diff options
Diffstat (limited to 'FSF-2020')
20 files changed, 1087 insertions, 0 deletions
diff --git a/FSF-2020/approximations-and-optimizations/Critical Points/example.py b/FSF-2020/approximations-and-optimizations/Critical Points/example.py new file mode 100644 index 0000000..3a41be7 --- /dev/null +++ b/FSF-2020/approximations-and-optimizations/Critical Points/example.py @@ -0,0 +1,32 @@ +from manimlib.imports import* + +class ExampleAnimation(ThreeDScene): + def construct(self): + axes = ThreeDAxes() + + f_text = TextMobject("$f(x,y) = (y-x)(1-2x-3y)$").to_corner(UL) + d = Dot(np.array([0,0,0]), color = '#800000') #---- Critical Point + d_text = TextMobject("$(0.2,0.2)$",color = '#DC143C').scale(0.5).shift(0.2*UP) #----x = 0.2, y = 0.2 + r_text=TextMobject("Critical Point",color = '#00FFFF').shift(0.3*DOWN).scale(0.6) + + #----f(x,y) = (y-x)(1-2x-3y) + f = ParametricSurface( + lambda u, v: np.array([ + u, + v, + (v-u)*(1-2*u-3*v) + ]),v_min = -1, v_max = 1, u_min = -1, u_max = 1, checkerboard_colors = [PURPLE_D, PURPLE_E], + resolution=(20, 20)).scale(1) + + self.set_camera_orientation(phi = 75 * DEGREES) + self.begin_ambient_camera_rotation(rate=0.5) + + self.add_fixed_in_frame_mobjects(f_text) + self.wait(1) + self.add(axes) + self.play(Write(f),Write(d)) + self.wait(1) + self.add_fixed_in_frame_mobjects(d_text) + self.wait(1) + self.add_fixed_in_frame_mobjects(r_text) + self.wait(3) diff --git a/FSF-2020/approximations-and-optimizations/Critical Points/motivation.py b/FSF-2020/approximations-and-optimizations/Critical Points/motivation.py new file mode 100644 index 0000000..27354ef --- /dev/null +++ b/FSF-2020/approximations-and-optimizations/Critical Points/motivation.py @@ -0,0 +1,30 @@ +from manimlib.imports import* + +class MotivationAnimation(Scene): + def construct(self): + + r = Rectangle(height = 7,breadth = 2,color = BLUE, fill_opacity = 0.3).scale(0.6) #----metal strip + b = Brace(r,UP) + r_text = TextMobject("$x$ metres",color = YELLOW).shift(3*UP) + m_text = TextMobject("Metal Strip").shift(3*DOWN) + a = Arc(radius=2).rotate(1).shift(LEFT+0.5*UP) + a2 = Arc(radius=2).rotate(5).shift(0.7*LEFT+0.9*UP).scale(0.2) + START = [1,0,0] + END = [0,3,0] + l = Line(START,END,color = RED).shift(0.9*DOWN) + a2_text = TextMobject("$\\theta$",color = PINK).shift(1.6*UP+0.4*RIGHT) + + group1 = VGroup(r_text,b,a,l,a2,a2_text) + f_text = TextMobject("$A = f(x,\\theta)$").shift(2*DOWN) + + ring = Annulus(inner_radius = 0.7, outer_radius = 1, color = BLUE) #--bent metal strip + + self.play(Write(r)) + self.wait(1) + self.play(ShowCreation(m_text)) + self.wait(1) + self.play(Write(group1)) + self.wait(2) + self.play(FadeOut(group1)) + self.wait(1) + self.play(ReplacementTransform(r,ring),ShowCreation(f_text)) diff --git a/FSF-2020/approximations-and-optimizations/Critical Points/theorem.py b/FSF-2020/approximations-and-optimizations/Critical Points/theorem.py new file mode 100644 index 0000000..7c82aa9 --- /dev/null +++ b/FSF-2020/approximations-and-optimizations/Critical Points/theorem.py @@ -0,0 +1,55 @@ +from manimlib.imports import* + +class TheoremAnimation(ThreeDScene): + def construct(self): + + axes = ThreeDAxes() + + #----parabola: x**2+y**2 + parabola1 = ParametricSurface( + lambda u, v: np.array([ + u, + v, + u**2+v**2 + ]),v_min = -1, v_max = 1, u_min = -1, u_max = 1, checkerboard_colors = [TEAL_E], + resolution = (20, 20)).scale(1) + + #----parabola: -x**2-y**2 + parabola2 = ParametricSurface( + lambda u, v: np.array([ + u, + v, + -u**2-v**2 + ]),v_min = -1, v_max = 1, u_min = -1, u_max = 1, checkerboard_colors = [PURPLE_E,PURPLE_E], + resolution = (20, 20)).scale(1) + + self.set_camera_orientation(phi = 75 * DEGREES) + self.begin_ambient_camera_rotation(rate = 0.4) + + d = Dot(np.array([0,0,0]), color = '#800000') #---- critical point + r = Rectangle(fill_color = '#C0C0C0',fill_opacity = 0.3).move_to(ORIGIN) #----tangent plane + + parabola1_text = TextMobject("Maximum with horizontal tangent plane").scale(0.7).to_corner(UL) + + parabola2_text = TextMobject("Minimum with horizontal tangent plane").scale(0.7).to_corner(UL) + + self.add(axes) + self.add_fixed_in_frame_mobjects(parabola2_text) + self.wait(1) + self.play(Write(parabola1)) + self.wait(1) + self.play(ShowCreation(d)) + self.wait(1) + self.play(ShowCreation(r)) + self.wait(2) + self.play(FadeOut(parabola2_text),FadeOut(parabola1),FadeOut(r),FadeOut(d)) + + self.wait(1) + self.add_fixed_in_frame_mobjects(parabola1_text) + self.wait(1) + self.play(Write(parabola2)) + self.wait(1) + self.play(ShowCreation(d)) + self.wait(1) + self.play(ShowCreation(r)) + self.wait(2) diff --git a/FSF-2020/approximations-and-optimizations/Critical Points/types_of_cp.py b/FSF-2020/approximations-and-optimizations/Critical Points/types_of_cp.py new file mode 100644 index 0000000..f9055e6 --- /dev/null +++ b/FSF-2020/approximations-and-optimizations/Critical Points/types_of_cp.py @@ -0,0 +1,70 @@ +from manimlib.imports import * + +class TypescpAnimation(ThreeDScene): + def construct(self): + axes = ThreeDAxes() + + r_text = TextMobject("Relative Maximum at ORIGIN",color ='#87CEFA') + f_text = TextMobject("$f(x,y) = -x^2-y^2$").to_corner(UL) + + #----graph of first function f(x,y) = -x**2-y**2 + f = ParametricSurface( + lambda u, v: np.array([ + u, + v, + -u**2-v**2 + ]),v_min = -1, v_max = 1, u_min = -1, u_max = 1, checkerboard_colors = [YELLOW_D, YELLOW_E], + resolution = (20, 20)).scale(1) + + r2_text = TextMobject("Saddle Point at ORIGIN",color ='#87CEFA') + f2_text = TextMobject("$f(x,y) = -x^2+y^2$").to_corner(UL) + + #----graph of second function f(x,y) = -x**2+y**2 + f2 = ParametricSurface( + lambda u, v: np.array([ + u, + v, + -u**2+v**2 + ]),v_min = -1, v_max = 1, u_min = -1, u_max = 1, checkerboard_colors = [RED_D, RED_E], + resolution = (20, 20)).scale(1) + + r3_text = TextMobject("Relative Minimum at ORIGIN",color ='#87CEFA') + f3_text = TextMobject("$f(x,y) = x^2+y^2$").to_corner(UL) + + #----graph of third function f(x,y) = x**2+y**2 + f3 = ParametricSurface( + lambda u, v: np.array([ + u, + v, + u**2+v**2 + ]),v_min = -1, v_max = 1, u_min = -1, u_max = 1, checkerboard_colors = [GREEN_D, GREEN_E], + resolution = (20, 20)).scale(1) + + self.set_camera_orientation(phi = 75 * DEGREES, theta = -45 * DEGREES ) + d = Dot(np.array([0,0,0]), color = '#800000') #---- critical point + + self.add_fixed_in_frame_mobjects(r_text) + self.wait(1) + self.play(FadeOut(r_text)) + self.add(axes) + self.play(Write(f),Write(d)) + self.add_fixed_in_frame_mobjects(f_text) + self.wait(2) + self.play(FadeOut(axes),FadeOut(f),FadeOut(f_text),FadeOut(d)) + + self.add_fixed_in_frame_mobjects(r2_text) + self.wait(1) + self.play(FadeOut(r2_text)) + self.add(axes) + self.play(Write(f2),Write(d)) + self.add_fixed_in_frame_mobjects(f2_text) + self.wait(2) + self.play(FadeOut(axes),FadeOut(f2),FadeOut(f2_text),FadeOut(d)) + + self.add_fixed_in_frame_mobjects(r3_text) + self.wait(1) + self.play(FadeOut(r3_text)) + self.add(axes) + self.play(Write(f3),Write(d)) + self.add_fixed_in_frame_mobjects(f3_text) + self.wait(2) 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 new file mode 100644 index 0000000..cd754cd --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file1_missile-example.py @@ -0,0 +1,37 @@ +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 new file mode 100644 index 0000000..7a95867 