3*DOWN) + 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) + 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)) + 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]) + + self.play(ShowCreation(dashedline1), ShowCreation(dashedline2)) + + line1 = Line(start = ORIGIN,end = 0.707*RIGHT + 0.707*UP) + line1.set_color(DARK_BLUE) + tip1 = Polygon(0.707*RIGHT + 0.707*UP, 0.707*RIGHT + 0.607*UP, 0.607*RIGHT + 0.707*UP) + tip1.set_opacity(1) + tip1.set_fill(DARK_BLUE) + tip1.set_color(DARK_BLUE) + self.play(ShowCreation(line1), ShowCreation(tip1)) + + line2 = Line(start = ORIGIN,end = 0.707*LEFT + 0.707*UP) + line2.set_color(RED) + tip2 = Polygon(0.707*LEFT + 0.707*UP, 0.707*LEFT + 0.607*UP, 0.607*LEFT + 0.707*UP) + tip2.set_opacity(1) + tip2.set_fill(RED) + tip2.set_color(RED) + + self.play(ShowCreation(line2), ShowCreation(tip2)) + + line3 = Line(start = ORIGIN,end = [0,0,1]) + line3.set_color(YELLOW) + tip3 = Polygon([0,0,1],[0,0,0.8]-0.2*RIGHT,[0,0,0.8]-0.2*LEFT) + tip3.set_opacity(1) + tip3.set_fill(YELLOW) + tip3.set_color(YELLOW) + self.play(ShowCreation(line3), ShowCreation(tip3)) + self.wait() + + self.play(FadeOut(text)) + + text = TextMobject("Take the projection of ", r"$v$", " on the mutually orthonormal vectors") + text[1].set_color(GOLD_E) + text.scale(0.75) + self.add_fixed_in_frame_mobjects(text) + text.move_to(3*DOWN) + self.play(Write(text)) + self.wait(2) + + 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.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.play(ShowCreation(dashedline3),ShowCreation(dashedline4),ShowCreation(dashedline5)) + self.wait(6) + + pv1 = Line(start = ORIGIN,end = 4*UP+3*RIGHT+[0,0,5]) + pv1.set_color(GOLD_E) + pv1tip = 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) + pv1tip.set_opacity(1) + pv1tip.set_fill(GOLD_E) + pv1tip.set_color(GOLD_E) + + v1_p = Line(start = ORIGIN,end = 3.5*RIGHT + 3.5*UP) + v1_p.set_color(BLUE_E) + v1_p_tip = Polygon(3.5*RIGHT + 3.5*UP, 3.5*RIGHT + 3.4*UP, 3.4*RIGHT + 3.5*UP) + v1_p_tip.set_opacity(1) + v1_p_tip.set_fill(BLUE_E) + v1_p_tip.set_color(BLUE_E) + + pv2 = Line(start = ORIGIN,end = 4*UP+3*RIGHT+[0,0,5]) + pv2.set_color(GOLD_E) + pv2tip = 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) + pv2tip.set_opacity(1) + pv2tip.set_fill(GOLD_E) + pv2tip.set_color(GOLD_E) + + v2_p = Line(start = ORIGIN,end = 0.5*LEFT + 0.5*UP) + v2_p.set_color(RED_E) + v2_p_tip = Polygon(0.5*LEFT + 0.5*UP, 0.5*LEFT + 0.4*UP, 0.4*LEFT + 0.5*UP) + v2_p_tip.set_opacity(1) + v2_p_tip.set_fill(RED_E) + v2_p_tip.set_color(RED_E) + + pv3 = Line(start = ORIGIN,end = 4*UP+3*RIGHT+[0,0,5]) + pv3.set_color(GOLD_E) + pv3tip = 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) + pv3tip.set_opacity(1) + pv3tip.set_fill(GOLD_E) + pv3tip.set_color(GOLD_E) + + 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.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.play(FadeOut(dashedline1), + FadeOut(dashedline2), + FadeOut(dashedline3), + FadeOut(dashedline4), + FadeOut(dashedline5), + FadeOut(line1), + FadeOut(tip1), + FadeOut(line2), + FadeOut(tip2), + FadeOut(line3), + FadeOut(tip3), + FadeOut(text)) + + text = TextMobject(r"$v$ is the sum of projections on the orthonormal vectors") + text.set_color(GOLD_E) + text.scale(0.75) + self.add_fixed_in_frame_mobjects(text) + text.move_to(3*DOWN) + self.play(Write(text), ApplyMethod(pv2.move_to,(3.5*RIGHT + 3.5*UP+3*RIGHT+4*UP)/2), ApplyMethod(pv2tip.move_to,(3.1*RIGHT + 3.9*UP))) + self.play(ApplyMethod(pv3.move_to,3*RIGHT + 4*UP + [0,0,2.5]), ApplyMethod(pv3tip.move_to,(3*RIGHT + 4*UP + [0,0,4.8]))) + + self.wait(3)
