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| author | Purusharth Saxena | 2020-06-23 18:06:56 +0530 |
|---|---|---|
| committer | GitHub | 2020-06-23 18:06:56 +0530 |
| commit | d0c1b826b41a0a0f93079b6ca755f2cef132ce6e (patch) | |
| tree | 6c851e4ea4e369c536bb183aa9378926b78dcee6 /FSF-2020 | |
| parent | a896e8b74b1b4864f24d860ea82e4de46d2ff2c7 (diff) | |
| parent | 959329ed76fb5350f5f68aeb8937a37b62138890 (diff) | |
| download | FSF-mathematics-python-code-archive-d0c1b826b41a0a0f93079b6ca755f2cef132ce6e.tar.gz FSF-mathematics-python-code-archive-d0c1b826b41a0a0f93079b6ca755f2cef132ce6e.tar.bz2 FSF-mathematics-python-code-archive-d0c1b826b41a0a0f93079b6ca755f2cef132ce6e.zip | |
Merge branch 'master' into master
Diffstat (limited to 'FSF-2020')
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/file5_Vertical_Shear_gif.gif?id=d0c1b826b41a0a0f93079b6ca755f2cef132ce6e){kind=link}
90 files changed, 1819 insertions, 3 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 diff --git a/FSF-2020/calculus/series-and-transformations/Laplace Transformations/README.md b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/README.md new file mode 100644 index 0000000..d4cd8bc --- /dev/null +++ b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/README.md @@ -0,0 +1,21 @@ +### Basic Intuition + + +### Solving D.E.intuition + + +### Unit Step Function +#### Part1 + +#### Part2 + +#### Part3 + + +### Dirac Delta Function +#### Part1 + +#### Part2 + +#### Part3 + diff --git a/FSF-2020/calculus/series-and-transformations/Laplace Transformations/file1_laplaceTransformBasic.py b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/file1_laplaceTransformBasic.py new file mode 100644 index 0000000..7a37ae8 --- /dev/null +++ b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/file1_laplaceTransformBasic.py @@ -0,0 +1,67 @@ +from manimlib.imports import * +import pylatex + +class depict(Scene): + def construct(self): + square=Square(side_length=2,fill_color=GREEN,fill_opacity=0.7) + inputText=TextMobject("$t$") + squareText=TextMobject("$f$") + outputText=TextMobject("$f($","$t$","$)$") + + inputText.scale(0.8) + outputText.scale(0.8) + inputText.shift(2.1*LEFT) + outputText.shift(1.5*RIGHT) + squareText.scale(1.2) + + outputText.set_color_by_tex_to_color_map({"$t$":RED}) + + self.play(ShowCreation(square)) + self.play(FadeIn(squareText)) + self.add(inputText) + self.wait(0.5) + self.play(ApplyMethod(inputText.shift,0.9*RIGHT)) + self.play(FadeOut(inputText),FadeIn(outputText)) + self.play(ApplyMethod(outputText.shift,1.5*RIGHT)) + self.wait(1) + + fOutGroup=VGroup(outputText,square,squareText) + self.play(ApplyMethod(fOutGroup.scale,0.6)) + self.play(ApplyMethod(fOutGroup.shift,5*LEFT)) + self.wait(0.8) + laplaceSquare=Square(side_length=3,fill_color=BLUE,fill_opacity=0.6) + laplaceText=TextMobject("$\mathscr{L}$") + outText=TextMobject("$F($","$s$","$)$") + outText.scale(0.8) + outText.set_color_by_tex_to_color_map({"$s$":RED}) + laplaceText.scale(1.5) + outText.shift(2*RIGHT) + self.play(ShowCreation(laplaceSquare)) + self.play(FadeIn(laplaceText)) + self.wait(0.5) + self.play(ApplyMethod(outputText.shift,RIGHT)) + self.play(FadeOut(outputText),FadeIn(outText)) + self.play(ApplyMethod(outText.shift,2*RIGHT)) + self.wait(1) + + updatedOutputText=TextMobject("$f($","$t$","$)$") + updatedOutputText.shift(2.5*LEFT) + updatedOutputText.set_color_by_tex_to_color_map({"$t$":RED}) + updatedInputText=TextMobject("$t$") + updatedInputText.shift(6*LEFT) + updatedInputText.scale(0.7) + updatedOutputText.scale(0.7) + + self.play(FadeIn(updatedInputText),FadeIn(updatedOutputText)) + self.wait(0.5) + + timeText=TextMobject("Time Domain") + frequencyText=TextMobject("Frequency Domain") + timeText.set_color(RED) + frequencyText.set_color(RED) + timeText.scale(0.35) + frequencyText.scale(0.35) + timeText.shift(2.5*LEFT+0.5*DOWN) + frequencyText.shift(4*RIGHT+0.5*DOWN) + self.play(Write(frequencyText),Write(timeText)) + self.wait(2)
\ No newline at end of file diff --git a/FSF-2020/calculus/series-and-transformations/Laplace Transformations/file2_differentialEqSimplification.py b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/file2_differentialEqSimplification.py new file mode 100644 index 0000000..33e9173 --- /dev/null +++ b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/file2_differentialEqSimplification.py @@ -0,0 +1,78 @@ +from manimlib.imports import * +import pylatex + +class scene(Scene): + def construct(self): + normalSq=Square(side_length=2,fill_color=BLUE,fill_opacity=0.6) + normalSqText=TextMobject("$\mathscr{L}$") + inputText=TextMobject("$f($","$y'(t)$","$)$") + outputText=TextMobject("$F($","$s$","$)$") + + inputText.scale(0.7) + outputText.scale(0.7) + inputText.shift(2.5*LEFT) + outputText.shift(1.7*RIGHT) + normalSq.scale(1.2) + + inputText.set_color_by_tex_to_color_map({"$y'(t)$":RED}) + outputText.set_color_by_tex_to_color_map({"$s$":RED}) + + self.play(ShowCreation(normalSq)) + self.play(FadeIn(normalSqText)) + self.add(inputText) + self.wait(0.5) + self.play(ApplyMethod(inputText.shift,0.7*RIGHT)) + self.play(FadeOut(inputText),FadeIn(outputText)) + self.play(ApplyMethod(outputText.shift,RIGHT)) + self.wait(1) + + group1=VGroup(outputText,normalSq,normalSqText) + self.play(ApplyMethod(group1.scale,0.6)) + self.play(ApplyMethod(group1.shift,4.7*LEFT)) + self.wait(0.6) + + inverseSq=Square(side_length=3,fill_color=GREEN,fill_opacity=0.6) + inverseSqText=TextMobject("$\mathscr{L}^{ -1 }$") + outText=TextMobject("$f($","$y(t)$","$)$") + inverseSqText.scale(0.7) + outText.scale(0.7) + outText.set_color_by_tex_to_color_map({"$y(t)$":RED}) + self.play(ShowCreation(inverseSq)) + self.play(FadeIn(inverseSqText)) + self.wait(0.5) + outText.shift(2*RIGHT) + self.play(ApplyMethod(outputText.shift,RIGHT)) + self.play(FadeOut(outputText),FadeIn(outText)) + self.play(ApplyMethod(outText.shift,2*RIGHT)) + self.wait(1) + + updatedOutputText=TextMobject("$F($","$s$","$)$") + updatedOutputText.shift(2.5*LEFT) + updatedInputText=TextMobject("$f($","$y'(t)$","$)$") + updatedInputText.shift(6*LEFT) + updatedInputText.scale(0.7) + updatedOutputText.scale(0.7) + updatedOutputText.set_color_by_tex_to_color_map({"$s$":RED}) + updatedInputText.set_color_by_tex_to_color_map({"$y'(t)$":RED}) + + self.play(FadeIn(updatedInputText),FadeIn(updatedOutputText)) + self.wait(0.5) + + deText=TextMobject("Differential