diff options
Diffstat (limited to 'FSF-2020/calculus-of-several-variables')
38 files changed, 788 insertions, 0 deletions
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/README.md b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/README.md index e69de29..b46936b 100644 --- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/README.md +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/README.md @@ -0,0 +1,9 @@ +This repository contains the codes written by [Saarth Deshpande](https://github.com/saarthdeshpande) during the course of FOSSEE Summer Fellowship 2020 under the FLOSS: Mathematics using Python. + +__Sub-topics covered__: +* Equations of Planes and Lines +* General Parametric Curves +* Space Curves (an Intro to Coordinates in 3D) +* Velocity and Differentiability +* Finding Arc Length and Curvature +* TNB Frame and Serret-Frenet Formulae 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 new file mode 100644 index 0000000..7ab8908 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file1_simple_visualization.py @@ -0,0 +1,69 @@ +from manimlib.imports import * + +class randomcurve(GraphScene): + CONFIG = { + "x_min": -4, + "x_max": 6, + "y_min": -6, + "y_max": 10, + "graph_origin": ORIGIN + } + def construct(self): + intro = TextMobject('Consider the following curve.') + mid = TextMobject(r'Notice how the direction of the unit tangent vectors\\changes with respect to the arc length.') + outro = TextMobject(r'The rate of change of unit tangents with \\ respect to the arc length $ds$ is called curvature.\\Mathematically, curvature $ = k = \left|{\frac{dT}{ds}}\right|$') + + XTD = self.x_axis_width/(self.x_max- self.x_min) + YTD = self.y_axis_height/(self.y_max- self.y_min) + + tgt1 = Arrow((-2.2*XTD,-0.5*YTD,0),(-1*XTD,1,0)) + tgt2 = Arrow((-1.2*XTD, 1.93*YTD,0),(0*XTD,1.6,0)).scale(1.2) + tgt3 = Arrow((-0.3*XTD,3*YTD, 0), (1.5*XTD, 3*YTD,0)) + tgt4 = Arrow((1.4*XTD, 2*YTD,0),(2.4*XTD, 1*YTD,0)).scale(2.8) + tgt5 = Arrow((2.4*XTD, 0, 0), (3.8*XTD,-2*YTD, 0)).scale(1.2).shift(0.26*RIGHT) + tgt6 = Arrow((3.8*XTD,-1*YTD, 0), (4.8*XTD, -1*YTD, 0)).scale(2.8).shift(0.26*RIGHT) + tgt7 = Arrow((5.3*XTD, 0, 0),(6.3*XTD,1,0)).shift(0.35*LEFT+0.1*DOWN).scale(1.3) + + dot1 = Dot(tgt1.get_start(), color = RED) + dot2 = Dot(tgt2.get_start(), color = RED) + dot3 = Dot(tgt3.get_start(), color = RED) + dot4 = Dot(tgt4.get_start(), color = RED) + dot5 = Dot(tgt5.get_start(), color = RED) + dot6 = Dot(tgt6.get_start(), color = RED) + dot7 = Dot(tgt7.get_start(), color = RED) + + dots = VGroup(*[dot1, dot2, dot3, dot4, dot5, dot6, dot7]) + + ds = CurvedArrow((-4, 2, 0), (tgt1.get_start() + tgt2.get_start()) / 2, color = YELLOW) + ds_text = TextMobject(r'$ds$').next_to(ds, UP, buff = 0.1).shift(1.3*LEFT) + + self.setup_axes(hideaxes=True) + graphobj = self.get_graph(self.curve) + self.play(FadeIn(intro)) + self.wait(2) + self.play(FadeOut(intro)) + self.setup_axes(hideaxes=False) + self.play(ShowCreation(graphobj), FadeIn(dots), FadeIn(ds), FadeIn(ds_text)) + 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(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) + self.wait(1) + tangents = VGroup(*tangents) + self.play(FadeOut(self.axes), FadeOut(graphobj), FadeOut(tangents), FadeOut(dots)) + self.wait(1) + self.play(FadeIn(outro)) + self.wait(2) + self.play(FadeOut(outro)) + self.wait(1) + + + def curve(self, x): + return 3 - (3653*x**2)/5292 + (2477*x**3)/31752 + (13*x**4)/784 - (17*x**5)/5292 + (17*x**6)/63504 diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file2_circle_curvature.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file2_circle_curvature.py new file mode 100644 index 0000000..232ac41 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file2_circle_curvature.py @@ -0,0 +1,27 @@ +from manimlib.imports import * + +class circleC(GraphScene): + CONFIG = { + "x_min": -6, + "x_max": 6, + "y_min": -6, + "y_max": 6, + "graph_origin": ORIGIN, + "x_axis_width": 12, + "y_axis_height": 12 + } + def construct(self): + epiphany = TextMobject(r'Driving a vehicle on which of \\ the two paths would be easier?').scale(0.6).shift(3.5*LEFT + 3*UP) + outro = TextMobject(r'The larger path, due to its \\ smaller curvature, since $k = \frac{1}{R}$.').scale(0.6).shift(3.7*LEFT + 3*UP) + XTD = self.x_axis_width/(self.x_max- self.x_min) + YTD = self.y_axis_height/(self.y_max- self.y_min) + + circle = Circle(radius = 2, color = BLUE) + circle2 = Circle(radius = 3, color = GREEN_E) + + self.setup_axes(hideaxes=True) + self.play(FadeIn(self.axes), Write(circle, run_time = 2), FadeIn(epiphany)) + self.play(Write(circle2, run_time = 3)) + self.play(ReplacementTransform(epiphany, outro)) + self.wait(2) + self.play(FadeOut(VGroup(*[self.axes, circle, circle2, epiphany, outro]))) 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 differnew file mode 100644 index 0000000..0d6fdcf --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_intuition.gif 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 new file mode 100644 index 0000000..d71adda --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file4_different_curvature_single_curve.py @@ -0,0 +1,56 @@ +from manimlib.imports import * + +class GR(GraphScene): + CONFIG = { + "x_axis_label": "", + "y_axis_label": "", + "x_min": -4, + "x_max": 6, + "y_min": -6, + "y_max": 10, + "graph_origin": ORIGIN + } + + def construct(self): + + self.setup_axes() + def curve(x): + return 3 - (3653*x**2)/5292 + (2477*x**3)/31752 + (13*x**4)/784 - (17*x**5)/5292 + (17*x**6)/63504 + + graph = FunctionGraph(curve, x_min=-3, x_max=6, stroke_width = 2, color = BLUE) + + 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) + + dot1 = Dot((0,3,0), color = YELLOW) + dot1label = TextMobject(r'$P_{1}$').next_to(dot1, UP+RIGHT, buff = 0.1) + dot2 = Dot((4,-1, 0), color = YELLOW) + dot2label = TextMobject(r'$P_{2}$').next_to(dot2, DOWN, buff = 0.1) + dots = VGroup(*[dot1, dot2, dot1label, dot2label]) + + def get_tangent_line(): + line = Line( + ORIGIN, 2 * RIGHT, + color=RED, + stroke_width=4, + ) + dx = 0.0001 + + x = tracker.get_value() + p0 = np.array([x-dx,curve(x-dx),0]) + p1 = np.array([x, curve(x), 0]) + p2 = np.array([x + dx, curve(x + dx), 0]) + + angle = angle_of_vector(p2 - p1) + line.rotate(angle) + line.move_to(p0) + return line + + 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.wait() diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/equations-of-planes-and-lines/__pycache__/file1_line_eqn.cpython-38.pyc b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/equations-of-planes-and-lines/__pycache__/file1_line_eqn.cpython-38.pyc Binary files differnew file mode 100644 index 0000000..e129d1d --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/equations-of-planes-and-lines/__pycache__/file1_line_eqn.cpython-38.pyc diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/equations-of-planes-and-lines/__pycache__/file4_point_normal_form_plane.cpython-38.pyc b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/equations-of-planes-and-lines/__pycache__/file4_point_normal_form_plane.cpython-38.pyc Binary files differnew file mode 100644 index 0000000..88377bb --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/equations-of-planes-and-lines/__pycache__/file4_point_normal_form_plane.cpython-38.pyc diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/equations-of-planes-and-lines/file1_line_eqn.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/equations-of-planes-and-lines/file1_line_eqn.py new file mode 100644 index 0000000..402775b --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/equations-of-planes-and-lines/file1_line_eqn.py @@ -0,0 +1,26 @@ +from manimlib.imports import * + +class three(ThreeDScene): + def construct(self): + axes = ThreeDAxes() + self.set_camera_orientation(phi=14.25* DEGREES,theta=0*DEGREES,distance=8) + self.play(FadeIn(axes)) + + plane = ParametricSurface( + lambda u,v: np.array([ + 6, + 8*v, + 3*u + ]), u_min = -0.8, u_max = 0.8, fill_opacity = 0.4).rotate(45*DEGREES).move_to(ORIGIN).shift(RIGHT+UP) + d2text = TextMobject(r'$\mathbb{R}^{2}: y = mx + c$').shift(3*LEFT + 2*UP).rotate(np.pi/2) + d3text = TextMobject(r'$\mathbb{R}^{3}: y = mx + c$').shift(4*RIGHT+3*UP) + self.play(FadeIn(plane), FadeIn(d2text)) + self.wait(3) + self.play(FadeOut(d2text)) + self.move_camera(phi = 60*DEGREES, theta=45*DEGREES,run_time=3) + self.begin_ambient_camera_rotation(rate=0.02) + self.add_fixed_in_frame_mobjects(d3text) + self.play(FadeIn(d3text)) + self.wait(3) + self.play(FadeOut(d3text), FadeOut(plane), FadeOut(axes)) + self.wait() diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/equations-of-planes-and-lines/file2_point_normal_form_plane.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/equations-of-planes-and-lines/file2_point_normal_form_plane.py new file mode 100644 index 0000000..122a9ff --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/equations-of-planes-and-lines/file2_point_normal_form_plane.py @@ -0,0 +1,39 @@ +from manimlib.imports import * + +class pointnormal(ThreeDScene): + def construct(self): + axes = ThreeDAxes() + + self.set_camera_orientation(phi = 75*DEGREES, theta=45*DEGREES) + normal = Arrow((0,-0.15,-0.25), (-3,0,3), color = YELLOW) + plane1 = Polygon(np.array([1,0,2]),np.array([-1,2.5,1]),np.array([-3,2,1]),np.array([-1,-1,2]), color = GREEN_E, fill_color = WHITE, fill_opacity=0.5) + plane2 = Polygon(np.array([1,0,2]),np.array([-1,2.5,1]),np.array([-3,2,1]),np.array([-1,-1,2]), color = BLUE, fill_color = WHITE, fill_opacity=0.3) + normalLabel = TextMobject(r'$\overrightarrow{n}$').shift((2,2.5,0)) + pointLabel = TextMobject(r'$P$').shift((2,1.2,0)) + xlabel = TextMobject(r'$x$').shift(4.5*LEFT + 1.7*DOWN) + ylabel = TextMobject(r'$y$').shift(4.5*RIGHT + 1.8*DOWN) + zlabel = TextMobject(r'$z$').shift(3.3*UP+0.5*RIGHT) + + normaltext = TextMobject(r'Consider an arbitrary \\ normal vector $\overrightarrow{n}$').scale(0.6).shift(2*UP + 2.5*LEFT) + planetext = TextMobject(r'A single vector is normal \\ to infinitely many planes.').scale(0.6).shift(2*UP + 