diff options
Diffstat (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions')
16 files changed, 534 insertions, 191 deletions
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..40add0f --- /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/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/file5_derivative_vectorvf.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file6_derivative_vectorvf.gif Binary files differindex a94de90..a94de90 100644 --- 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/file6_derivative_vectorvf.gif |