Equation") + deinterTexta=TextMobject("Transformed D.E") + deinterTextb=TextMobject("(Easy to simplify)!") + deOutText=TextMobject("Solution of D.E") + deText.set_color(RED) + deinterTexta.set_color(RED) + deOutText.set_color(RED) + deinterTextb.set_color(PURPLE_C) + deText.scale(0.35) + deinterTexta.scale(0.35) + deinterTextb.scale(0.35) + deOutText.scale(0.35) + deText.shift(6*LEFT+0.5*DOWN) + deinterTexta.shift(2.6*LEFT+0.5*DOWN) + deinterTextb.shift(2.6*LEFT+0.8*DOWN) + deOutText.shift(4*RIGHT+0.5*DOWN) + self.play(Write(deText),Write(deinterTexta),Write(deinterTextb),Write(deOutText)) + self.wait(2) diff --git a/FSF-2020/calculus/series-and-transformations/Laplace Transformations/file3_unitStepFunction.py b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/file3_unitStepFunction.py new file mode 100644 index 0000000..53c5f14 --- /dev/null +++ b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/file3_unitStepFunction.py @@ -0,0 +1,168 @@ +from manimlib.imports import * +import math +import pylatex + +class intro(GraphScene,Scene): + CONFIG = { + "x_min": -8, + "x_max": 8, + "y_min": -5, + "y_max": 5, + "graph_origin": ORIGIN+DOWN, + "function_color": RED, + "axes_color": GREEN, + "x_axis_label": "$t$", + "y_axis_label": "$\mu_{c}(t)$", + "exclude_zero_label": True, + "y_axis_height":4, + "x_axis_width":7 + } + def setup(self): + GraphScene.setup(self) + Scene.setup(self) + def construct(self): + introText=TextMobject("Unit","Step","Function") + introText.set_color_by_tex_to_color_map({"Unit":BLUE,"Step":YELLOW}) + introText.scale(0.8) + self.play(Write(introText)) + self.wait(0.5) + self.play(ApplyMethod(introText.shift,3*UP)) + formulaa=TextMobject("$\mu _{ c }(t)=0\quad$","$t<c$") + formulab=TextMobject("$\mu _{ c }(t)=1\quad$","$t\ge c$") + formulaa.set_color_by_tex_to_color_map({"$t<c$":RED}) + formulab.set_color_by_tex_to_color_map({"$t\ge c$":RED}) + formulaa.scale(0.8) + formulab.scale(0.8) + formulab.shift(0.5*DOWN) + self.play(FadeIn(formulaa),FadeIn(formulab)) + self.wait(1) + + self.play(FadeOut(formulaa),FadeOut(formulab)) + + x_each_unit = self.x_axis_width / (self.x_max - self.x_min) + y_each_unit = self.y_axis_height / (self.y_max - self.y_min) + + self.setup_axes(animate=True) + self.wait(0.8) + + c=TextMobject("c") + c.scale(0.5) + c.set_color(RED) + c.shift(self.graph_origin+3*x_each_unit*RIGHT+y_each_unit*0.4*DOWN) + self.play(Write(c)) + smallCircle=Circle(radius=0.03,fill_color=WHITE,color=WHITE) + smallCircle.shift(self.graph_origin+3*x_each_unit*RIGHT) + downLine=Line(start=self.graph_origin,end=self.graph_origin+RIGHT*3*x_each_unit,color=BLUE) + upLine=Line(start=self.graph_origin+3*x_each_unit*RIGHT+y_each_unit*UP,end=self.graph_origin+8*x_each_unit*RIGHT+y_each_unit*UP,color=BLUE) + + self.play(Write(downLine)) + self.play(Write(smallCircle)) + self.play(Write(upLine)) + self.wait(1.5) + self.play(FadeOut(self.axes),FadeOut(smallCircle),FadeOut(c),FadeOut(upLine),FadeOut(downLine),FadeOut(introText)) + self.wait(0.5) + + +class example(GraphScene): + CONFIG = { + "x_min": -3, + "x_max": 8, + "y_min": -4, + "y_max": 5, + "graph_origin": ORIGIN+LEFT+DOWN, + "function_color": RED, + "axes_color": GREEN, + "x_axis_label": "$t$", + "y_axis_label": "$y$", + "exclude_zero_label": True, + "y_axis_height":4, + "x_axis_width":6 + } + def construct(self): + x_each_unit = self.x_axis_width / (self.x_max - self.x_min) + y_each_unit = self.y_axis_height / (self.y_max - self.y_min) + + text1=TextMobject("Consider the","formation","of","following graph!"," (a part of $f(t))$") + text1.set_color_by_tex_to_color_map({"following graph!":BLUE,"formation":YELLOW}) + text1.scale(0.6) + ft=TextMobject("$f(t)$") + ftminusc=TextMobject("$f(t-c)$") + final=TextMobject("$\mu_{c}(t)f(t-c)$") + ft.set_color(PURPLE_C) + ftminusc.set_color(PURPLE_C) + final.set_color(PURPLE_C) + c=TextMobject("c") + c.scale(0.5) + c.set_color(RED) + c.shift(self.graph_origin+RIGHT*x_each_unit*3+DOWN*y_each_unit*0.5) + ft.scale(0.5) + ftminusc.scale(0.5) + final.scale(0.5) + + self.play(Write(text1)) + self.play(ApplyMethod(text1.shift,3*UP)) + + self.setup_axes(animate=True) + y=self.get_graph(lambda x:(math.pow((x-3),3)/3)-math.pow((x-3),2)-(x-3)+3,x_min=3,x_max=7,color=RED) + f=self.get_graph(lambda x:(math.pow(x,3)/3)-math.pow(x,2)-x+3,x_min=-2,x_max=4,color=RED) + yFull=self.get_graph(lambda x:(math.pow((x-3),3)/3)-math.pow((x-3),2)-(x-3)+3,x_min=1,x_max=7,color=RED) + + self.play(Write(c)) + self.play(ShowCreation(y)) + self.wait(1) + self.play(FadeOut(self.axes),FadeOut(y),FadeOut(c)) + + belowText1=TextMobject("Consider its","normal form",", $f(t)$") + belowText1.set_color_by_tex_to_color_map({"normal form":BLUE}) + belowText2=TextMobject("Shift it to","x=c") + belowText2.set_color_by_tex_to_color_map({"x=c":RED}) + belowText3a=TextMobject("Now to remove the","left part","of","$c$,") + belowText3a.set_color_by_tex_to_color_map({"left part":YELLOW,"$c$,":YELLOW}) + belowText3b=TextMobject("multiply it with the","unit step function",", $\mu_{c}(t)$") + belowText3b.set_color_by_tex_to_color_map({"unit step function":BLUE}) + belowText1.scale(0.4) + belowText2.scale(0.4) + belowText3a.scale(0.4) + belowText3b.scale(0.4) + belowText1.shift(2.7*DOWN+4*RIGHT) + belowText2.shift(2.7*DOWN+4*RIGHT) + belowText3a.shift(2.7*DOWN+4*RIGHT) + belowText3b.shift(3.1*DOWN+4*RIGHT) + self.setup_axes(animate=True) + self.play(Write(belowText1)) + self.play(ShowCreation(f)) + ft.shift(1.5*RIGHT+UP*0.8) + self.play(FadeIn(ft)) + self.play(ReplacementTransform(belowText1,belowText2)) + ftminusc.shift(3.5*RIGHT+UP*0.8) + self.play(ReplacementTransform(f,yFull),ReplacementTransform(ft,ftminusc),Write(c)) + self.wait(1) + + self.play(ReplacementTransform(belowText2,belowText3a)) + self.play(Write(belowText3b)) + final.shift(3.7*RIGHT+UP*0.8) + self.play(ReplacementTransform(ftminusc,final),ReplacementTransform(yFull,y)) + + finalText=TextMobject("We got our required