2.5*LEFT) + pointtext = TextMobject(r'Given a fixed point $P$, \\ a plane is obtained as:').scale(0.6).shift(2*UP + 2.5*LEFT) + + point = Dot(color = RED).shift((1.6,1.3,0)) + self.play(FadeIn(axes)) + self.add_fixed_in_frame_mobjects(xlabel, ylabel, zlabel) + self.wait(1) + self.play(FadeIn(normal)) + self.add_fixed_in_frame_mobjects(normalLabel, normaltext) + self.play(FadeIn(normaltext)) + self.wait(2) + self.add_fixed_in_frame_mobjects(planetext) + self.play(ReplacementTransform(normaltext, planetext), run_time=0.01) + self.play(MoveAlongPath(plane1, normal), run_time = 6) + self.add_fixed_in_frame_mobjects(pointtext) + self.play(ReplacementTransform(planetext, pointtext)) + self.add_fixed_in_frame_mobjects(point, pointLabel) + self.wait(1) + self.play(Transform(plane1, plane2)) + self.wait(2) + self.play(FadeOut(axes), FadeOut(plane2), FadeOut(plane1), FadeOut(point), FadeOut(pointLabel), FadeOut(normal), FadeOut(normalLabel), FadeOut(planetext), FadeOut(pointtext), FadeOut(normaltext), FadeOut(VGroup(*[xlabel, ylabel, zlabel]))) + self.wait(1) diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/equations-of-planes-and-lines/file3_intercept_form_plane.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/equations-of-planes-and-lines/file3_intercept_form_plane.gif Binary files differnew file mode 100644 index 0000000..a8b7d75 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/equations-of-planes-and-lines/file3_intercept_form_plane.gif diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/equations-of-planes-and-lines/file3_intercept_form_plane.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/equations-of-planes-and-lines/file3_intercept_form_plane.py new file mode 100644 index 0000000..258ac3c --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/equations-of-planes-and-lines/file3_intercept_form_plane.py @@ -0,0 +1,29 @@ +from manimlib.imports import * + +class pointnormal(ThreeDScene): + def construct(self): + axes = ThreeDAxes(x_min = 0, y_min = 0, z_min = 0) + self.set_camera_orientation(phi = 75*DEGREES, theta=45*DEGREES) + + plane1 = Polygon(np.array([2,-3,2.5]),np.array([-1.45,2,2.5]),np.array([-0.5,4.5,-0.1]),np.array([3.5,-1,-0.2]), fill_color = WHITE, fill_opacity=0.3) + + xlabel = TextMobject(r'$x$').shift(5*LEFT + 1.5*DOWN) + ylabel = TextMobject(r'$y$').shift(5*RIGHT + 1.5*DOWN) + zlabel = TextMobject(r'$z$').shift(3.3*UP + 0.5*LEFT) + + zintercept = Dot().shift(2.5*UP) + zinterceptlabel = TextMobject(r'$(0,0,c\prime)$').shift(2.8*UP + RIGHT).scale(0.7) + + yintercept = Dot().shift(3.7*RIGHT + 0.925*DOWN) + yinterceptlabel = TextMobject(r'$(0,b\prime ,0)$').shift(3.7*RIGHT+1.5*DOWN).scale(0.7) + + xintercept = Dot().shift(2.9*LEFT + 0.75*DOWN) + xinterceptlabel = TextMobject(r'$(a\prime ,0,0)$').shift(3*LEFT+1.3*DOWN).scale(0.7) + + self.play(FadeIn(axes), FadeIn(plane1)) + self.add_fixed_in_frame_mobjects(xlabel, ylabel, zlabel, zintercept, zinterceptlabel, yintercept, yinterceptlabel, xintercept, xinterceptlabel) + self.wait(2) + self.remove(zintercept, zinterceptlabel, yintercept, yinterceptlabel, xintercept, xinterceptlabel, xlabel, ylabel, zlabel) + self.begin_ambient_camera_rotation(rate=0.5) + self.wait(5) + self.play(FadeOut(axes), FadeOut(plane1)) diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/equations-of-planes-and-lines/file4_3d_plane.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/equations-of-planes-and-lines/file4_3d_plane.gif Binary files differnew file mode 100644 index 0000000..b4c259e --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/equations-of-planes-and-lines/file4_3d_plane.gif diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/equations-of-planes-and-lines/file4_3d_plane.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/equations-of-planes-and-lines/file4_3d_plane.py new file mode 100644 index 0000000..26ad825 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/equations-of-planes-and-lines/file4_3d_plane.py @@ -0,0 +1,49 @@ +from manimlib.imports import * + +class pointnormal(ThreeDScene): + CONFIG = { + 'x_axis_label': '$x$', + 'y_axis_label': '$y$' + } + def construct(self): + axes = ThreeDAxes() + axes.add(axes.get_axis_labels()) + self.set_camera_orientation(phi = 75*DEGREES, theta=45*DEGREES) + + plane = Polygon( + np.array([2,0,2.7]), + np.array([0,0,0.4]), + np.array([-3.2,0,0.55]), + np.array([-3,-2,2.5]), + fill_color = WHITE, fill_opacity = 0.25) + + normal = Arrow((0.25,2,0), (1.5,3.5,0)) + normalLabel = TextMobject(r'$\overrightarrow{n}$').shift((1.5,2.8,0)) + + point = Dot(color = RED).shift((1.6,1.3,0)) + pointLabel = TextMobject(r'$P_{0}$').shift((2,1.2,0)) + + point2 = Dot(color = RED).shift((-0.2,1.8,0)) + point2Label = TextMobject(r'$P$').shift((-0.3,2,0)) + + arrow1 = Arrow((0,-0.25,-0.2), (-2.55,0,1), color = YELLOW).set_stroke(width=3) + arrow2 = Arrow((0,0,-0.25), (0.3,0,2), color = YELLOW).set_stroke(width=3) + res = Arrow((1.8,1.23,0),(-0.35,1.85,0), color = BLUE).set_stroke(width=3) + + arrow1label = TextMobject(r'$\overrightarrow{r_{0}}$').next_to(arrow2, UP).shift(RIGHT + 0.16*DOWN).scale(0.7) + arrow2label = TextMobject(r'$\overrightarrow{r}$').next_to(arrow2, UP).shift(0.7*LEFT).scale(0.7) + reslabel = TextMobject(r'$\overrightarrow{r} - \overrightarrow{r_{0}}$').next_to(arrow2, UP).shift(0.7*RIGHT + 1.2*UP).scale(0.7) + + self.play(FadeIn(axes), FadeIn(plane)) + self.wait(1) + self.add_fixed_in_frame_mobjects(normal, normalLabel) + self.wait(1) + self.add_fixed_in_frame_mobjects(point, pointLabel) + self.add_fixed_in_frame_mobjects(point2, point2Label) + self.play(Write(arrow1), Write(arrow2)) + self.add_fixed_in_frame_mobjects(arrow2label, arrow1label) + self.wait(1) + self.add_fixed_in_frame_mobjects(res, reslabel) + self.play(Write(res), FadeIn(reslabel)) + self.wait(1) + self.play(FadeOut(axes), FadeOut(plane), FadeOut(point), FadeOut(pointLabel), FadeOut(normal), FadeOut(normalLabel), FadeOut(point2), FadeOut(point2Label), FadeOut(arrow1label), FadeOut(arrow2label), FadeOut(reslabel), FadeOut(arrow1), FadeOut(arrow2), FadeOut(res))
\ No newline at end of file diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/equations-of-planes-and-lines/file5_vector_form_line.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/equations-of-planes-and-lines/file5_vector_form_line.py new file mode 100644 index 0000000..e25c4eb --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/equations-of-planes-and-lines/file5_vector_form_line.py @@ -0,0 +1,47 @@ +from manimlib.imports import * + +class line_(ThreeDScene): + def construct(self): + axes = ThreeDAxes() + xlabel = TextMobject(r'$x$').shift(4.5*LEFT + 1.7*DOWN) + ylabel = TextMobject(r'$y$').shift(4.5*RIGHT + 1.8*DOWN) + zlabel = TextMobject(r'$z$').shift(3.3*UP+0.5*RIGHT) + + self.set_camera_orientation(phi = 75*DEGREES, theta=45*DEGREES) + pointLabel = TextMobject(r'$P$').shift((2.28,2.12,0)).scale(0.7) + point = Dot(color = RED).shift((1.95,1.9,0)) + + vlabel = TextMobject(r'$\overrightarrow{v}$').shift((0.5,1.3,0)).scale(0.7) + + inf_text = TextMobject(r'Infinitely many lines pass \\ through a single point.').scale(0.6).shift(2*UP + 2.5*LEFT) + pointtext = TextMobject(r'Given a direction vector $\overrightarrow{v}$, \\ a line is obtained as:').scale(0.6).shift(2*UP + 2.5*LEFT) + + + line = Line((0.7,0.7,0), (2,3,0)).shift(0.06*UP+0.6*RIGHT) + v = Vector((0.8,1,0), color = GREEN_E) + #finalLine = Line((-1.56,0,0.5),(-4,0,2.42), color = YELLOW) + finalLine = Line((1,0.8,0),(3,3,0), color = YELLOW).shift(0.05*LEFT) + self.play(FadeIn(axes)) + self.add_fixed_in_frame_mobjects(zlabel, ylabel, xlabel) + self.wait(1) + self.add_fixed_in_frame_mobjects(point, pointLabel) + self.wait(1) + self.add_fixed_in_frame_mobjects(inf_text) + self.wait(1) + self.add_fixed_in_frame_mobjects(line) + + for i in range(9): + self.play(ApplyMethod(line.rotate, -np.pi/12), run_time = 0.7) + if i == 8: + self.add_fixed_in_frame_mobjects(pointtext) + self.play(ReplacementTransform(inf_text, pointtext)) + self.add_fixed_in_frame_mobjects(v, vlabel) + # if i == 13: + # self.add_fixed_in_frame_mobjects(pointtext) + + self.add_fixed_in_frame_mobjects(finalLine) + self.play(FadeIn(finalLine)) + self.play(Transform(line, finalLine), run_time = 4) + #self.play(FadeOut(line), FadeIn(finalLine)) + self.wait(1.5) + self.play(FadeOut(VGroup(*[axes, xlabel, ylabel, zlabel, finalLine, v, vlabel, point, pointLabel, pointtext, line]))) diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/__pycache__/file1_parametric_circle.cpython-38.pyc b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/__pycache__/file1_parametric_circle.cpython-38.pyc Binary files differnew file mode 100644 index 0000000..ad30b2a --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/__pycache__/file1_parametric_circle.cpython-38.pyc diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/__pycache__/file4_helix_visualization.cpython-38.pyc b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/__pycache__/file4_helix_visualization.cpython-38.pyc Binary files differnew file mode 100644 index 0000000..144d78d --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/__pycache__/file4_helix_visualization.cpython-38.pyc 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 new file mode 100644 index 0000000..40b5150 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file1_parametric_circle.py @@ -0,0 +1,78 @@ +from manimlib.imports import * + +class parametricCircle(ThreeDScene, GraphScene): + def construct(self): + self.x_min = -5 + self.y_min = -5 + self.graph_origin = ORIGIN + self.x_max = 5 + self.y_max = 5 + self.x_axis_label = "" + self.y_axis_label = "" + self.x_axis_width = 10 + self.y_axis_height = 10 + + axes = [] + + self.setup_axes() + self.axes.scale(0.5).shift(3*LEFT) + axes.append(self.axes) + self.setup_axes() + self.axes.scale(0.3).shift(3*RIGHT + 2*UP) + axes.append(self.axes) + self.setup_axes() + self.axes.scale(0.3).shift(3*RIGHT + 2*DOWN) + axes.append(self.axes) + + axes = VGroup(*axes) + t_value = ValueTracker(-3.14) + t_tex = DecimalNumber(t_value.get_value()).add_updater(lambda v: v.set_value(t_value.get_value())) + t_label = TexMobject("t = ") + group = VGroup(t_tex,t_label).shift(3*DOWN) + t_label.next_to(t_tex,LEFT, buff=0.2,aligned_edge=t_label.get_bottom()) + + asint_text = TextMobject(r'$x = a\sin{t}$').scale(0.7).shift(4*RIGHT + 3*UP) + xlabel1 = TextMobject(r'$x$').shift(3.3*RIGHT + 3.7*UP).scale(0.7) + tlabel1 = TextMobject(r'$t$').shift(4.8*RIGHT + 2*UP).scale(0.7) + up_text = VGroup(*[asint_text, xlabel1, tlabel1]) + asint = ParametricFunction( + lambda t: np.array([ + t, + np.sin(t), + 0 + ]), t_min = -np.pi, t_max = np.pi, color = GREEN_E + ).shift(3*RIGHT + 2*UP).scale(0.4) + + acost_text = TextMobject(r'$y = a\cos{t}$').scale(0.7).shift(4*RIGHT + DOWN) + ylabel1 = TextMobject(r'$y$').shift(3.3*RIGHT+0.3*DOWN).scale(0.7) + tlabel2 = TextMobject(r'$t$').shift(4.8*RIGHT + 2*DOWN).scale(0.7) + down_text = VGroup(*[acost_text, ylabel1, tlabel2]) + acost = ParametricFunction( + lambda t: np.array([ + t, + np.cos(t), + 0 + ]), t_min = -np.pi, t_max = np.pi, color = BLUE + ).shift(3*RIGHT + 2*DOWN).scale(0.4) + + up_dot = Dot(color = RED) + down_dot = Dot(color = RED) + circle_dot = Dot(color = RED) + + ylabel2 = TextMobject(r'$y$').scale(0.7).shift(3*UP + 3*LEFT) + xlabel2 = TextMobject(r'$x$').scale(0.7) + ellipse_text = TextMobject(r'$x = a\sin{t}$ \\ $y = a\cos{t}$').scale(0.7).shift(2*UP + 1.3*LEFT) + main_text = VGroup(*[xlabel2, ylabel2, ellipse_text]) + circle = ParametricFunction( + lambda t: np.array([ + np.cos(t), + np.sin(t), + 0 + ]), t_min = -np.pi, t_max = np.pi, color = WHITE + ).shift(3*LEFT) + self.play(FadeIn(axes), FadeIn(asint), FadeIn(acost), FadeIn(circle), FadeIn(up_text), FadeIn(down_text), FadeIn(main_text), FadeIn(group)) + self.wait(1) + self.play(MoveAlongPath(up_dot, asint, run_time = 7), MoveAlongPath(down_dot, acost, run_time = 7), MoveAlongPath(circle_dot, circle, run_time = 7), t_value.set_value,3.14, rate_func=linear, run_time=7) + self.wait(1) + self.play(FadeOut(VGroup(*[axes, asint, acost, circle, up_text, down_text, main_text, up_dot, down_dot, circle_dot, group]))) + self.wait(1) 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 differnew file mode 100644 index 0000000..39656de --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file2_cycloid.gif diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file2_cycloid_manim.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file2_cycloid_manim.gif Binary files differnew file mode 100644 index 0000000..e68b841 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file2_cycloid_manim.gif diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file2_cycloid_manim.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file2_cycloid_manim.py new file mode 100644 index 0000000..7b6c0d1 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file2_cycloid_manim.py @@ -0,0 +1,46 @@ +from manimlib.imports import * + +t_offset = 0 +c_t = 0 + +class cycloid(Scene): + def construct(self): + + cycl = ParametricFunction( + lambda t: np.array([ + t - np.sin(t), + 1 - np.cos(t), + 0 + ]), t_min = -2.75*np.pi, t_max = 3*np.pi, color = BLUE + ).shift(0.73*RIGHT) + wheel_radius = 1 + wheel_function_path = lambda x : 0 + wheel_radius + + line = FunctionGraph(lambda x : 0, color = BLACK) + wheel_path = FunctionGraph(wheel_function_path) + + velocity_factor = 0.25 + frame_rate = self.camera.frame_rate + self.dt = 1 / frame_rate + + wheel = Circle(color = BLACK, radius = 1) + dot = Dot(radius = 0.16, color = RED) + #dot.move_to(wheel.get_arc_center() + np.array([0,2,0])) + + def update_dot(mob,dt): + global t_offset,c_t + if dt == 0 and c_t == 0: + rate= - velocity_factor * self.dt + c_t += 1 + else: + rate = - dt*velocity_factor + if dt > 0: + c_t = 0 + mob.move_to(wheel.point_from_proportion(((t_offset + rate))%1)) + t_offset += rate + #self.add(mob.copy()) + + #dot.move_to(wheel.get_arc_center() + np.array([0,2,0])) + dot.add_updater(update_dot) + self.add(wheel,dot, line, cycl) + self.play(MoveAlongPath(wheel, wheel_path, run_time = 9, rate_func = linear)) diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file3_brachistochrone.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file3_brachistochrone.gif Binary files differnew file mode 100644 index 0000000..8daf4c0 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file3_brachistochrone.gif diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file3_brachistochrone.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file3_brachistochrone.py new file mode 100644 index 0000000..633e500 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file3_brachistochrone.py @@ -0,0 +1,13 @@ +from manimlib.imports import * + +class brachistochrone(Scene): + def construct(self): + curve = ParametricFunction( + lambda t: np.array([ + 0.5*(t - np.sin(t)), + 0.5*(1 - np.cos(t)), + 0 + ]), t_max = np.pi + ).scale(5).rotate(540*DEGREES) + dot = Dot(color = RED, radius = 0.2) + self.play(FadeIn(curve), MoveAlongPath(dot, curve, run_time = 2)) diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file4_helix_visualization.