\ No newline at end of file diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file1_Column_Space.py b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file10_NOT_in_lecture_note_Column_Space.py index afe4f9a..afe4f9a 100644 --- a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file1_Column_Space.py +++ b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file10_NOT_in_lecture_note_Column_Space.py diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file1_Axb.py b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file1_Axb.py new file mode 100755 index 0000000..95d1021 --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file1_Axb.py @@ -0,0 +1,77 @@ +from manimlib.imports import *
+
+class Axb(Scene):
+
+ def construct(self):
+
+ text0 = TextMobject("Linear System Of Equations")
+ text1 = TextMobject(r"$x_{1}+x_{2}+x_{3} =b_{1}$")
+ text2 = TextMobject(r"$x_{1}+2x_{2}+x_{3} =b_{2}$")
+ text3 = TextMobject(r"$x_{1}+x_{2}+3x_{3} =b_{3}$")
+ text0.move_to(UP*2+LEFT*2)
+ text0.set_color(DARK_BLUE)
+ text1.move_to(UP)
+ text2.move_to(ORIGIN)
+ text3.move_to(DOWN)
+
+ text0.scale(0.75)
+ text1.scale(0.75)
+ text2.scale(0.75)
+ text3.scale(0.75)
+ self.play(Write(text0))
+ self.play(Write(text1))
+ self.play(Write(text2))
+ self.play(Write(text3))
+ self.play(ApplyMethod(text0.move_to,3*UP+LEFT*2), ApplyMethod(text1.move_to,2.5*UP), ApplyMethod(text2.move_to,2*UP), ApplyMethod(text3.move_to,1.5*UP))
+
+ A = TextMobject(r"$\left( \begin{array}{c c c} 1 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 3 \end{array}\right) \left[ \begin{array} {c} x_{1} \\ x_{2} \\ x_{3} \end{array}\right] =$", r"$\left[ \begin{array}{c} x_{1}+x_{2}+x_{3} \\ x_{1}+2x_{2}+x_{3} \\ x_{1}+x_{2}+3x_{3} \end{array}\right]$")
+ A.scale(0.75)
+ self.play(FadeIn(A))
+
+ textA = TextMobject("A")
+ textx = TextMobject("x")
+ textb = TextMobject("Ax")
+
+ textA.move_to(DOWN+3*LEFT)
+ textx.move_to(1.1*DOWN+0.5*LEFT)
+ textb.move_to(DOWN-2*LEFT)
+
+ self.play(Write(textA), Write(textx), Write(textb))
+
+ circle1 = Circle(radius = 0.24)
+ circle2 = Circle(radius = 0.24)
+ square = Square(side_length = 0.6)
+
+ circle1.move_to(UP*0.5+LEFT*3.05)
+ circle2.move_to(UP*0.4+LEFT*0.5)
+ square.move_to(UP*0.4+RIGHT*1.3)
+
+ self.play(FadeIn(circle1), FadeIn(circle2),FadeIn(square))
+
+ self.play(ApplyMethod(circle1.move_to,UP*0.5+LEFT*2.45), ApplyMethod(circle2.move_to,LEFT*0.5), ApplyMethod(square.move_to,UP*0.4+RIGHT*2.2))
+ self.play(ApplyMethod(circle1.move_to,UP*0.5+LEFT*1.85), ApplyMethod(circle2.move_to,DOWN*0.5+LEFT*0.5), ApplyMethod(square.move_to,UP*0.4+RIGHT*3.1))
+
+ self.play(ApplyMethod(circle1.move_to,LEFT*3.05), ApplyMethod(circle2.move_to,UP*0.4+LEFT*0.5), ApplyMethod(square.move_to,RIGHT*1.3))
+ self.play(ApplyMethod(circle1.move_to,LEFT*2.45), ApplyMethod(circle2.move_to,LEFT*0.5), ApplyMethod(square.move_to,RIGHT*2.2))