Graph!") + finalText.scale(0.55) + finalText.shift(2.7*DOWN+4*RIGHT) + self.play(FadeOut(belowText3b),ReplacementTransform(belowText3a,finalText)) + self.wait(1.5) + + self.play(FadeOut(finalText),FadeOut(text1)) + + graphGrup=VGroup(self.axes,c,final,y) + self.play(ApplyMethod(graphGrup.scale,0.45)) + box=Square(side_length=2,fill_color=BLUE,fill_opacity=0.7) + boxtext=TextMobject("$\mathscr{L}$") + boxtext.scale(0.8) + self.play(ApplyMethod(graphGrup.shift,5.5*LEFT+UP)) + self.play(ShowCreation(box),Write(boxtext)) + outText=TextMobject("${ e }^{ -cs }F(s)$") + outText.set_color(GREEN) + outText.scale(0.65) + outText.shift(2*RIGHT) + self.play(ApplyMethod(graphGrup.shift,2*RIGHT)) + self.play(FadeOut(graphGrup),FadeIn(outText)) + self.play(ApplyMethod(outText.shift,RIGHT)) + self.wait(2) diff --git a/FSF-2020/calculus/series-and-transformations/Laplace Transformations/file4_diracBasic.py b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/file4_diracBasic.py new file mode 100644 index 0000000..0c7f8e4 --- /dev/null +++ b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/file4_diracBasic.py @@ -0,0 +1,61 @@ +from manimlib.imports import * +import math +import pylatex + +class intro(GraphScene,Scene): + CONFIG = { + "x_min": -9, + "x_max": 9, + "y_min": -5, + "y_max": 5, + "graph_origin": ORIGIN+DOWN, + "function_color": RED, + "axes_color": GREEN, + "x_axis_label": "$x$", + "y_axis_label": "$\delta (x)$", + "y_axis_height":4, + "x_axis_width":7 + } + def setup(self): + GraphScene.setup(self) + Scene.setup(self) + def construct(self): + introText=TextMobject("Dirac","Delta","Function") + introText.set_color_by_tex_to_color_map({"Dirac":BLUE,"Delta":YELLOW}) + introText.scale(0.8) + self.play(Write(introText)) + self.wait(0.5) + self.play(ApplyMethod(introText.shift,3*UP)) + formulaa=TextMobject("$\delta (x)=\infty$","$x=0$") + formulab=TextMobject("$\delta (x)=0$","$x\\neq 0$") + formulaa.set_color_by_tex_to_color_map({"$x=0$":RED}) + formulab.set_color_by_tex_to_color_map({"$x\\neq 0$":RED}) + formulaa.scale(0.8) + formulab.scale(0.8) + formulab.shift(0.5*DOWN) + self.play(FadeIn(formulaa),FadeIn(formulab)) + self.wait(1) + + self.play(FadeOut(formulaa),FadeOut(formulab)) + + x_each_unit = self.x_axis_width / (self.x_max - self.x_min) + y_each_unit = self.y_axis_height / (self.y_max - self.y_min) + + self.setup_axes(animate=True) + self.wait(0.8) + + functionUpLine=Line(start=self.graph_origin,end=self.graph_origin+UP*y_each_unit*5,color=RED) + functionDownLine=Line(start=self.graph_origin+UP*y_each_unit*5,end=self.graph_origin,color=RED) + functinLeftLine=Line(start=self.graph_origin+LEFT*x_each_unit*9,end=self.graph_origin,color=RED) + functionRightLine=Line(start=self.graph_origin,end=self.graph_origin+RIGHT*x_each_unit*9,color=RED) + functionUpLine.shift(0.02*LEFT) + functionRightLine.shift(0.02*RIGHT) + + self.play(ShowCreation(functinLeftLine)) + self.play(ShowCreation(functionUpLine)) + self.play(ShowCreation(functionDownLine)) + self.play(ShowCreation(functionRightLine)) + self.wait(1.5) + + self.play(FadeOut(self.axes),FadeOut(introText),FadeOut(functinLeftLine),FadeOut(functionRightLine),FadeOut(functionUpLine),FadeOut(functionDownLine)) + self.wait(0.5) diff --git a/FSF-2020/calculus/series-and-transformations/Laplace Transformations/file5_formationDiracDeltaFunction.py b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/file5_formationDiracDeltaFunction.py new file mode 100644 index 0000000..565a7cb --- /dev/null +++ b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/file5_formationDiracDeltaFunction.py @@ -0,0 +1,142 @@ +from manimlib.imports import * +import math +import pylatex + +def func(x,t): + if(x>-t and x<t): + return 1/(2*t) + else: + return 0 + + +class formation(GraphScene): + CONFIG = { + "x_min": -7, + "x_max": 7, + "y_min": -2, + "y_max": 2, + "graph_origin": ORIGIN, + "function_color": RED, + "axes_color": GREEN, + "x_axis_label": "$t$", + "y_axis_label": "$y$", + "y_labeled_nums":range(-2,3), + "y_axis_height":4, + "x_axis_width":7 + } + def construct(self): + x_each_unit = self.x_axis_width / (self.x_max - self.x_min) + y_each_unit = self.y_axis_height / (self.y_max - self.y_min) + + text1=TextMobject("Consider the","following function's graph!") + text1.set_color_by_tex_to_color_map({"following function's graph!":BLUE}) + text1.scale(0.6) + + equation1=TextMobject("$\delta _{ \\tau }(t)=\\frac { 1 }{ 2\\tau } \quad$","$-\\tau <t<\\tau$") + equation2=TextMobject("$\delta _{ \\tau }(t)=0\quad \quad$","$t\in (-\infty ,-\\tau ]\cup [\\tau ,\infty )$") + equation1.scale(0.7) + equation2.scale(0.7) + equation1.shift(0.2*UP) + equation2.shift(0.4*DOWN+RIGHT*0.8) + equation1.set_color_by_tex_to_color_map({"$-\\tau <t<\\tau$":RED}) + equation2.set_color_by_tex_to_color_map({"$t\in (-\infty ,-\\tau ]\cup [\\tau ,\infty )$":RED}) + + self.play(Write(text1)) + self.play(ApplyMethod(text1.shift,3*UP)) + self.play(Write(equation1)) + self.play(Write(equation2)) + self.wait(1) + + self.play(FadeOut(equation1),FadeOut(equation2)) + self.wait(0.5) + + pointes1=TextMobject("$-\\tau$") + pointes2=TextMobject("$\\tau$") + pointes1.set_color(RED) + pointes2.set_color(RED) + pointes1.scale(0.65) + pointes2.scale(0.65) + + bottomText1=TextMobject("Here","$\int _{ -\infty }^{ \infty }{ \delta _{ \\tau }(t)dt }$","=","$1$") + bottomText2=TextMobject("Now as","$\\tau \\rightarrow 0$") + bottomText3=TextMobject("We get our","Dirac Function!") + bottomText4=TextMobject("i.e.","$\lim _{ \\tau \\rightarrow 0 }{ \delta _{ \\tau }(t)}$","$=$","$\delta (t)$") + textFinal=TextMobject("Area=1") + bottomText1.set_color_by_tex_to_color_map({"$\int _{ -\infty }^{ \infty }{ \delta _{ \\tau }(t)dt }$":BLUE,"$1$":YELLOW}) + textFinal.set_color(PURPLE_B) + bottomText2.set_color_by_tex_to_color_map({"$\\tau \\rightarrow 0$":YELLOW}) + bottomText3.set_color_by_tex_to_color_map({"Dirac Function!":RED}) + bottomText4.set_color_by_tex_to_color_map({"$\lim _{ \\tau \\rightarrow 0 }{ \delta _{ \\tau }(t)}$":BLUE,"$\delta (t)$":YELLOW}) + + bottomText1.scale(0.6) + bottomText2.scale(0.6) + bottomText3.scale(0.6) + bottomText4.scale(0.6) + textFinal.scale(0.9) + + bottomText1.shift(4*RIGHT+3*DOWN) + bottomText2.shift(4*RIGHT+3*DOWN) + bottomText3.shift(4*RIGHT+3*DOWN) + bottomText4.shift(4*RIGHT+3*DOWN) + textFinal.shift(5*RIGHT+2*UP) + + self.setup_axes(animate=True) + + graphs=[ + self.get_graph(lambda x:func(x,3),x_min=-7,x_max=7,color=RED), + self.get_graph(lambda x:func(x,2),x_min=-7,x_max=7,color=RED), + self.get_graph(lambda x:func(x,1),x_min=-7,x_max=7,color=RED), + self.get_graph(lambda x:func(x,0.5),x_min=-7,x_max=7,color=RED), + self.get_graph(lambda x:func(x,0.3),x_min=-7,x_max=7,color=RED), + self.get_graph(lambda x:func(x,0.15),x_min=-7,x_max=7,color=RED), + self.get_graph(lambda x:func(x,0.05),x_min=-7,x_max=7,color=RED), + self.get_graph(lambda x:func(x,0.01),x_min=-7,x_max=7,color=RED) + ] + pointes1.shift(self.graph_origin+3*LEFT*x_each_unit+0.4*DOWN*y_each_unit) + pointes2.shift(self.graph_origin+3*RIGHT*x_each_unit+0.4*DOWN*y_each_unit) + + functionUpLine=Line(start=self.graph_origin,end=self.graph_origin+UP*y_each_unit*2,color=RED) + functionDownLine=Line(start=self.graph_origin+UP*y_each_unit*2,end=self.graph_origin,color=RED) + functinLeftLine=Line(start=self.graph_origin+LEFT*x_each_unit*7,end=self.graph_origin,color=RED) + functionRightLine=Line(start=self.graph_origin,end=self.graph_origin+RIGHT*x_each_unit*7,color=RED) + functionUpLine.shift(0.02*LEFT) + functionRightLine.shift(0.02*RIGHT) + + self.play(Write(pointes1),Write(pointes2),ShowCreation(graphs[0])) + self.play(Write(bottomText1)) + self.wait(0.7) + + self.play(ReplacementTransform(bottomText1,bottomText2),Write(textFinal)) + self.wait(0.5) + self.play(ReplacementTransform(graphs[0],graphs[1]),ApplyMethod(pointes2.shift,LEFT*x_each_unit),ApplyMethod(pointes1.shift,RIGHT*x_each_unit)) + self.play(ReplacementTransform(graphs[1],graphs[2]),ApplyMethod(pointes2.shift,LEFT*x_each_unit),ApplyMethod(pointes1.shift,RIGHT*x_each_unit)) + self.wait(0.5) + self.play(ReplacementTransform(graphs[2],graphs[3]),FadeOut(pointes1),FadeOut(pointes2)) + self.play(ReplacementTransform(graphs[3],graphs[4])) + self.wait(1) + self.play(ReplacementTransform(bottomText2,bottomText3)) + self.wait(1) + self.play(FadeOut(graphs[4]),ReplacementTransform(bottomText3,bottomText4)) + self.wait(0.5) + self.play(ShowCreation(functinLeftLine)) + self.play(ShowCreation(functionUpLine)) + self.play(ShowCreation(functionDownLine)) + self.play(ShowCreation(functionRightLine)) + self.wait(2) + + self.play(FadeOut(bottomText4),FadeOut(textFinal)) + graphGrup=VGroup(self.axes,functinLeftLine,functionDownLine,functionRightLine,functionUpLine) + self.play(ApplyMethod(graphGrup.scale,0.5)) + box=Square(side_length=2,fill_color=BLUE,fill_opacity=0.6) + boxtext=TextMobject("$\mathscr{L}$") + boxtext.scale(0.8) + self.play(ApplyMethod(graphGrup.shift,4.9*LEFT)) + self.play(ShowCreation(box),Write(boxtext)) + outText=TextMobject("$f(0)$") + outText.set_color(GREEN) + outText.scale(0.65) + outText.shift(1.5*RIGHT) + self.play(ApplyMethod(graphGrup.shift,2*RIGHT)) + self.play(FadeOut(graphGrup),FadeIn(outText)) + self.play(ApplyMethod(outText.shift,RIGHT)) + self.wait(2)
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+ +#### Convergence Intuition + + +#### Convergence of a function + + +#### Radius and IntervalOfConvergence + + +#### Uniform Convergence + diff --git a/FSF-2020/calculus/series-and-transformations/Power Series/gifs/file1_pieChart.gif b/FSF-2020/calculus/series-and-transformations/Power Series/gifs/file1_pieChart.gif Binary files differnew file mode 100644 index 0000000..f102f6d --- /dev/null +++ b/FSF-2020/calculus/series-and-transformations/Power Series/gifs/file1_pieChart.gif diff --git a/FSF-2020/calculus/series-and-transformations/Power Series/gifs/file2_convergence_Intuition.gif b/FSF-2020/calculus/series-and-transformations/Power Series/gifs/file2_convergence_Intuition.gif Binary files differnew file mode 100644 index 0000000..9463ac2 --- /dev/null +++ b/FSF-2020/calculus/series-and-transformations/Power Series/gifs/file2_convergence_Intuition.gif diff --git a/FSF-2020/calculus/series-and-transformations/Power Series/gifs/file3_convergence_of_a_function.gif 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b/FSF-2020/calculus/series-and-transformations/Power Series/gifs/file5_UniformConvergence.gif diff --git a/FSF-2020/calculus/series-and-transformations/Power Series/script1.py b/FSF-2020/calculus/series-and-transformations/Power Series/video1_pieChart.py index 28eb07c..28eb07c 100644 --- a/FSF-2020/calculus/series-and-transformations/Power Series/script1.py +++ b/FSF-2020/calculus/series-and-transformations/Power Series/video1_pieChart.py diff --git a/FSF-2020/calculus/series-and-transformations/Power Series/script2.py b/FSF-2020/calculus/series-and-transformations/Power Series/video2_convergence_Intuition.py index 72356c6..72356c6 100644 --- a/FSF-2020/calculus/series-and-transformations/Power Series/script2.py +++ b/FSF-2020/calculus/series-and-transformations/Power Series/video2_convergence_Intuition.py diff --git a/FSF-2020/calculus/series-and-transformations/Power Series/script3.py b/FSF-2020/calculus/series-and-transformations/Power Series/video3_convergence_of_a_function.py index f710f42..f710f42 100644 --- a/FSF-2020/calculus/series-and-transformations/Power Series/script3.py +++ b/FSF-2020/calculus/series-and-transformations/Power Series/video3_convergence_of_a_function.py diff --git a/FSF-2020/calculus/series-and-transformations/Power Series/script4.py b/FSF-2020/calculus/series-and-transformations/Power Series/video4_radius_and_intervalOfConvergence.py index 412d20c..412d20c 100644 --- a/FSF-2020/calculus/series-and-transformations/Power Series/script4.py +++ b/FSF-2020/calculus/series-and-transformations/Power Series/video4_radius_and_intervalOfConvergence.py diff --git a/FSF-2020/calculus/series-and-transformations/Power Series/script5.py b/FSF-2020/calculus/series-and-transformations/Power Series/video5_UniformConvergence.py index e9681aa..e9681aa 100644 --- a/FSF-2020/calculus/series-and-transformations/Power Series/script5.py +++ b/FSF-2020/calculus/series-and-transformations/Power Series/video5_UniformConvergence.py diff --git a/FSF-2020/calculus/series-and-transformations/Taylor