diff options
Diffstat (limited to 'FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient')
8 files changed, 19 insertions, 382 deletions
diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/README.md b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/README.md new file mode 100644 index 0000000..c284f76 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/README.md @@ -0,0 +1,19 @@ +**Gradient_file1_analogy.py** <br> + +**Gradient_file2_input-output.py** <br> + +**Gradient_file3_input-output2.py** <br> + +**Gradient_file4_why-partials.py** <br> + +**Gradient_file5_contour-lines-and-map.ipynb** <br> + +**Gradient_file6_surf-contour-plot.ipynb** <br> + +**Gradient_file7_missiles.py** <br> + +**Gradient_file8_fluid-flow.py** <br> + + + + diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file1_missile-example.py b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file1_missile-example.py deleted file mode 100644 index cd754cd..0000000 --- a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file1_missile-example.py +++ /dev/null @@ -1,37 +0,0 @@ -from manimlib.imports import * -import numpy as np - - -def function(coordinate): - x,y = coordinate[:2] - return np.array([ - np.sin(x-y), - np.exp(y), - 0 - ]) -def func(coordinate): - x,y = coordinate[:2] - return np.array([ - -2*x, - y, - 0]) - -class Missiles(GraphScene): - def construct(self): - - field = VectorField(function) - #path = ParametricFunction(lambda x: -2*x) - - dot = SVGMobject("miss").move_to(DL).scale(0.09).set_color(WHITE).rotate(PI/4 + PI) - path = ArcBetweenPoints(dot.get_center(), UP+0.2*LEFT) - - self.play(FadeIn(field)) - self.wait() - self.play(FadeIn(dot)) - self.wait() - self.play(MoveAlongPath(dot, path)) - self.play(ApplyMethod(dot.rotate, PI/4), rate = 0.2) - self.play(ApplyMethod(dot.move_to, 3.5*UP), rate = 0.3) - #self.play(ApplyMethod(dot.move_to, 3.5*UP)) - #self.add_fixed_in_frame_mobjects(text_field) - self.wait()
\ No newline at end of file diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file2_gradient-example-1.py b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file2_gradient-example-1.py deleted file mode 100644 index 7a95867..0000000 --- a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file2_gradient-example-1.py +++ /dev/null @@ -1,43 +0,0 @@ -from manimlib.imports import * -import numpy as np - - -def function(coordinate): - x,y = coordinate[:2] - return np.array([ - 0.4*x, - 0.4*y, - 0.4*np.cos(np.sqrt((x**2)+(y**2)) - )]) - -class ThreeDVector(ThreeDScene): - def construct(self): - axes = ThreeDAxes() - self.add(axes) - self.set_camera_orientation(phi=45*DEGREES,theta=60*DEGREES,distance=40) - self.begin_ambient_camera_rotation(rate=0.5) - - surface = ParametricSurface( - lambda u, v: np.array([ - 0.4*u, - 0.4*v, - 0.4*np.cos(np.sqrt((u**2)+(v**2))) - ]),u_min=-20,u_max=20, v_min=-10,v_max=10).set_color(BLUE_E).fade(0.7) - - text_func = TexMobject(r"\textbf{Input: Function}").shift(4.4*LEFT+3.3*UP).scale(0.7) - text_field = TexMobject(r"\textbf{Output: Vector Field}").shift(4.4*LEFT+3.3*UP).scale(0.7) - - - self.add_fixed_in_frame_mobjects(text_func) - self.play(ShowCreation(surface)) - self.wait(3) - - field = VectorField(function) - self.play(FadeIn(field), FadeOut(text_func)) - self.add_fixed_in_frame_mobjects(text_field) - self.wait() - self.play(FadeOut(surface)) - self.wait() - - - diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file3_gradient-example-2.py b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file3_gradient-example-2.py deleted file mode 100644 index e37581d..0000000 --- a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file3_gradient-example-2.py +++ /dev/null @@ -1,39 +0,0 @@ -from manimlib.imports import * -import numpy as np - - -def function(coordinate): - x,y = coordinate[:2] - return np.array([ - x, - y, - x**2 - y**2 - ]) - -class ThreeDVector_three(ThreeDScene): - def construct(self): - axes = ThreeDAxes() - self.add(axes) - self.set_camera_orientation(phi=45*DEGREES,theta=85*DEGREES,distance=40) - self.begin_ambient_camera_rotation(rate=0.5) - - surface = ParametricSurface( - lambda x, y: np.array([ - x, - y, - x**2 - y**2 - ]),u_min=-2,u_max=2, v_min=-1.5,v_max=1.5).set_color(BLUE_E).fade(0.7).scale(1.7) - - text_func = TexMobject(r"\textbf{Input: Function}").shift(4.4*LEFT+3.3*UP).scale(0.7) - text_field = TexMobject(r"\textbf{Output: Vector Field}").shift(4.4*LEFT+3.3*UP).scale(0.7) - - self.add_fixed_in_frame_mobjects(text_func) - self.play(ShowCreation(surface)) - self.wait(3) - - field = VectorField(function) - self.play(FadeIn(field), FadeOut(text_func)) - self.add_fixed_in_frame_mobjects(text_field) - self.wait() - self.play(FadeOut(surface)) - self.wait(2)
\ No newline at end of file diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file4-multidimensional-gradient.py b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file4-multidimensional-gradient.py deleted file mode 100644 index e9c8fd0..0000000 --- a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file4-multidimensional-gradient.py +++ /dev/null @@ -1,113 +0,0 @@ -from manimlib.imports import * -import numpy as np - - -class Hills(ThreeDScene): - def construct(self): - axes = ThreeDAxes( - number_line_config={ - "color": GREEN, - "include_tip": False, - "exclude_zero_from_default_numbers": True, - } - ) - self.add(axes) - - self.set_camera_orientation(phi=45*DEGREES,theta=45*DEGREES,distance=40) - #self.begin_ambient_camera_rotation(rate=0.5) - self.wait() - - cylinder_1 = ParametricSurface( - lambda u, v: np.array([ - u, - v, - 7*u*v/np.exp(u**2+v**2) - ]),u_min=-3,u_max=3, v_min=-1,v_max=-0.95).set_color(YELLOW_E).rotate(PI/2).shift(LEFT).fade(0.5) - cylinder = ParametricSurface( - lambda u, v: np.array([ - u, - v, - 7*u*v/np.exp(u**2+v**2) - ]),u_min=-3,u_max=3, v_min=-3,v_max=3).set_color(YELLOW_E).rotate(PI/2).shift(LEFT).fade(0.5) - text_one = TexMobject(r"\textrm{Single variable functions slope up and down}") - #name = TexMobject(r"\textrm{PROBE}").next_to(text_one, DOWN, buff = SMALL_BUFF).scale(0.7) - text_one_a = TexMobject(r"\textrm{Position }", r" \rightarrow ").next_to(text_one, DOWN, buff = SMALL_BUFF) - probe = Sphere(radius = 0.2).next_to(text_one_a, RIGHT).set_color(BLUE_E) - text_one_b = TexMobject(r" \rightarrow ", r"\textrm{ slope }").next_to(probe, RIGHT, buff = SMALL_BUFF) - name = TextMobject("PROBE").next_to(probe, DOWN, buff = SMALL_BUFF).scale(0.5) - text = VGroup(text_one, text_one_a, probe, text_one_b, name).to_edge(UP+1.5*LEFT).scale(0.5) - - text_two = TexMobject(r"\textrm{Multivariable functions slope in infinitely many directions!}") - #name_two = TexMobject(r"\textrm{PROBE2.0}").next_to(text_two, DOWN, buff = SMALL_BUFF).scale(0.7) - text_two_a = TexMobject(r"\textrm{Position, Direction }", r" \rightarrow ").next_to(text_two, DOWN, buff = SMALL_BUFF) - probe_two = Sphere(radius = 0.2).next_to(text_two_a, RIGHT).set_color(PURPLE_E) - text_two_b = TexMobject(r" \rightarrow ", r"\textrm{ slope }").next_to(probe_two, RIGHT, buff = SMALL_BUFF) - name_two = TextMobject("PROBE2.0").next_to(probe_two, DOWN, buff = SMALL_BUFF).scale(0.5) - two = VGroup(text_two, text_two_a, probe_two, text_two_b, name_two).to_edge(UP+LEFT).scale(0.5).shift(3.5*LEFT) - - - - - - - self.play(ShowCreation(cylinder_1)) - self.wait() - self.add_fixed_in_frame_mobjects(text) - self.wait(3.5) - self.play(FadeOut(text)) - self.play(ReplacementTransform(cylinder_1, cylinder)) - self.wait() - self.add_fixed_in_frame_mobjects(two) - self.begin_ambient_camera_rotation(rate=0.5) - self.wait(4) - -class OneMore(ThreeDScene, GraphScene): - def setup(self): - GraphScene.setup(self) - ThreeDScene.setup(self) - - def construct(self): - axes = ThreeDAxes( - number_line_config={ - "color": GREEN, - "include_tip": False, - "exclude_zero_from_default_numbers": True, - } - ) - self.add(axes) - - self.set_camera_orientation(phi=90*DEGREES,theta=90*DEGREES,distance=40) - #self.begin_ambient_camera_rotation(rate=0.5) - self.wait() - - shape = ParametricSurface( - lambda u, v: np.array([ - u, - v, - 2 - u**2 - v**2, - ]),u_min=0,u_max =0.01, v_min=-2,v_max=2).set_color(GREEN_C) - - shape_A = ParametricSurface( - lambda u, v: np.array([ - 0*u, - 0, - v, - ]),u_min=-2,u_max = 2, v_min=-2,v_max=2).set_color(GREEN_C) - - - ''' - path = self.get_graph(lambda u,v: np.array([ - u, - 2 - u**2 - v**2]), u_min=-2,u_max=2, v_min=-2,v_max=2) - location = np.array([-2,-2, -2]) #location: Point - dot = Dot(location) - ''' - - self.play(ShowCreation(shape)) - self.add(shape_A) - #self.play(ShowCreation(path), ShowCreation(dot)) - #self.play(MoveAlongPath(dot, path)) - #self.wait(3) - self.play(ApplyMethod(shape.fade, 0.5)) - self.begin_ambient_camera_rotation(rate = 0.5) - self.wait(3) diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file4_gradient-example-3.py b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file4_gradient-example-3.py deleted file mode 100644 index 7c0ef54..0000000 --- a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file4_gradient-example-3.py +++ /dev/null @@ -1,40 +0,0 @@ -from manimlib.imports import * -import numpy as np - - -def function(coordinate): - x,y = coordinate[:2] - return np.array([ - x, - y, - 1/np.cos(x*y), - ]) - -class ThreeDVector(ThreeDScene): - def construct(self): - axes = ThreeDAxes() - self.add(axes) - self.set_camera_orientation(phi=45*DEGREES,theta=45*DEGREES,distance=40) - self.begin_ambient_camera_rotation(rate=0.5) - - surface = ParametricSurface( - lambda x, y: np.array([ - x, - y, - 1/np.cos(x*y), - ]),u_min=-1.15,u_max=1.15, v_min=-1.15,v_max=1.15).set_color(BLUE_E).fade(0.7).scale(1.4) - - text_func = TexMobject(r"\textbf{Input: Function}").shift(4.4*LEFT+3.3*UP).scale(0.3) - text_field = TexMobject(r"\textbf{Output: Vector Field}").shift(4.4*LEFT+3.3*UP).scale(0.7) - - self.add_fixed_in_frame_mobjects(text_func) - self.play(ShowCreation(surface)) - self.wait(2) - - field = VectorField(function).scale(0.7) - self.play(FadeIn(field), FadeOut(text_func)) - self.add_fixed_in_frame_mobjects(text_field) - self.wait() - - self.play(FadeOut(surface)) - self.wait(2) diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file5_steepest-ascent-analogy.py b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file5_steepest-ascent-analogy.py deleted file mode 100644 index 803ea4a..0000000 --- a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file5_steepest-ascent-analogy.py +++ /dev/null @@ -1,71 +0,0 @@ -from manimlib.imports import * -import numpy as np - -class Rules(ThreeDScene): - - def setup(self): - ThreeDScene.setup(self) - - def construct(self): - axes = ThreeDAxes()#.scale(0.8)#.shift(2*RIGHT, 2*DOWN) - self.set_camera_orientation(phi=PI/3 + 10*DEGREES,theta=-PI/4 + 25*DEGREES,distance=60) - - plane = Polygon(np.array([4,4,0]), np.array([4, -4, 0]), np.array([-4, -4, 0]), np.array([-4, 4, 0]), color = BLACK, fill_color = YELLOW_E, fill_opacity = 0.3) - - path_one = Line(start = ORIGIN, end = np.array([3, 0, 0])).set_color(BLUE_E) - path_one_text = TexMobject(r"\textrm{3 steps in the x direction}").shift(2*DOWN+3.5*LEFT).scale(0.5).set_color(BLUE_E) - path_two_text = TexMobject(r"\textrm{2 steps in the y direction}").next_to(path_one_text, DOWN, buff = SMALL_BUFF).scale(0.5).set_color(GREEN_C) - path_three_text = TexMobject(r"\textrm{2 steps in the z direction}").next_to(path_two_text, DOWN, buff = SMALL_BUFF).scale(0.5).set_color(PURPLE_E) - obj = TextMobject("Objective: ", "Maximise points for a set number of steps").scale(0.8).to_edge(UP+LEFT) - - steps = TexMobject(r"\textrm{Total steps = 7}").to_edge(RIGHT, buff = LARGE_BUFF).set_color(YELLOW_E).scale(0.7).shift(1*UP) - points_one = TexMobject(r"\textrm{Total points = 13}").next_to(steps, DOWN, buff = SMALL_BUFF).scale(0.7).set_color(YELLOW_E) - question = TexMobject(r"\textrm{Change direction to score more points?