+ self.play(ApplyMethod(circle1.move_to,LEFT*1.85), ApplyMethod(circle2.move_to,DOWN*0.5+LEFT*0.5), ApplyMethod(square.move_to,RIGHT*3.1))
+
+ self.play(ApplyMethod(circle1.move_to,0.4*DOWN+LEFT*3.05), ApplyMethod(circle2.move_to,UP*0.4+LEFT*0.5), ApplyMethod(square.move_to,0.4*DOWN+RIGHT*1.3))
+ self.play(ApplyMethod(circle1.move_to,0.4*DOWN+LEFT*2.45), ApplyMethod(circle2.move_to,LEFT*0.5), ApplyMethod(square.move_to,0.4*DOWN+RIGHT*2.2))
+ self.play(ApplyMethod(circle1.move_to,0.4*DOWN+LEFT*1.85), ApplyMethod(circle2.move_to,DOWN*0.5+LEFT*0.5), ApplyMethod(square.move_to,0.4*DOWN+RIGHT*3.1))
+
+ self.play(FadeOut(circle1), FadeOut(circle2), FadeOut(square))
+ self.play(FadeOut(A[0]), ApplyMethod(A[1].move_to,2*LEFT),ApplyMethod(textb.move_to,DOWN+1.7*LEFT), FadeOut(textx), FadeOut(textA))
+ b = TextMobject(r"$=\left[ \begin{array}{c} b_{1} \\ b_{2} \\ b_{3} \end{array}\right]$")
+ b.move_to(RIGHT)
+ textB = TextMobject("b")
+ textB.move_to(1.2*DOWN+1.1*RIGHT)
+ self.play(FadeIn(b),FadeIn(textB))
+
+ self.wait()
+
+ self.play(FadeOut(text0), FadeOut(text1), FadeOut(text2), FadeOut(text3))
+
+ axb = TextMobject("Ax = b")
+ self.play(FadeIn(axb), FadeOut(textb), FadeOut(textB), FadeOut(b), FadeOut(A[1]))
+
+ self.wait()
\ No newline at end of file diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file1_Column_Space.gif b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file1_Column_Space.gif Binary files differdeleted file mode 100644 index 7d8d2e1..0000000 --- a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file1_Column_Space.gif +++ /dev/null diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file2_CSasImage.py b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file2_CSasImage.py new file mode 100644 index 0000000..70547cb --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file2_CSasImage.py @@ -0,0 +1,169 @@ +from manimlib.imports import * + +class Column_Space(Scene): + def construct(self): + + 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) + + 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.scale(0.75) + + self.play(Write(CS_A),run_time = 2) + + 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(arrow3),run_time = 1) + self.wait(1) + +class solution(LinearTransformationScene): + def construct(self): + + self.setup() + self.wait() + + o = TextMobject(r"Consider the vector space $R^2$") + o.move_to(2*DOWN) + o.scale(0.75) + o.add_background_rectangle() + self.play(Write(o)) + self.wait() + self.play(FadeOut(o)) + + 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() + self.play(Write(A)) + matrix = [[1,-1],[1,-1]] + self.apply_matrix(matrix) + self.wait() + self.play(FadeOut(A)) + + o = TextMobject(r"This is the transformed vector space") + o.move_to(2*DOWN) + o.scale(0.75) + o.add_background_rectangle() + self.play(Write(o)) + self.wait() + self.play(FadeOut(o)) + + texti = TextMobject(r"$\left[\begin{array}{c}1\\1\end{array}\right]$") + textj = TextMobject(r"$\left[\begin{array}{c}-1\\-1\end{array}\right]$") + texti.set_color(GREEN) + textj.set_color(RED) + texti.scale(0.7) + textj.scale(0.7) + texti.move_to(1.35*RIGHT+0.5*UP) + textj.move_to(-(1.5*RIGHT+0.5*UP)) + + text1 = TextMobject("[") + text2 = TextMobject(r"$\begin{array}{c} 1 \\ 1 \end{array}$") + text3 = TextMobject(r"$\begin{array}{c} -1 \\ -1 \end{array}$") + text4 = TextMobject("]") + + text2.set_color(GREEN) + text3.set_color(RED) + + text1.scale(2) + text4.scale(2) + text2.scale(0.7) + text3.scale(0.7) + + text1.move_to(2.5*UP+6*LEFT) + text2.move_to(2.5*UP+5.75*LEFT) + text3.move_to(2.5*UP+5.25*LEFT) + text4.move_to(2.5*UP+5*LEFT) + + self.play(Write(texti), Write(textj)) + self.wait() + self.play(FadeIn(text1), Transform(texti,text2), Transform(textj,text3), FadeIn(text4)) + self.wait() + + o = TextMobject(r"Now, you can observe the Image of Linear Transformation") + o1 = TextMobject(r"and Column Space(i.e. span of columns of matrix $A$) are same") + o.move_to(2.5*DOWN) + o1.move_to(3*DOWN) + o.scale(0.75) + o1.scale(0.75) + o.add_background_rectangle() + o1.add_background_rectangle() + self.play(Write(o)) + self.play(Write(o1)) + self.wait() + self.play(FadeOut(o),FadeOut(o1)) + +class solution2nd(LinearTransformationScene): + def construct(self): + + self.setup() + self.wait() + + arrow1 = Arrow(start = ORIGIN,end = 2*DOWN+RIGHT) + arrow2 = Arrow(start = ORIGIN,end = UP+LEFT) + arrow3 = Arrow(start = ORIGIN,end = 3*UP+4*RIGHT) + arrow1.set_color(YELLOW) + arrow2.set_color(ORANGE) + arrow3.set_color(PURPLE) + arrow1.scale(1.3) + arrow2.scale(1.5) + arrow3.scale(1.1) + + self.play(ShowCreation(arrow1), ShowCreation(arrow2), ShowCreation(arrow3)) + + self.add_transformable_mobject(arrow1) + self.add_transformable_mobject(arrow2) + self.add_transformable_mobject(arrow3) + o = TextMobject(r"Consider any vector in the original vector space $R^2$") + o.move_to(2.5*DOWN) + o.scale(0.75) + o.add_background_rectangle() + self.play(Write(o)) + self.wait() + self.play(FadeOut(o)) + + 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() + self.play(Write(A)) + matrix = [[1,-1],[1,-1]] + self.apply_matrix(matrix) + self.wait() + self.play(FadeOut(A)) + + o = TextMobject(r"This is the transformed vector space") + o.move_to(2*DOWN) + o.scale(0.75) + o.add_background_rectangle() + self.play(Write(o)) + self.wait() + self.play(FadeOut(o)) + + o = TextMobject(r"Each and every vector of original vector space $R^2$ will transform") + o1 = TextMobject(r"to this new vector space which is spanned by $\mathbf{CS}(A)$") + o.move_to(2.5*DOWN) + o1.move_to(3*DOWN) + o.scale(0.75) + o1.scale(0.75) + o.add_background_rectangle() + o1.add_background_rectangle() + self.play(Write(o)) + self.play(Write(o1)) + self.wait() + self.play(FadeOut(o)) + self.play(FadeOut(o1))
\ No newline at end of file diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file3_solution.py b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file3_solution.py new file mode 100644 index 0000000..eb310f3 --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file3_solution.py @@ -0,0 +1,77 @@ +from manimlib.imports import * +class solution(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(3*DOWN) + o.scale(0.75) + o.add_background_rectangle() + self.play(Write(o)) + self.wait() + self.play(FadeOut(o)) + + 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)) + matrix = [[1,-1],[1,-1]] + self.apply_matrix(matrix) + self.wait() + self.play(FadeOut(A)) + + 