Series/README.md b/FSF-2020/calculus/series-and-transformations/Taylor Series/README.md new file mode 100644 index 0000000..ce3b088 --- /dev/null +++ b/FSF-2020/calculus/series-and-transformations/Taylor Series/README.md @@ -0,0 +1,11 @@ +#### Example of Taylors expansion + + +#### Taylor Series GeneralForm + + +#### Radius Of Convergence + + +#### Divergence of a Remainder + diff --git a/FSF-2020/calculus/series-and-transformations/Taylor Series/TaylorSeriesQuestions.pdf b/FSF-2020/calculus/series-and-transformations/Taylor Series/TaylorSeriesQuestions.pdf Binary files differindex 2096f52..46d46e1 100644 --- a/FSF-2020/calculus/series-and-transformations/Taylor Series/TaylorSeriesQuestions.pdf +++ b/FSF-2020/calculus/series-and-transformations/Taylor Series/TaylorSeriesQuestions.pdf diff --git a/FSF-2020/calculus/series-and-transformations/Taylor Series/gifs/file1_Example_TaylorExpansion.gif b/FSF-2020/calculus/series-and-transformations/Taylor Series/gifs/file1_Example_TaylorExpansion.gif Binary files differnew file mode 100644 index 0000000..ecd3272 --- /dev/null +++ b/FSF-2020/calculus/series-and-transformations/Taylor Series/gifs/file1_Example_TaylorExpansion.gif diff --git a/FSF-2020/calculus/series-and-transformations/Taylor Series/gifs/file2_TaylorExpansionGeneralForm.gif b/FSF-2020/calculus/series-and-transformations/Taylor Series/gifs/file2_TaylorExpansionGeneralForm.gif Binary files differnew file mode 100644 index 0000000..e6d9171 --- /dev/null +++ b/FSF-2020/calculus/series-and-transformations/Taylor Series/gifs/file2_TaylorExpansionGeneralForm.gif diff --git a/FSF-2020/calculus/series-and-transformations/Taylor Series/gifs/file3_radiusOfConvergence.gif b/FSF-2020/calculus/series-and-transformations/Taylor Series/gifs/file3_radiusOfConvergence.gif Binary files differnew file mode 100644 index 0000000..6b22d8d --- /dev/null +++ b/FSF-2020/calculus/series-and-transformations/Taylor Series/gifs/file3_radiusOfConvergence.gif diff --git a/FSF-2020/calculus/series-and-transformations/Taylor Series/gifs/file4_DivergentRemainder.gif b/FSF-2020/calculus/series-and-transformations/Taylor Series/gifs/file4_DivergentRemainder.gif Binary files differnew file mode 100644 index 0000000..2bb5185 --- /dev/null +++ b/FSF-2020/calculus/series-and-transformations/Taylor Series/gifs/file4_DivergentRemainder.gif diff --git a/FSF-2020/calculus/series-and-transformations/Taylor Series/script1.py b/FSF-2020/calculus/series-and-transformations/Taylor Series/video1_Example_TaylorExpansion.py index e83eff8..e83eff8 100644 --- a/FSF-2020/calculus/series-and-transformations/Taylor Series/script1.py +++ b/FSF-2020/calculus/series-and-transformations/Taylor Series/video1_Example_TaylorExpansion.py diff --git a/FSF-2020/calculus/series-and-transformations/Taylor Series/script2.py b/FSF-2020/calculus/series-and-transformations/Taylor Series/video2_TaylorExpansionGeneralForm.py index b5d0a53..f84cfe9 100644 --- a/FSF-2020/calculus/series-and-transformations/Taylor Series/script2.py +++ b/FSF-2020/calculus/series-and-transformations/Taylor Series/video2_TaylorExpansionGeneralForm.py @@ -192,4 +192,4 @@ class graphScene(GraphScene): self.play(FadeOut(self.axes),FadeOut(textFinal),FadeOut(thirdGraph),FadeOut(trTextGrup),FadeOut(mainfunction),FadeOut(fx),FadeOut(coeff[0]),FadeOut(coeff[1]),FadeOut(coeff[2])) self.play(Write(finalFormula)) - self.wait(2)
\ No newline at end of file + self.wait(2) diff --git a/FSF-2020/calculus/series-and-transformations/Taylor Series/script3.py b/FSF-2020/calculus/series-and-transformations/Taylor Series/video3_radiusOfConvergence.py index a2870d4..a68afb6 100644 --- a/FSF-2020/calculus/series-and-transformations/Taylor Series/script3.py +++ b/FSF-2020/calculus/series-and-transformations/Taylor Series/video3_radiusOfConvergence.py @@ -108,4 +108,4 @@ class graphScene(GraphScene): self.wait(0.6) self.play(Write(radiusLine)) self.play(FadeIn(radius)) - self.wait(2)
\ No newline at end of file + self.wait(2) diff --git a/FSF-2020/calculus/series-and-transformations/Taylor Series/script4.py b/FSF-2020/calculus/series-and-transformations/Taylor Series/video4_DivergentRemainder.py index 1f41c97..5389039 100644 --- a/FSF-2020/calculus/series-and-transformations/Taylor Series/script4.py +++ b/FSF-2020/calculus/series-and-transformations/Taylor Series/video4_DivergentRemainder.py @@ -79,4 +79,4 @@ class graphScene(GraphScene): self.play(Write(increasingText)) self.play(FadeIn(followupText)) self.wait(2) -
\ No newline at end of file + diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file.txt b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file.txt new file mode 100644 index 0000000..cae98ce --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file.txt @@ -0,0 +1,3 @@ +file 'text.mp4' +file 'LinearTransformation.mp4' +file 'NonLinearTransformation.mp4' diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file1_transformations.py b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file1_transformations.py new file mode 100644 index 0000000..677f890 --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file1_transformations.py @@ -0,0 +1,45 @@ +from manimlib.imports import * + +class text(Scene): + def construct(self): + text1 = TextMobject("For a grid, undergoing a linear transformation, all it's straight lines") + text1.scale(0.9) + text2 = TextMobject("must either remain straight lines or sends to a point in the grid formed") + text2.scale(0.9) + text1.move_to(ORIGIN+UP) + text2.move_to(ORIGIN) + self.play(Write(text1)) + self.play(Write(text2)) + self.wait() + self.play(FadeOut(text1),FadeOut(text2)) + +class LinearTransformation(LinearTransformationScene): + CONFIG = { + "basis_vector_stroke_width": 3, + "leave_ghost_vectors": True, + } + + def construct(self): + self.setup() + matrix = [[0.866,-0.5],[0.5,0.866]] + self.apply_matrix(matrix) + text = TextMobject("This is a Linear","Trasformation") + text[0].move_to(DOWN+4*LEFT) + text[1].move_to(1.5*DOWN+4*LEFT) + text.add_background_rectangle() + self.play(Write(text)) + self.wait() + +class NonLinearTransformation(Scene): + def construct(self): + grid = NumberPlane() + self.play(ShowCreation(grid),run_time =2) + NonLinearTrans = lambda coordinates : coordinates + np.array([np.sin(coordinates[1]),np.sin(coordinates[0]),0,]) + grid.prepare_for_nonlinear_transform() + self.play(grid.apply_function,NonLinearTrans) + text = TextMobject("While, this is not a","Linear Trasformation") + text[0].move_to(DOWN+4*LEFT) + text[1].move_to(1.5*DOWN+4*LEFT) + text.add_background_rectangle() + self.play(Write(text)) + self.wait()