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file4_helix_visualization.py new file mode 100644 index 0000000..eddd3fe --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file4_helix_visualization.py @@ -0,0 +1,31 @@ +from manimlib.imports import * + +class helix_(ThreeDScene): + CONFIG = { + "x_min": -6, + "x_max": 6, + "y_min": -6, + "y_max": 6, + "graph_origin": ORIGIN + } + def construct(self): + axes = ThreeDAxes() + helix = ParametricFunction( + lambda t: np.array([ + 1.5*np.cos(TAU*t), + 1.5*np.sin(TAU*t), + 2*t + ]), t_min = -1, t_max = 2, color = RED + ) + cylinder = ParametricSurface( + lambda u, v: np.array([ + 1.5*np.cos(TAU*v), + 1.5*np.sin(TAU*v), + 2*u + ]), u_min = -1, u_max = 2, fill_opacity = -.4, fill_color = WHITE, color = WHITE + ) + self.set_camera_orientation(phi=60* DEGREES,theta=45*DEGREES) + self.play(FadeIn(axes), FadeIn(cylinder), ShowCreation(helix, run_time = 4)) + self.begin_ambient_camera_rotation(rate=0.5) + self.wait(5) + self.play(FadeOut(axes),FadeOut(helix), FadeOut(cylinder)) diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/__pycache__/file1_parametric_ellipse.cpython-38.pyc b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/__pycache__/file1_parametric_ellipse.cpython-38.pyc Binary files differnew file mode 100644 index 0000000..a732643 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/__pycache__/file1_parametric_ellipse.cpython-38.pyc diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/__pycache__/file2_parametric_helix.cpython-38.pyc b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/__pycache__/file2_parametric_helix.cpython-38.pyc Binary files differnew file mode 100644 index 0000000..c8e3e2a --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/__pycache__/file2_parametric_helix.cpython-38.pyc diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/__pycache__/file3_circletosphere.cpython-38.pyc b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/__pycache__/file3_circletosphere.cpython-38.pyc Binary files differnew file mode 100644 index 0000000..bca0d91 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/__pycache__/file3_circletosphere.cpython-38.pyc diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/__pycache__/file3_cone.cpython-38.pyc b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/__pycache__/file3_cone.cpython-38.pyc Binary files differnew file mode 100644 index 0000000..ae954c3 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/__pycache__/file3_cone.cpython-38.pyc diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file1_parametric_ellipse.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file1_parametric_ellipse.py new file mode 100644 index 0000000..1ce29d7 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file1_parametric_ellipse.py @@ -0,0 +1,78 @@ +from manimlib.imports import * + +class parametricEllipse(ThreeDScene, GraphScene): + def construct(self): + self.x_min = -5 + self.y_min = -5 + self.graph_origin = ORIGIN + self.x_max = 5 + self.y_max = 5 + self.x_axis_label = "" + self.y_axis_label = "" + self.x_axis_width = 10 + self.y_axis_height = 10 + + axes = [] + + self.setup_axes() + self.axes.scale(0.5).shift(3*LEFT) + axes.append(self.axes) + self.setup_axes() + self.axes.scale(0.3).shift(3*RIGHT + 2*UP) + axes.append(self.axes) + self.setup_axes() + self.axes.scale(0.3).shift(3*RIGHT + 2*DOWN) + axes.append(self.axes) + + axes = VGroup(*axes) + t_value = ValueTracker(-3.14) + t_tex = DecimalNumber(t_value.get_value()).add_updater(lambda v: v.set_value(t_value.get_value())) + t_label = TexMobject("t = ") + group = VGroup(t_tex,t_label).shift(3*DOWN) + t_label.next_to(t_tex,LEFT, buff=0.2,aligned_edge=t_label.get_bottom()) + + asint_text = TextMobject(r'$x = a\sin{t}$').scale(0.7).shift(4*RIGHT + 3*UP) + xlabel1 = TextMobject(r'$x$').shift(3.3*RIGHT + 3.7*UP).scale(0.7) + tlabel1 = TextMobject(r'$t$').shift(4.8*RIGHT + 2*UP).scale(0.7) + up_text = VGroup(*[asint_text, xlabel1, tlabel1]) + asint = ParametricFunction( + lambda t: np.array([ + t, + np.sin(t), + 0 + ]), t_min = -np.pi, t_max = np.pi, color = GREEN_E + ).shift(3*RIGHT + 2*UP).scale(0.4) + + bcost_text = TextMobject(r'$y = b\cos{t}$').scale(0.7).shift(4*RIGHT + DOWN) + ylabel1 = TextMobject(r'$y$').shift(3.3*RIGHT+0.3*DOWN).scale(0.7) + tlabel2 = TextMobject(r'$t$').shift(4.8*RIGHT + 2*DOWN).scale(0.7) + down_text = VGroup(*[bcost_text, ylabel1, tlabel2]) + bcost = ParametricFunction( + lambda t: np.array([ + t, + 1.5*np.cos(t), + 0 + ]), t_min = -np.pi, t_max = np.pi, color = BLUE + ).shift(3*RIGHT + 2*DOWN).scale(0.4) + + up_dot = Dot(color = RED) + down_dot = Dot(color = RED) + ellipse_dot = Dot(color = RED) + + ylabel2 = TextMobject(r'$y$').scale(0.7).shift(3*UP + 3*LEFT) + xlabel2 = TextMobject(r'$x$').scale(0.7) + ellipse_text = TextMobject(r'$x = a\sin{t}$ \\ $y = b\cos{t}$').scale(0.7).shift(2*UP + 1.3*LEFT) + main_text = VGroup(*[xlabel2, ylabel2, ellipse_text]) + ellipse = ParametricFunction( + lambda t: np.array([ + 1.5*np.cos(t), + np.sin(t), + 0 + ]), t_min = -np.pi, t_max = np.pi, color = WHITE + ).shift(3*LEFT) + self.play(FadeIn(axes), FadeIn(asint), FadeIn(bcost), FadeIn(ellipse), FadeIn(up_text), FadeIn(down_text), FadeIn(main_text), FadeIn(group)) + self.wait(1) + self.play(MoveAlongPath(up_dot, asint, run_time = 7), MoveAlongPath(down_dot, bcost, run_time = 7), MoveAlongPath(ellipse_dot, ellipse, run_time = 7), t_value.set_value,3.14, rate_func=linear, run_time=7) + self.wait(1) + self.play(FadeOut(VGroup(*[axes, asint, bcost, ellipse, up_text, down_text, main_text, up_dot, down_dot, ellipse_dot, group]))) + self.wait(1) diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file2_parametric_helix.