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file2_gradient-example-1.py @@ -0,0 +1,43 @@ +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 new file mode 100644 index 0000000..e37581d --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file3_gradient-example-2.py @@ -0,0 +1,39 @@ +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 new file mode 100644 index 0000000..e9c8fd0 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file4-multidimensional-gradient.py @@ -0,0 +1,113 @@ +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 new file mode 100644 index 0000000..7c0ef54 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file4_gradient-example-3.py @@ -0,0 +1,40 @@ +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 new file mode 100644 index 0000000..803ea4a --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file5_steepest-ascent-analogy.py @@ -0,0 +1,71 @@ +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 new file mode 100644 index 0000000..255a0eb --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file6-maximum.py @@ -0,0 +1,39 @@ +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) diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/area_Under_func.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/area_Under_func.gif Binary files differnew file mode 100644 index 0000000..223218b --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/area_Under_func.gif diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/elementary_area.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/elementary_area.gif Binary files differnew file mode 100644 index 0000000..5c9ac03 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/elementary_area.gif diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/non_rect_region.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/non_rect_region.gif Binary files differnew file mode 100644 index 0000000..c8e7c8c --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/non_rect_region.gif diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/surface.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/surface.gif Binary files differnew file mode 100644 index 0000000..ae23a7b --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/surface.gif diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/YlimitXdependent.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/y_limit_dependent_on_x.gif Binary files differindex a2bfd9d..a2bfd9d 100644 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/YlimitXdependent.gif +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/y_limit_dependent_on_x.gif diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's_theorem/surface1.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's_theorem/surface1.gif Binary files differnew file mode 100644 index 0000000..8c9fa0a --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's_theorem/surface1.gif diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's_theorem/surface1.py b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's_theorem/surface1.py new file mode 100644 index 0000000..a590a53 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's_theorem/surface1.py @@ -0,0 +1,232 @@ +from manimlib.imports import * + +class SurfacesAnimation(ThreeDScene): + + CONFIG = { + "axes_config": { + "x_min": 0, + "x_max": 4, + "y_min": 0, + "y_max": 4, + "z_min": -4, + "z_max": 4, + "a":0 ,"b": 4, "c":0 , "d":4, + "axes_shift":IN+LEFT, + "x_axis_config": { + "tick_frequency": 1, + "include_tip": False, + }, + "y_axis_config": { + "tick_frequency": 1, + "include_tip": False, + }, + "z_axis_config": { + "tick_frequency": 1, + # "include_tip": False, + }, + "num_axis_pieces": 