\ No newline at end of file diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/file1_Understand_Linear_Transformations_visually.py b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file2_Understand_Linear_Transformations_visually.py index 577032d..577032d 100644 --- a/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/file1_Understand_Linear_Transformations_visually.py +++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file2_Understand_Linear_Transformations_visually.py diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/file2_Uniform_Scaling.py b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file3_Uniform_Scaling.py index a7856a5..a7856a5 100644 --- a/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/file2_Uniform_Scaling.py +++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file3_Uniform_Scaling.py diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/file3_Horizontal_Shear.py b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file4_Horizontal_Shear.py index 91f098e..91f098e 100644 --- a/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/file3_Horizontal_Shear.py +++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file4_Horizontal_Shear.py diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/file3_Horizontal_Shear_gif.gif b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file4_Horizontal_Shear_gif.gif Binary files differindex 9bef1b6..9bef1b6 100644 --- a/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/file3_Horizontal_Shear_gif.gif +++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file4_Horizontal_Shear_gif.gif diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/file4_Vertical_Shear.py b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file5_Vertical_Shear.py index 718e4e0..718e4e0 100644 --- a/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/file4_Vertical_Shear.py +++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file5_Vertical_Shear.py diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/file4_Vertical_Shear_gif.gif b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file5_Vertical_Shear_gif.gif Binary files differindex 7ca323f..7ca323f 100644 --- a/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/file4_Vertical_Shear_gif.gif +++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file5_Vertical_Shear_gif.gif diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file6_linear_transformation.py b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file6_linear_transformation.py new file mode 100755 index 0000000..01a0cef --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file6_linear_transformation.py @@ -0,0 +1,27 @@ +from manimlib.imports import *
+class LinearTrans(LinearTransformationScene,MovingCameraScene):
+ CONFIG = {
+ "basis_vector_stroke_width": 1,
+ "leave_ghost_vectors": True,
+ }
+
+ def setup(self):
+ LinearTransformationScene.setup(self)
+ MovingCameraScene.setup(self)
+
+ def construct(self):
+ self.setup()
+ self.camera_frame.save_state()
+ self.play(self.camera_frame.set_width, 7)
+ matrix = [[0.866,-0.5],[0.5,0.866]]
+ self.apply_matrix(matrix)
+ arc1 = Arc(radius = 0.25,angle=TAU/12)
+ arc2 = Arc(radius = 0.25,angle=TAU/12,start_angle=TAU/4)
+ text1 = TextMobject(r"$\theta$")
+ text1.scale(0.5)
+ text1.move_to(0.5*UP+0.125*LEFT)
+ text2 = TextMobject(r"$\theta$")
+ text2.scale(0.5)
+ text2.move_to(0.5*RIGHT+0.125*UP)
+ self.play(ShowCreation(arc1),ShowCreation(arc2),Write(text1),Write(text2),run_time=1)
+ self.wait()
diff --git a/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file1_orthogonal.py b/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file1_orthogonal.py new file mode 100755 index 0000000..b400f93 --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file1_orthogonal.py @@ -0,0 +1,34 @@ +from manimlib.imports import *
+
+class Orthogonal(ThreeDScene):
+ def construct(self):
+ axes = ThreeDAxes()
+ self.play(ShowCreation(axes))
+ self.move_camera(phi=30*DEGREES,theta=-45*DEGREES,run_time=3)
+ line1 = Line(start = ORIGIN,end = -3*LEFT)
+ line1.set_color(DARK_BLUE)
+ tip1 = Polygon(-LEFT,-0.8*LEFT-0.2*DOWN,-0.8*LEFT-0.2*UP)
+ tip1.move_to(-3*LEFT)
+ tip1.set_opacity(1)
+ tip1.set_fill(DARK_BLUE)
+ tip1.set_color(DARK_BLUE)
+
+ arrow2 = Line(start = ORIGIN,end = -3*UP)
+ arrow2.set_color(DARK_BLUE)
+ tip2 = Polygon(DOWN,0.8*DOWN-0.2*RIGHT,0.8*DOWN-0.2*LEFT)
+ tip2.move_to(3*DOWN)
+ tip2.set_opacity(1)
+ tip2.set_fill(DARK_BLUE)
+ tip2.set_color(DARK_BLUE)
+ arrow2.set_color(DARK_BLUE)
+
+ arrow3 = Line(start = ORIGIN,end = [0,0,3])
+ arrow3.set_color(DARK_BLUE)
+ tip3 = Polygon([0,0,3],[0,0,2.8]-0.2*RIGHT,[0,0,2.8]-0.2*LEFT)
+ tip3.set_opacity(1)
+ tip3.set_fill(DARK_BLUE)
+ tip3.set_color(DARK_BLUE)
+
+ self.play(ShowCreation(line1), ShowCreation(tip1), ShowCreation(arrow2), ShowCreation(tip2), ShowCreation(arrow3), ShowCreation(tip3))
+
+ self.wait()