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file2_parametric_helix.py new file mode 100644 index 0000000..3791752 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file2_parametric_helix.py @@ -0,0 +1,91 @@ +from manimlib.imports import * + +class parametricHelix(ThreeDScene, GraphScene): + def construct(self): + self.x_min = -5 + self.y_min = -4 + self.graph_origin = ORIGIN + self.x_max = 5 + self.y_max = 4 + self.x_axis_label = "" + self.y_axis_label = "" + self.x_axis_width = 10 + self.y_axis_height = 7.5 + ax1 = ThreeDAxes().scale(0.65).shift(2.6*RIGHT+DOWN+np.array([0,0,0.5])) + axes_group = [] + + self.setup_axes() + self.axes.shift(3*RIGHT + 2*UP).scale(0.3) + axes_group.append(self.axes) + + self.setup_axes() + self.axes.shift(3*RIGHT + 2*DOWN).scale(0.3) + axes_group.append(self.axes) + + axes_group = VGroup(*axes_group) + + asint_text = TextMobject(r'$x = a\sin{t}$').scale(0.7).shift(4*RIGHT + 3*UP) + xlabel1 = TextMobject(r'$x$').shift(3.3*RIGHT + 3.7*UP).scale(0.7) + tlabel1 = TextMobject(r'$t$').shift(5*RIGHT + 2*UP).scale(0.7) + up_text = VGroup(*[asint_text, xlabel1, tlabel1]) + asint = ParametricFunction( + lambda t: np.array([ + t, + np.sin(t), + 0 + ]), t_min = -4*np.pi, t_max = 4*np.pi, color = GREEN_E + ).shift(3*RIGHT + 2*UP).scale(0.12) + + acost_text = TextMobject(r'$y = a\cos{t}$').scale(0.7).shift(4*RIGHT + DOWN) + ylabel1 = TextMobject(r'$y$').shift(3.3*RIGHT+0.3*DOWN).scale(0.7) + tlabel2 = TextMobject(r'$t$').shift(5*RIGHT + 2*DOWN).scale(0.7) + down_text = VGroup(*[acost_text, ylabel1, tlabel2]) + acost = ParametricFunction( + lambda t: np.array([ + t, + np.cos(t), + 0 + ]), t_min = -4*np.pi, t_max = 4*np.pi, color = BLUE + ).shift(3*RIGHT + 2*DOWN).scale(0.12) + + up_dot = Dot(color = RED).scale(0.6) + down_dot = Dot(color = RED).scale(0.6) + helix_dot = Dot(radius = 0.16, color = RED) + + zlabel = TextMobject(r'$z$').scale(0.7).shift(3*UP + 2.8*LEFT) + ylabel2 = TextMobject(r'$y$').scale(0.7).shift(0.3*DOWN+0.15*RIGHT) + xlabel2 = TextMobject(r'$x$').scale(0.7).shift(0.5*DOWN + 6.4*LEFT) + helix_text = TextMobject(r'$x = a\sin{t}$ \\ $y = a\cos{t}$ \\ $z = ct$').scale(0.7).shift(2.3*UP + 1.3*LEFT) + main_text = VGroup(*[xlabel2, ylabel2, zlabel, helix_text]) + helix = ParametricFunction( + lambda t: np.array([ + np.cos(TAU*t), + np.sin(TAU*t), + 0.4*t + ]), t_min = -2*np.pi/3, t_max = 1.8*np.pi/3, color = WHITE + ).shift(ax1.get_center()) + + self.set_camera_orientation(phi = 75*DEGREES, theta=45*DEGREES) + + t_tracker = ValueTracker(-12.56) + t=t_tracker.get_value + + t_label = TexMobject( + "t = ",color=WHITE + ).next_to(helix_text,DOWN, buff=0.2).scale(0.6) + + t_text = always_redraw( + lambda: DecimalNumber( + t(), + color=WHITE, + ).next_to(t_label, RIGHT, buff=0.2) + ).scale(0.6) + + group = VGroup(t_text,t_label).scale(1.5).move_to(ORIGIN).shift(2*DOWN) + self.add_fixed_in_frame_mobjects(axes_group, main_text, up_text, down_text, acost, asint) + self.play(FadeIn(ax1), FadeIn(axes_group), FadeIn(asint), FadeIn(acost), FadeIn(helix), FadeIn(up_text), FadeIn(down_text), FadeIn(main_text)) + #self.begin_ambient_camera_rotation(rate = 0.06) + self.add_fixed_in_frame_mobjects(up_dot, down_dot, group) + self.play(MoveAlongPath(up_dot, asint, run_time = 8), MoveAlongPath(down_dot, acost, run_time = 8), MoveAlongPath(helix_dot, helix, run_time = 8), t_tracker.set_value,12.56, rate_func=linear, run_time=8) + self.play(FadeOut(VGroup(*[ax1, axes_group, asint, acost, helix, up_text, down_text, main_text, up_dot, down_dot, helix_dot, group]))) + self.wait(1) diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file3_circletosphere.