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)) + self.wait() + self.play(FadeOut(o)) + + arrow2 = Arrow(start = ORIGIN, end = 2*DOWN+2*LEFT) + arrow2.set_color(PURPLE) + arrow2.scale(1.2) + self.play(ShowCreation(arrow2)) + self.wait() + + o1 = TextMobject("If the ","vector b"," lies in the transformed vector space") + o2 = TextMobject("(the line) then the solution exist") + 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() + o2.add_background_rectangle() + self.play(Write(o1)) + self.play(Write(o2)) + self.wait() + self.play(FadeOut(o1), FadeOut(o2)) + + self.play(FadeOut(arrow2)) + + arrow1 = Arrow(start = ORIGIN, end = 2*UP+RIGHT) + arrow1.set_color(ORANGE) + arrow1.scale(1.3) + self.play(ShowCreation(arrow1)) + self.wait() + + o1 = TextMobject("If the ","vector b"," does lies in the transformed") + o2 = TextMobject("vector space then the does not solution exist") + o1.move_to(2.5*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() + o2.add_background_rectangle() + self.play(Write(o1)) + self.play(Write(o2)) + self.wait() + self.play(FadeOut(o1), FadeOut(o2)) + + self.play(FadeOut(arrow1)) +
\ No newline at end of file diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file4_null_space.py b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file4_null_space.py new file mode 100644 index 0000000..3c52677 --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file4_null_space.py @@ -0,0 +1,91 @@ +from manimlib.imports import * +class null_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(3*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 particular vector $\left(\begin{array}{c} 1 \\ 1 \end{array}\right)$") + 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) + arrow1 = Arrow(start = ORIGIN, end = 2*(UP+RIGHT)) + arrow2 = Arrow(start = ORIGIN, end = 3*(UP+RIGHT)) + arrow3 = Arrow(start = ORIGIN, end = 4*(UP+RIGHT)) + arrow4 = Arrow(start = ORIGIN, end = DOWN+LEFT) + arrow5 = Arrow(start = ORIGIN, end = 2*(DOWN+LEFT)) + arrow6 = Arrow(start = ORIGIN, end = 3*(DOWN+LEFT)) + arrow7 = Arrow(start = ORIGIN, end = 4*(DOWN+LEFT)) + + 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)) + + 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) + + 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) + 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() + + 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(3*DOWN) + o.scale(0.75) + o.add_background_rectangle() + self.play(Write(o)) + self.wait(2) + self.play(FadeOut(o), FadeOut(arrow), FadeOut(arrow1), FadeOut(arrow2), FadeOut(arrow3), FadeOut(arrow4), FadeOut(arrow5), FadeOut(arrow6), FadeOut(arrow7)) 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)) |
%3dk.gif?id=b4a0a3d3a896d9e45cd92c89bb665d65e34db309){kind=link}
%3dk.gif?id=0aba6d36ed8aee098edbb01bff0e1cc0577770f9){kind=link}
/file4_Horizontal_Shear_gif.gif?id=b4a0a3d3a896d9e45cd92c89bb665d65e34db309){kind=link}
/file6_Horizontal_Shear_gif.gif?id=0aba6d36ed8aee098edbb01bff0e1cc0577770f9){kind=link}
/file5_Vertical_Shear_gif.gif?id=b4a0a3d3a896d9e45cd92c89bb665d65e34db309){kind=link}
/file7_Vertical_Shear_gif.gif?id=0aba6d36ed8aee098edbb01bff0e1cc0577770f9){kind=link}