\ No newline at end of file diff --git a/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file2_OrthonormalBasis.py b/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file2_OrthonormalBasis.py new file mode 100644 index 0000000..0a28f22 --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file2_OrthonormalBasis.py @@ -0,0 +1,82 @@ +from manimlib.imports import * +class OrthonormalBasis(GraphScene): + CONFIG = { + "x_min" : -6, + "x_max" : 6, + "y_min" : -4, + "y_max" : 4, + "graph_origin" : ORIGIN , +} + + def construct(self): + self.setup_axes(animate=True) + + XTD = self.x_axis_width/(self.x_max-self.x_min) + YTD = self.y_axis_height/(self.y_max-self.y_min) + + arrow1 = Arrow(start = ORIGIN,end = 0.707*YTD*UP+0.707*XTD*RIGHT) + arrow1.scale(2.25) + arrow1.set_color(DARK_BLUE) + + arrow2 = Arrow(start = ORIGIN,end = 0.707*YTD*UP+0.707*XTD*LEFT) + arrow2.scale(2.25) + arrow2.set_color(DARK_BLUE) + + square = Polygon(UP*0.4*YTD,0.2*(YTD*UP+XTD*RIGHT),ORIGIN,0.2*(YTD*UP+XTD*LEFT)) + square.set_color(DARK_BLUE) + self.play(ShowCreation(arrow2), ShowCreation(arrow1), ShowCreation(square)) + + ortho = TextMobject("Orthonormal Vectors") + ortho.scale(0.75) + ortho.move_to(DOWN+3*RIGHT) + self.play(Write(ortho)) + self.wait() + self.play(FadeOut(ortho)) + + arrow3 = Arrow(start = ORIGIN,end = YTD*3*UP+XTD*LEFT) + arrow3.scale(1.25) + arrow3.set_color(GOLD_E) + self.play(ShowCreation(arrow3)) + + arrow4 = Arrow(start = ORIGIN,end = YTD*UP+XTD*RIGHT) + arrow4.scale(1.8) + arrow4.set_color(GOLD_A) + + arrow5 = Arrow(start = ORIGIN,end = 2*YTD*UP-2*XTD*RIGHT) + arrow5.scale(1.3) + arrow5.set_color(GOLD_A) + + self.play(ShowCreation(arrow5), ShowCreation(arrow4)) + + self.wait() + + self.play(FadeOut(arrow1), FadeOut(arrow2), FadeOut(square)) + + self.wait() + + text1 = TextMobject(r"$<v,v_1> v_1$") + text1.move_to(UP+2*RIGHT) + text1.scale(0.75) + text2 = TextMobject(r"$<v,v_2> v_2$") + text2.move_to(UP+3*LEFT) + text2.scale(0.75) + + text3 = TextMobject("v") + text3.move_to(YTD*3.5*UP+XTD*1.5*LEFT) + + self.play(Write(text1), Write(text2), Write(text3)) + self.wait() + + line1 = DashedLine(start = YTD*UP+XTD*RIGHT, end = YTD*3*UP+XTD*1*LEFT) + line2 = DashedLine(start = YTD*2*UP+XTD*2*LEFT, end = YTD*3*UP+XTD*1*LEFT) + self.play(ShowCreation(line1),ShowCreation(line2)) + + self.wait() + + text = TextMobject(r"$v$ is the sum of projections","on the orthonormal vectors") + text[0].move_to(DOWN+3.2*RIGHT) + text[1].move_to(1.5*DOWN+3.2*RIGHT) + self.play(Write(text)) + self.wait(2) + self.play(FadeOut(arrow3), FadeOut(arrow4), FadeOut(arrow5), FadeOut(text1), FadeOut(text2), FadeOut(text3), FadeOut(self.axes), FadeOut(line1), FadeOut(line2)) + self.play(FadeOut(text)) diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file1_Column_Space.gif b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file1_Column_Space.gif Binary files differnew file mode 100644 index 0000000..7d8d2e1 --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file1_Column_Space.gif diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file1_Column_Space.py b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file1_Column_Space.py new file mode 100644 index 0000000..afe4f9a --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file1_Column_Space.py @@ -0,0 +1,30 @@ +from manimlib.imports import * + +class Column_Space(Scene): + def construct(self): + + A = TextMobject(r"$A = $",r"$\left( \begin{array}{c c c} 1 & 2 & 1 \\ 1 & 3 & 1 \\ 2 & 1 & 4 \\ 3 & 2 & 3 \end{array} \right)$") + A.move_to(2*UP) + A[1].set_color(color = DARK_BLUE) + A.scale(0.75) + + self.play(Write(A),run_time = 1) + + CS_A = TextMobject(r"Column Space of $A = x_{1}$",r"$\left( \begin{array}{c} 1 \\ 1 \\ 2 \\ 3 \end{array} \right)$",r"$+x_{2}$",r"$ \left( \begin{array}{c} 2 \\ 3 \\ 1 \\ 2 \end{array} \right)$",r"$ + x_{3}$",r"$\left( \begin{array}{c} 1 \\ 1 \\ 4 \\ 3 \end{array} \right)$") + CS_A.move_to(1.5*LEFT+1*DOWN) + CS_A[1].set_color(color = DARK_BLUE) + CS_A[3].set_color(color = DARK_BLUE) + CS_A[5].set_color(color = DARK_BLUE) + CS_A.scale(0.75) + + self.play(Write(CS_A),run_time = 2) + + arrow1 = Arrow(start = 1.25*UP,end = 0.25*DOWN+1.75*LEFT) + arrow2 = Arrow(start = 1.35*UP+0.5*RIGHT,end = 0.25*DOWN+0.5*RIGHT) + arrow3 = Arrow(start = 1.25*UP+0.75*RIGHT,end = 0.25*DOWN+2.9*RIGHT) + + Defn = TextMobject("Linear Combination of Columns of Matrix") + Defn.move_to(3*DOWN) + + self.play(Write(Defn), ShowCreation(arrow1), ShowCreation(arrow2), ShowCreation(arrow3),run_time = 1) + self.wait(1)
\ No newline at end of file diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file2_Row_Space.py b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file2_Row_Space.py new file mode 100644 index 0000000..b16a32a --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file2_Row_Space.py @@ -0,0 +1,145 @@ +from manimlib.imports import * + +class Row_Space(Scene): + def construct(self): + + Heading = TextMobject("Row Space") + defn1 = TextMobject("Definition 1: Row Space of a matrix is the linear combination of the rows of that matrix.") + defn2 = TextMobject("Definition 2: It is a vector space generated by a linear combination of the columns of $A^{T}$.") + equivalent = TextMobject(r"Definition 1 $\equiv$ Definition 2") + + Heading.move_to(2*UP) + Heading.set_color(color = DARK_BLUE) + + defn1.move_to(UP) + defn1.scale(0.75) + + defn2.scale(0.75) + + equivalent.move_to(DOWN) + + self.play(Write(Heading)) + self.play(Write(defn1)) + self.play(Write(defn2)) + self.play(Write(equivalent)) + + self.wait(2) + self.play(FadeOut(Heading),FadeOut(defn1),FadeOut(defn2),ApplyMethod(equivalent.move_to,2*UP)) + + how = TextMobject("Let us see, How?") + how.move_to(UP) + self.play(Write(how)) + self.play(FadeOut(equivalent),FadeOut(how)) + + A = TextMobject(r"$A = $",r"$\left( \begin{array}{c c c} 1 & 2 & 1 \\ 1 & 3 & 1 \\ 2 & 1 & 4 \\ 3 & 2 & 3 \end{array} \right)$") + A.move_to(2*UP+3*LEFT) + A[1].set_color(color = DARK_BLUE) + A.scale(0.80) + + self.play(Write(A)) + + rows = TextMobject(r"Rows of A $\rightarrow$", + r"$\left( \begin{array}{c c c} 1 & 2 & 1 \end{array} \right)$,", + r"$ \left( \begin{array}{c c c} 1 & 3 & 1 \end{array} \right)$,", + r"$\left( \begin{array}{c c c} 2 & 1 & 4 \end{array} \right)$,", + r"$ \left( \begin{array}{c c c} 3 & 2 & 3 \end{array} \right)$") + rows.scale(0.75) + rows[1:5].set_color(DARK_BLUE) + self.play(Write(rows)) + + ac_defn1 = TextMobject("According to Definition 1 : ") + ac_defn1.move_to(DOWN) + + RS_A = TextMobject(r"Row Space of $A = x_{1}$", + r"$\left( \begin{array}{c c c} 1 & 2 & 1 \end{array} \right)$", + r"$+x_{2}$", + r"$ \left( \begin{array}{c c c} 1 & 3 & 1 \end{array} \right)$", + r"$ + x_{3}$", + r"$\left( \begin{array}{c c c} 2 & 1 & 4 \end{array} \right)$", + r"$+x_{4}$", + r"$ \left( \begin{array}{c c c} 3 & 2 & 3 \end{array} \right)$") + RS_A.move_to(DOWN+DOWN) + RS_A[6].move_to(2*DOWN+DOWN) + RS_A[7].move_to(2*DOWN+2*RIGHT+DOWN) + RS_A[1].set_color(color = DARK_BLUE) + RS_A[3].set_color(color = DARK_BLUE) + RS_A[5].set_color(color = DARK_BLUE) + RS_A[7].set_color(color = DARK_BLUE) + RS_A.scale(0.75) + + self.play(FadeOut(rows[0]),Transform(rows[1],RS_A[1]),Transform(rows[2],RS_A[3]),Transform(rows[3],RS_A[5]),Transform(rows[4],RS_A[7])) + self.play(FadeIn(ac_defn1), Write(RS_A)) + self.wait(1) + + self.play(FadeOut(rows[1]), FadeOut(rows[2]), FadeOut(rows[3]), FadeOut(rows[4]), FadeOut(RS_A), FadeOut(ac_defn1)) + + A_T = TextMobject(r"$A^{T} = $",r"$\left( \begin{array}{c c c c} 1 & 1 & 2 & 3 \\ 2 & 3 & 1 & 2 \\ 1 & 1 & 4 & 3 \end{array} \right)$") + A_T.move_to(2*UP+3*RIGHT) + A_T[1].set_color(color = DARK_BLUE) + A_T.scale(0.80) + + self.play(Write(A_T)) + + change1 = TextMobject(r"Rows of $A\equiv$ Columns of $A^{T}$") + change2 = TextMobject(r"Columns of $A\equiv$ Rows of $A^{T}$") + change2.move_to(DOWN) + + change3 = TextMobject(r"Row Space of $A$ = Linear Combination of",r"Rows","of",r"A") + change3.move_to(2*DOWN) + change3[1].set_color(DARK_BLUE) + change3[3].set_color(DARK_BLUE) + + self.play(Write(change1)) + self.play(Write(change2)) + self.play(Write(change3)) + + columns = TextMobject("Columns") + columns.scale(0.6) + columns.set_color(DARK_BLUE) + columns.move_to(2*DOWN+4.1*RIGHT) + + a = TextMobject(r"$A^{T}$") + a.set_color(DARK_BLUE) + a.move_to(1.95*DOWN+5.6*RIGHT) + + self.wait(0.5) + + self.play(Transform(change3[1],columns), Transform(change3[3],a)) + + equal = TextMobject(r"= Column Space($A^{T}$)") + equal.move_to(3*DOWN+0.5*RIGHT) + + self.play(Write(equal)) + + self.play(FadeOut(A_T), FadeOut(change1), FadeOut(change2), FadeOut(change3), FadeOut(A), FadeOut(equal)) + + ac_defn1.move_to(3*UP) + RS_A.move_to(1.5*UP) + RS_A[6].move_to(UP) + RS_A[7].move_to(UP+1.5*RIGHT) + + self.play(Write(RS_A),FadeIn(ac_defn1)) + + CS_AT = TextMobject(r"Row Space of $A = x_{1}$", + r"$\left( \begin{array}{c} 1 \\ 2 \\ 1 \end{array} \right)$", + r"$+x_{2}$", + r"$ \left( \begin{array}{c} 1 \\ 3 \\ 1 \end{array} \right)$", + r"$ + x_{3}$", + r"$\left( \begin{array}{c} 2 \\ 1 \\ 4 \end{array} \right)$", + r"$+x_{4}$", + r"$ \left( \begin{array}{c} 3 \\ 2 \\ 3 \end{array} \right)$") + CS_AT.move_to(1.5*DOWN) + CS_AT[1].set_color(color = DARK_BLUE) + CS_AT[3].set_color(color = DARK_BLUE) + CS_AT[5].set_color(color = DARK_BLUE) + CS_AT[7].set_color(color = DARK_BLUE) + CS_AT.scale(0.75) + + ac_defn2 = TextMobject("According to Definition 2 : ") + equivalent = TextMobject(r"Hence, Definition 1 $\equiv$ Definition 2") + equivalent.move_to(3*DOWN) + + self.play(Write(CS_AT),FadeIn(ac_defn2)) + self.play(Write(equivalent)) + + self.wait() diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file.txt b/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file.txt new file mode 100644 index 0000000..5c48a13 --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file.txt @@ -0,0 +1,3 @@ +file 'RN_Line.mp4' +file 'RN_Point.mp4' +file 'RN_SameDim.mp4' diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file1_RN_Theorem.py b/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file1_RN_Theorem.py new file mode 100755 index 0000000..e54276c --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file1_RN_Theorem.py @@ -0,0 +1,97 @@ +from manimlib.imports import *
+class RN_Line(LinearTransformationScene):
+ def construct(self):
+
+ self.setup()
+ self.wait()
+
+ predim = TextMobject("Dimension of this vector space is 2")
+ predim.move_to(DOWN+4*LEFT)
+ predim.scale(0.75)
+ predim.add_background_rectangle()
+ self.play(Write(predim))
+ self.wait()
+ self.play(FadeOut(predim))
+
+ afterlt = TextMobject("After Linear transformation")
+ afterlt.move_to(DOWN+4*LEFT)
+ afterlt.scale(0.75)
+ afterlt.add_background_rectangle()
+
+ afterlt2 = TextMobject("Dimension of the vector space","changes to 1")
+ afterlt2[0].move_to(1.5*DOWN+4*LEFT)
+ afterlt2[1].move_to(2*DOWN+4*LEFT)
+ afterlt2.scale(0.75)
+ afterlt2.add_background_rectangle()
+ matrix = [[1,1],[1,1]]
+ self.apply_matrix(matrix)
+ self.play(Write(afterlt))
+ self.play(Write(afterlt2))
+ self.wait()
+ nullity = TextMobject("Hence, nullity = 1")
+ nullity.move_to(DOWN+4*LEFT)
+ self.play(FadeOut(afterlt),FadeOut(afterlt2),Write(nullity))
+ self.wait(1)
+ self.play(FadeOut(nullity))
+
+class RN_Point(LinearTransformationScene):
+ def construct(self):
+ self.setup()
+ self.wait()
+ predim = TextMobject("Another One")
+ predim.move_to(DOWN+4*LEFT)
+ predim.scale(0.75)
+ predim.add_background_rectangle()
+ self.play(Write(predim))
+ self.wait()
+ self.play(FadeOut(predim))
+ afterlt = TextMobject("After Linear transformation")
+ afterlt.move_to(DOWN+4*LEFT)
+ afterlt.scale(0.75)
+ afterlt.add_background_rectangle()
+ afterlt2 = TextMobject("Dimension of the vector space","changes to 0")
+ afterlt2[0].move_to(1.5*DOWN+4*LEFT)
+ afterlt2[1].move_to(2*DOWN+4*LEFT)
+ afterlt2.scale(0.75)
+ afterlt2.add_background_rectangle()
+ matrix = [[0,0],[0,0]]
+ self.apply_matrix(matrix)
+ self.play(Write(afterlt))
+ self.play(Write(afterlt2))
+ self.wait()
+ nullity = TextMobject("Hence, nullity = 2")
+ nullity.move_to(DOWN+4*LEFT)
+ self.play(FadeOut(afterlt),FadeOut(afterlt2),Write(nullity))
+ self.wait(1)
+ self.play(FadeOut(nullity))
+
+class RN_SameDim(LinearTransformationScene):
+ def construct(self):
+ self.setup()
+ self.wait()
+ predim = TextMobject("Let us look at another example")
+ predim.add_background_rectangle()
+ predim.move_to(DOWN+4*LEFT)
+ predim.scale(0.75)
+ self.play(Write(predim))
+ self.wait()
+ self.play(FadeOut(predim))
+ afterlt = TextMobject("After Linear transformation")
+ afterlt.move_to(DOWN+4*LEFT)
+ afterlt.scale(0.75)
+ afterlt.add_background_rectangle()
+ afterlt2 = TextMobject("Dimension of the vector space","remains to be 2")
+ afterlt2[0].move_to(1.5*DOWN+4*LEFT)
+ afterlt2[1].move_to(2*DOWN+4*LEFT)
+ afterlt2.scale(0.75)
+ afterlt2.add_background_rectangle()
+ matrix = [[1,1],[0,1]]
+ self.apply_matrix(matrix)
+ self.play(Write(afterlt))
+ self.play(Write(afterlt2))
+ self.wait()
+ nullity = TextMobject("Hence, nullity = 0")
+ nullity.move_to(DOWN+4*LEFT)
+ self.play(FadeOut(afterlt),FadeOut(afterlt2),Write(nullity))
+ self.wait(1)
+ self.play(FadeOut(nullity))
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