1, + }, + "default_graph_style": { + "stroke_width": 2, + "stroke_color": WHITE, + }, + "default_surface_config": { + "fill_opacity": 0.5, + "checkerboard_colors": [LIGHT_GREY], + "stroke_width": 0.5, + "stroke_color": WHITE, + "stroke_opacity": 0.5, + }, + "Func": lambda x,y: 5*(x**2-y**2)/((1e-4+x**2+y**2)**2) + } + + + def construct(self): + + self.setup_axes() + self.set_camera_orientation(#distance=10, + phi=80 * DEGREES, + theta=35 * DEGREES, + ) + + fn_text=TextMobject("$z=\dfrac{x^2-y^2}{(x^2+y^2)^2}$").set_color(BLUE) + fn_text.to_corner(UR,buff=1) + self.add_fixed_in_frame_mobjects(fn_text) + + R=TextMobject("R").set_color(BLACK).scale(2).rotate(180*DEGREES , OUT) + R.move_to(self.axes.input_plane,IN) + self.add(R) + + #get the surface + surface= self.get_surface( + self.axes, lambda x , y: + self.Func(x,y) + ) + surface.set_style( + fill_opacity=0.6, + fill_color=BLUE_E, + stroke_width=0.8, + stroke_color=WHITE, + ) + + + self.begin_ambient_camera_rotation(rate=0.2) + self.play(Write(surface)) + + self.get_lines() + self.wait(4) + + def get_surface(self,axes, func, **kwargs): + config = { + "u_min": axes.x_max, + "u_max": axes.x_min, + "v_min": axes.y_max, + "v_max": axes.y_min, + "resolution": (10,10), + } + + config.update(self.default_surface_config) + config.update(kwargs) + return ParametricSurface( + lambda x,y : axes.c2p( + x, y, func(x, y) + ), + **config + ) + + def get_lines(self): + axes = self.axes + labels=[axes.x_axis.n2p(axes.a), axes.x_axis.n2p(axes.b), axes.y_axis.n2p(axes.c), + axes.y_axis.n2p(axes.d)] + + + surface_corners=[] + for x,y,z in self.region_corners: + surface_corners.append([x,y,self.Func(x,y)]) + + lines=VGroup() + for start , end in zip(surface_corners, + self.region_corners): + lines.add(self.draw_lines(start,end,"YELLOW")) + + for start , end in zip(labels, + self.region_corners): + # lines.add(self.draw_lines(start,end,"BLUE")) + # print (start,end) + pass + self.play(ShowCreation(lines)) + + + def draw_lines(self,start,end,color): + start=self.axes.c2p(*start) + end=self.axes.c2p(*end) + line=DashedLine(start,end,color=color) + + return line + + def get_three_d_axes(self, include_labels=True, include_numbers=True, **kwargs): + config = dict(self.axes_config) + config.update(kwargs) + axes = ThreeDAxes(**config) + axes.set_stroke(width=2) + + if include_numbers: + self.add_axes_numbers(axes) + + if include_labels: + self.add_axes_labels(axes) + + # Adjust axis orientation + axes.x_axis.rotate( + 90 * DEGREES, LEFT, + about_point=axes.c2p(0, 0, 0), + ) + axes.y_axis.rotate( + 90 * DEGREES, UP, + about_point=axes.c2p(0, 0, 0), + ) + + # Add xy-plane + input_plane = self.get_surface( + axes, lambda x, t: 0 + ) + input_plane.set_style( + fill_opacity=0.3, + fill_color=PINK, + stroke_width=.2, + stroke_color=WHITE, + ) + + axes.input_plane = input_plane + + self.region_corners=[ + input_plane.get_corner(pos) for pos in (DL,DR,UR,UL)] + + return axes + + + def setup_axes(self): + axes = self.get_three_d_axes(include_labels=True) + axes.add(axes.input_plane) + axes.scale(1) + # axes.center() + axes.shift(axes.axes_shift) + + self.add(axes) + self.axes = axes + + def add_axes_numbers(self, axes): + x_axis = axes.x_axis + y_axis = axes.y_axis + tex_vals_x = [ + ("a", axes.a+.4), + ("b", axes.b), + ] + tex_vals_y=[ + ("c", axes.c+.4), + ("d", axes.d) + ] + x_labels = VGroup() + y_labels = VGroup() + for tex, val in tex_vals_x: + label = TexMobject(tex) + label.scale(1) + label.next_to(x_axis.n2p(val), DOWN) + label.rotate(180 * DEGREES) + x_labels.add(label) + x_axis.add(x_labels) + x_axis.numbers = x_labels + + for tex, val in tex_vals_y: + label = TexMobject(tex) + label.scale(1) + label.next_to(y_axis.n2p(val), LEFT) + label.rotate(90 * DEGREES) + y_labels.add(label) + + y_axis.add(y_labels) + y_axis.numbers = y_labels + + return axes + + def add_axes_labels(self, axes): + x_label = TexMobject("x") + x_label.next_to(axes.x_axis.get_end(), RIGHT) + axes.x_axis.label = x_label + + y_label = TextMobject("y") + y_label.rotate(90 * DEGREES, OUT) + y_label.next_to(axes.y_axis.get_end(), UP) + axes.y_axis.label = y_label + + z_label = TextMobject("z") + z_label.rotate(90 * DEGREES, LEFT) + z_label.next_to(axes.z_axis.get_zenith(), LEFT) + axes.z_axis.label = z_label + for axis in axes: + axis.add(axis.label) + return axes + +#uploaded by Somnath Pandit.FSF2020_Fubini's_Theorem + + diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's_theorem/surface2.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's_theorem/surface2.gif Binary files differnew file mode 100644 index 0000000..ac13f21 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's_theorem/surface2.gif diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's_theorem/surface2.py b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's_theorem/surface2.py new file mode 100644 index 0000000..c998f3b --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's_theorem/surface2.py @@ -0,0 +1,286 @@ +from manimlib.imports import * + +class SurfacesAnimation(ThreeDScene): + + CONFIG = { + "axes_config": { + "x_min": 0, + "x_max": 4, + "y_min": 0, + "y_max": 4, + "z_min": -2, + "z_max": 4, + "a":0 ,"b": 4, "c":0 , "d":4, + "axes_shift":IN+2*LEFT+2*DOWN, + "x_axis_config": { + "tick_frequency": 1, + "include_tip": False, + }, + "y_axis_config": { + "tick_frequency": 1, + "include_tip": False, + }, + "z_axis_config": { + "tick_frequency": 1, + # "include_tip": False, + }, + "num_axis_pieces": 1, + }, + "default_graph_style": { + "stroke_width": 2, + "stroke_color": WHITE, + }, + "default_surface_config": { + "fill_opacity": 0.5, + "checkerboard_colors": [LIGHT_GREY], + "stroke_width": 0.5, + "stroke_color": WHITE, + "stroke_opacity": 0.5, + }, + "Func": lambda x,y: x*y/4 + } + + + def construct(self): + + self.setup_axes() + self.set_camera_orientation( + distance=30, + phi=75 * DEGREES, + theta=20 * DEGREES, + ) + + fn_text=TextMobject("$z=xy$").set_color(BLUE).scale(1.5) + fn_text.to_corner(UR,buff=2) + self.add_fixed_in_frame_mobjects(fn_text) + + + #get the surface + surface= self.get_surface( + self.axes, lambda x , y: + self.Func(x,y) + ) + surface.set_style( + fill_opacity=.5, + fill_color=BLUE_E, + stroke_width=0.2, + stroke_color=WHITE, + ) + #get boundary curves + c1=self.get_curve( + self.axes, lambda x: x**2/4 + ) + c1_label=TextMobject("$y=x^2$").next_to(c1,IN+OUT).shift(DOWN+RIGHT) + c1_label.rotate(PI) + c1_group=VGroup(c1,c1_label).set_color(ORANGE) + + c2=self.get_curve( + self.axes, lambda x: x + ).set_color(PINK) + c2_label=TextMobject("$y=x$").next_to(c2,IN+OUT) + c2_label.rotate(PI/2,about_point=(c2_label.get_corner(UL))) + c2_group=VGroup(c2,c2_label).set_color(YELLOW_E) + + + + self.add(c1,c2,c1_label,c2_label) + + self.begin_ambient_camera_rotation(rate=0.4) + self.get_region(self.axes,c1,c2) + self.play(Write(surface)) + self.get_lines() + self.wait(1) + self.stop_ambient_camera_rotation() + self.move_camera( + distance=20, + phi=10 * DEGREES, + theta=80 * DEGREES, + run_time=2.5 + ) + self.wait(2) + + + + def get_curve(self,axes, func, **kwargs): + config = { + "t_min": axes.x_min, + "t_max": axes.x_max, + } + config.update(kwargs) + return ParametricFunction( + lambda x : axes.c2p( + x, func(x),0 + ), + **config + ) + + def get_region(self,axes,curve1,curve2,**kwargs): + x_vals=np.arange(axes.x_min,axes.x_max,.1) + c1_points=[curve1.get_point_from_function(x) for