}").shift(2*DOWN+2.5*RIGHT).scale(0.9) - - path_two = Line(start = np.array([3, 0, 0]), end = np.array([3, 2, 0])).set_color(GREEN_C) - path_three = Line(start = np.array([3, 2, 0]), end = np.array([3, 2, 2])).set_color(PURPLE_E) - total = Line(start = np.array([0, 0, 0]), end = np.array([3, 2, 2])).set_color(YELLOW_E) - projection_total = Line(start = np.array([0, 0, 0]), end = np.array([3, 2, 0])) - paths = VGroup(path_one, path_two, path_three, path_one_text, path_two_text, path_three_text) - - total_one = VGroup(total, projection_total) - - total_two = Line(start = np.array([0, 0, 0]), end = np.array([4, 1, 2])).set_color(YELLOW_E) - projection_total_two = Line(start = np.array([0, 0, 0]), end = np.array([4, 1, 0])) - points_two = TexMobject(r"\textrm{Total points = 12}").next_to(steps, DOWN, buff = SMALL_BUFF).scale(0.7).set_color(YELLOW_E) - - total_three = Line(start = np.array([0, 0, 0]), end = np.array([1, 4, 2])).set_color(YELLOW_E) - projection_total_three = Line(start = np.array([0, 0, 0]), end = np.array([1, 4, 0])) - points_three = TexMobject(r"\textrm{Total points = 15}").next_to(steps, DOWN, buff = SMALL_BUFF).scale(0.7).set_color(YELLOW_E) - - everything = VGroup(axes, plane, path_one, path_two, path_three, total, projection_total, total_two, projection_total_two, total_three, projection_total_three) - everything.scale(0.7).shift(2*LEFT+1*DOWN) - self.add_fixed_in_frame_mobjects(obj) - self.add(axes, plane) - self.wait() - self.add_fixed_in_frame_mobjects(path_one_text) - self.play(ShowCreation(path_one)) - self.wait() - self.add_fixed_in_frame_mobjects(path_two_text) - self.play(ShowCreation(path_two)) - self.wait() - self.add_fixed_in_frame_mobjects(path_three_text) - self.play(ShowCreation(path_three)) - self.add_fixed_in_frame_mobjects(steps, points_one) - self.wait() - self.play(ShowCreation(total)) - self.play(ReplacementTransform(total.copy(), projection_total)) - self.wait() - self.play(FadeOut(paths)) - self.add_fixed_in_frame_mobjects(question) - self.wait() - self.play(ReplacementTransform(total, total_two), ReplacementTransform(projection_total, projection_total_two)) - self.play(FadeOut(points_one)) - self.add_fixed_in_frame_mobjects(points_two) - self.wait() - self.play(ReplacementTransform(total_two, total_three), ReplacementTransform(projection_total_two, projection_total_three)) - self.play(FadeOut(points_two)) - self.add_fixed_in_frame_mobjects(points_three) - self.wait() - - diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file6-maximum.py b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file6-maximum.py deleted file mode 100644 index 255a0eb..0000000 --- a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file6-maximum.py +++ /dev/null @@ -1,39 +0,0 @@ -from manimlib.imports import * -import numpy as np - - -def function(coordinate): - x,y = coordinate[:2] - return np.array([ - x, - y, - 2 - x**2 - y**2 - ]) - -class ThreeDVector_one(ThreeDScene): - def construct(self): - axes = ThreeDAxes() - self.add(axes) - self.set_camera_orientation(phi=75*DEGREES,theta=45*DEGREES,distance=40) - self.begin_ambient_camera_rotation(rate=0.5) - - surface = ParametricSurface( - lambda x, y: np.array([ - x, - y, - 2 - x**2 - y**2 - ]),u_min=-2,u_max=2, v_min=-2,v_max=2).set_color(RED_E).fade(0.7) - - probe = Sphere(radius = 0.2).set_color(PURPLE_E) - probe_one = Sphere(radius = 0.1).set_color(PURPLE_E).move_to(np.array([0,0,2.1])) - text_one_b = TexMobject(r" \textrm{ reads 0 at local maximum }").next_to(probe, RIGHT, buff = SMALL_BUFF) - name = TextMobject("PROBE2.0 ").next_to(probe, DOWN, buff = SMALL_BUFF).scale(0.5) - text = VGroup(probe, text_one_b, name).to_edge(1.5*UP+0.5*LEFT).scale(0.5) - - - self.play(ShowCreation(surface)) - self.add(probe_one) - field = VectorField(function).scale(0.8) - self.play(FadeIn(field)) - self.add_fixed_in_frame_mobjects(text) - self.wait(3) |