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file3_circletosphere.py new file mode 100644 index 0000000..6c0e810 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file3_circletosphere.py @@ -0,0 +1,45 @@ +from manimlib.imports import * + +class sphere(GraphScene, ThreeDScene): + CONFIG = { + 'x_min': -10, + 'x_max': 10, + 'y_min': -10, + 'y_max': 10, + 'graph_origin': ORIGIN, + "x_axis_width": 10, + "y_axis_height": 10, + } + 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) + circleeqn = TextMobject(r'Hence, $x^{2} + y^{2} = 2(r^{2} - u^{2})$') + plottext = TextMobject(r'$x = \sqrt{r^{2} - u^{2}}cos\theta$ \\ $y = \sqrt{r^{2} - u^{2}}sin\theta$').shift(2*UP + 3*RIGHT) + + + self.setup_axes() + self.play(FadeIn(self.axes), FadeIn(plottext)) + + dots = [] + for t in range(19): + dot = Dot().shift((3*XTD*np.cos(t), 3*YTD*np.sin(t),0)) + dots.append(dot) + self.play(FadeIn(dot), run_time = 0.2) + dots = VGroup(*dots) + circle = Circle(radius = 3*XTD).set_color(WHITE).set_stroke(width = 10) + self.play(FadeIn(circle), FadeOut(dots), FadeOut(plottext)) + self.wait(2) + + + axes = ThreeDAxes(**self.CONFIG) + sph = Sphere(radius = 3).scale(0.5) + text2 = TextMobject(r'Setting $u = 3$,\\$z = u$').shift(4*YTD*UP + 5*XTD*RIGHT) + + self.play(Transform(self.axes,axes), ReplacementTransform(circle, sph)) + self.add(text2) + self.wait(2) + self.remove(text2) + self.move_camera(phi = 60*DEGREES, theta=45*DEGREES,run_time=5) + self.begin_ambient_camera_rotation(rate=0.03) + self.play(FadeOut(axes), FadeOut(sph), FadeOut(self.axes)) + self.wait(1) diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file4_cone.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file4_cone.py new file mode 100644 index 0000000..e6ae1c6 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/file4_cone.py @@ -0,0 +1,33 @@ +from manimlib.imports import * + +class cone(ThreeDScene): + def construct(self): + axes = ThreeDAxes() + eqn = TextMobject(r'$z^{2} = x^{2} + y^{2}$') + + conecurve = ParametricFunction( + lambda t: np.array([ + t*np.cos(TAU*t), + t*np.sin(TAU*t), + t + ]), t_min = -2.6, t_max = 2.6 + ).scale(0.85) + + conesurface = ParametricSurface( + lambda u,v: np.array([ + 3*np.sin(u)*np.cos(TAU*v), + 3*np.sin(u)*np.sin(TAU*v), + 2.7*u + ]), u_min = -1 + ).scale(0.85) + + self.play(FadeIn(eqn)) + self.wait(2) + self.play(FadeOut(eqn)) + self.set_camera_orientation(phi = 75*DEGREES, theta=50*DEGREES) + self.play(FadeIn(axes), ShowCreation(conecurve, run_time = 3)) + self.play(FadeOut(conecurve), FadeIn(conesurface)) + self.begin_ambient_camera_rotation(rate=0.03) + self.wait(2) + self.play(FadeOut(axes), FadeOut(conesurface)) + self.wait(2) 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 differnew file mode 100644 index 0000000..c8668e3 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_prescribed_plane.gif 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 differnew file mode 100644 index 0000000..097652f --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_TNB_frame.gif diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/velocity-and-differentiability/__pycache__/file2_tangent_spaceCurve.cpython-38.pyc b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/velocity-and-differentiability/__pycache__/file2_tangent_spaceCurve.cpython-38.pyc Binary files differnew file mode 100644 index 0000000..8967b87 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/velocity-and-differentiability/__pycache__/file2_tangent_spaceCurve.cpython-38.pyc diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/velocity-and-differentiability/file1_smooth_curves.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/velocity-and-differentiability/file1_smooth_curves.gif Binary files differnew file mode 100644 index 0000000..5801796 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/velocity-and-differentiability/file1_smooth_curves.gif diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/velocity-and-differentiability/file2_tangent_space_curve.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/velocity-and-differentiability/file2_tangent_space_curve.py new file mode 100644 index 0000000..67c675e --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/velocity-and-differentiability/file2_tangent_space_curve.py @@ -0,0 +1,22 @@ +from manimlib.imports import * + +class tangent(ThreeDScene): + def construct(self): + axes = ThreeDAxes() + self.set_camera_orientation(phi = 125*DEGREES, theta = 135*DEGREES) + h = ParametricFunction( + lambda t: np.array([ + 4*(t**3) + 5, + t**2 + 2*(t**4), + -2*np.log(2*t) + ]), t_min = -3, t_max = 1.18 + ).shift(5*LEFT) + tgtR = Line((4,3,-2*np.log(2)), (19.5, 16, -4.772588), color=YELLOW) + tgtL =Line((4,3,-2*np.log(2)), (-11.5, -10, 2), color=YELLOW) + dot = Dot((4,3,-2*np.log(2)), color=RED, radius=0.08) + self.play(FadeIn(axes),FadeIn(h), FadeIn(dot)) + self.begin_ambient_camera_rotation(rate=0.4) + self.wait(2) + self.play(FadeIn(tgtL), FadeIn(tgtR)) + self.wait(5) + self.play(FadeOut(axes), FadeOut(h), FadeOut(dot), FadeOut(tgtL), FadeOut(tgtR)) diff --git a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/divergence-gauss-theorem/README.md b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/divergence-gauss-theorem/README.md new file mode 100644 index 0000000..e69de29 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/divergence-gauss-theorem/README.md diff --git a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/strokes-theorem/README.md b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/strokes-theorem/README.md new file mode 100644 index 0000000..e69de29 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/strokes-theorem/README.md |