x in x_vals] + c2_points=[curve2.get_point_from_function(x) for x in x_vals] + c2_points.reverse() + points=c1_points+c2_points + region=Polygon(*points, + stroke_width=0, + fill_color=PINK, + fill_opacity=.5 + ) + R=TextMobject("R").set_color(PINK).scale(2).rotate(180*DEGREES , OUT) + R.move_to(region,IN+RIGHT) + + self.play(Write(region)) + self.add(R) + + def get_surface(self,axes, func, **kwargs): + config = { + "u_min": axes.x_max, + "u_max": axes.x_min, + "v_min": axes.y_max, + "v_max": axes.y_min, + "resolution": (10,10), + } + + config.update(self.default_surface_config) + config.update(kwargs) + return ParametricSurface( + lambda x,y : axes.c2p( + x, y, func(x, y) + ), + **config + ) + + def get_lines(self): + axes = self.axes + labels=[axes.x_axis.n2p(axes.a), axes.x_axis.n2p(axes.b), axes.y_axis.n2p(axes.c), + axes.y_axis.n2p(axes.d)] + + + surface_corners=[] + for x,y,z in self.region_corners: + surface_corners.append([x,y,self.Func(x,y)]) + + lines=VGroup() + for start , end in zip(surface_corners, + self.region_corners): + lines.add(self.draw_lines(start,end,"YELLOW")) + + for start , end in zip(labels, + self.region_corners): + # lines.add(self.draw_lines(start,end,"BLUE")) + # print (start,end) + pass + self.play(ShowCreation(lines)) + + + def draw_lines(self,start,end,color): + start=self.axes.c2p(*start) + end=self.axes.c2p(*end) + line=DashedLine(start,end,color=color) + + return line + + #customize 3D axes + def get_three_d_axes(self, include_labels=True, include_numbers=True, **kwargs): + config = dict(self.axes_config) + config.update(kwargs) + axes = ThreeDAxes(**config) + axes.set_stroke(width=2) + + if include_numbers: + self.add_axes_numbers(axes) + + if include_labels: + self.add_axes_labels(axes) + + # Adjust axis orientation + axes.x_axis.rotate( + 90 * DEGREES, LEFT, + about_point=axes.c2p(0, 0, 0), + ) + axes.y_axis.rotate( + 90 * DEGREES, UP, + about_point=axes.c2p(0, 0, 0), + ) + + # Add xy-plane + input_plane = self.get_surface( + axes, lambda x, t: 0 + ) + input_plane.set_style( + fill_opacity=0.3, + fill_color=PINK, + stroke_width=.2, + stroke_color=WHITE, + ) + + axes.input_plane = input_plane + + self.region_corners=[ + input_plane.get_corner(pos) for pos in (DL,DR,UR,UL)] + + return axes + + + def setup_axes(self): + axes = self.get_three_d_axes(include_labels=True) + # axes.add(axes.input_plane) + axes.scale(1) + # axes.center() + axes.shift(axes.axes_shift) + + self.add(axes) + self.axes = axes + + def add_axes_numbers(self, axes): + x_axis = axes.x_axis + y_axis = axes.y_axis + tex_vals_x = [ + ("1", axes.b), + ] + tex_vals_y=[ + ("1", axes.d) + ] + x_labels = VGroup() + y_labels = VGroup() + for tex, val in tex_vals_x: + label = TexMobject(tex) + label.scale(1) + label.next_to(x_axis.n2p(val), DOWN) + label.rotate(180 * DEGREES) + x_labels.add(label) + x_axis.add(x_labels) + x_axis.numbers = x_labels + + for tex, val in tex_vals_y: + label = TexMobject(tex) + label.scale(1) + label.next_to(y_axis.n2p(val), LEFT) + label.rotate(90 * DEGREES) + y_labels.add(label) + + y_axis.add(y_labels) + y_axis.numbers = y_labels + + return axes + + def add_axes_labels(self, axes): + x_label = TexMobject("x") + x_label.next_to(axes.x_axis.get_end(), RIGHT) + axes.x_axis.label = x_label + + y_label = TextMobject("y") + y_label.rotate(90 * DEGREES, OUT) + y_label.next_to(axes.y_axis.get_end(), UP) + axes.y_axis.label = y_label + + z_label = TextMobject("z") + z_label.rotate(90 * DEGREES, LEFT) + z_label.next_to(axes.z_axis.get_zenith(), LEFT) + axes.z_axis.label = z_label + for axis in axes: + axis.add(axis.label) + return axes + + #uploaded by Somnath Pandit.FSF2020_Fubini's_Theorem + + |
