From a240c40156d5a05eb0ec95d2002241ab84ebca81 Mon Sep 17 00:00:00 2001 From: Purusharth S Date: Sat, 23 May 2020 18:32:54 +0530 Subject: add topic folders --- .../multivariable-functions-and-paritial-derivatives/README.md | 0 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/README.md (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives') diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/README.md b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/README.md new file mode 100644 index 0000000..e69de29 -- cgit From 29d18cfc55db1775f1c34a068ba9632bf7514d27 Mon Sep 17 00:00:00 2001 From: nishanpoojary Date: Sun, 24 May 2020 17:43:30 +0530 Subject: added scalar functions folder --- .../scalar_function_application.py | 129 +++++++++++++++ .../scalar_function_domain_range.py | 132 +++++++++++++++ .../scalar_function_level_curves.mp4 | Bin 0 -> 726339 bytes .../scalar_function_level_curves2.mp4 | Bin 0 -> 2088849 bytes .../scalar_function_neural_nets.py | 177 +++++++++++++++++++++ .../scalar_function_parabola_example.py | 35 ++++ 6 files changed, 473 insertions(+) create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_application.py create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_domain_range.py create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_level_curves.mp4 create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_level_curves2.mp4 create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_neural_nets.py create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_parabola_example.py (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives') diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_application.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_application.py new file mode 100644 index 0000000..56b3e53 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_application.py @@ -0,0 +1,129 @@ +from manimlib.imports import * + +class ScalarApplication(ThreeDScene): + def construct(self): + axes = ThreeDAxes() # creates a 3D Axis + + cube = Cube() + cube.set_fill(YELLOW_E, opacity = 0.1) + cube.scale(2) + self.set_camera_orientation(phi=0 * DEGREES,theta=270*DEGREES) + self.play(ShowCreation(cube),ShowCreation(axes)) + + dot = Sphere() + dot.scale(0.1) + dot.move_to(np.array([1,0.5,1])) + dot.set_fill(RED) + + #dot = Dot(np.array([1,0.5,1]), color = RED) + temp_func = TextMobject("T(x,y,z)") + temp_func.next_to(dot,RIGHT) + temp_func.set_color(RED) + temp_func_trans = TextMobject("T(1,0.5,1)") + temp_func_trans.next_to(dot,RIGHT) + temp_func_trans.set_color(RED) + temp = TextMobject(r"$36 ^\circ$") + temp.next_to(dot,RIGHT) + temp.set_color(RED_E) + + + self.play(ShowCreation(dot)) + self.play(ShowCreation(temp_func)) + self.play(Transform(temp_func, temp_func_trans)) + self.wait(1) + self.play(Transform(temp_func, temp)) + + + + + dot1 = Sphere() + dot1.scale(0.1) + dot1.move_to(np.array([-1,-0.8,-1.5])) + dot1.set_fill(BLUE_E) + #dot1 = Dot(np.array([-1,-0.8,-1.5]), color = BLUE) + temp_func1 = TextMobject("T(x,y,z)") + temp_func1.next_to(dot1,LEFT) + temp_func1.set_color(BLUE) + temp_func_trans1 = TextMobject("T(-1,-0.8,-1.5)") + temp_func_trans1.next_to(dot1,LEFT) + temp_func_trans1.set_color(BLUE) + temp1 = TextMobject(r"$24 ^\circ$") + temp1.next_to(dot1,LEFT) + temp1.set_color(BLUE) + + self.play(ShowCreation(dot1)) + self.play(ShowCreation(temp_func1)) + self.play(Transform(temp_func1, temp_func_trans1)) + self.wait(1) + self.play(Transform(temp_func1, temp1)) + + self.play(FadeOut(temp_func)) + self.play(FadeOut(temp_func1)) + + + self.move_camera(phi=80* DEGREES,theta=45*DEGREES,run_time=3) + + self.begin_ambient_camera_rotation(rate=0.2) + self.wait(4) + self.stop_ambient_camera_rotation() + self.wait(2) + + + + +class AddTempScale(Scene): + def construct(self): + temp_scale = ImageMobject("tempscale.png") + temp_scale.scale(4) + temp_scale.move_to(2*RIGHT) + self.play(ShowCreation(temp_scale)) + + + temp_func = TextMobject("T(x,y,z)") + temp_func.move_to(3*UP +2*LEFT) + temp_func.set_color(RED) + temp_func_trans = TextMobject("T(1,0.5,1)") + temp_func_trans.move_to(3*UP +2*LEFT) + temp_func_trans.set_color(RED) + temp = TextMobject(r"$36 ^\circ$") + temp.set_color(RED) + temp.move_to(3*UP +2*LEFT) + temp.scale(0.7) + + self.play(ShowCreation(temp_func)) + self.play(Transform(temp_func, temp_func_trans)) + self.wait(1) + self.play(Transform(temp_func, temp)) + self.play(ApplyMethod(temp_func.move_to, 1.8*UP +1.8*RIGHT)) + + + temp_func1 = TextMobject("T(x,y,z)") + temp_func1.move_to(2*UP +2*LEFT) + temp_func1.set_color(BLUE) + temp_func_trans1 = TextMobject("T(-1,-0.8,-1.5)") + temp_func_trans1.move_to(2*UP +2*LEFT) + temp_func_trans1.set_color(BLUE) + temp1 = TextMobject(r"$24 ^\circ$") + temp1.set_color(BLUE) + temp1.move_to(2*UP +2*LEFT) + temp1.scale(0.7) + + self.play(ShowCreation(temp_func1)) + self.play(Transform(temp_func1, temp_func_trans1)) + self.wait(1) + self.play(Transform(temp_func1, temp1)) + self.play(ApplyMethod(temp_func1.move_to, 0.6*UP +1.8*RIGHT)) + + + + transtext = TextMobject("Scalar Function Transform:") + transtext.set_color(GREEN) + transtext1 = TextMobject(r"$\mathbb{R}^3 \rightarrow \mathbb{R}$") + transtext1.set_color(YELLOW_E) + transtext.move_to(3*UP +3*LEFT) + transtext1.next_to(transtext,DOWN) + self.play(Write(transtext)) + self.play(Write(transtext1)) + self.wait(2) + + diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_domain_range.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_domain_range.py new file mode 100644 index 0000000..9b1ca7b --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_domain_range.py @@ -0,0 +1,132 @@ +# Plotting Graphs +from manimlib.imports import * + +class PlotGraphs(GraphScene): + CONFIG = { + "x_min": -5, + "x_max": 5, + "y_min": 0, + "y_max": 4, + "graph_origin": ORIGIN + 2.5* DOWN, + "x_labeled_nums": list(range(-5, 6)), + "y_labeled_nums": list(range(0, 5)), + } + def construct(self): + + topic = TextMobject("Domain and Range") + topic.scale(2) + topic.set_color(YELLOW) + self.play(Write(topic)) + self.play(FadeOut(topic)) + self.wait(1) + + + XTD = self.x_axis_width/(self.x_max- self.x_min) + YTD = self.y_axis_height/(self.y_max- self.y_min) + + self.setup_axes(animate = True) + + graphobj = self.get_graph(lambda x : np.sqrt(x + 4), x_min = -4, x_max = 5) + graph_lab = self.get_graph_label(graphobj, label = r"\sqrt{x + 4}") + + + rangeline1 = Arrow(self.graph_origin+2.2*YTD*UP+5*XTD*LEFT, self.graph_origin+4.1*YTD*UP+5*XTD*LEFT) + rangeline2 = Arrow(self.graph_origin+1.7*YTD*UP+5*XTD*LEFT, self.graph_origin+5*XTD*LEFT) + rangeline1.set_color(RED) + rangeline2.set_color(RED) + + rangeMsg = TextMobject(r"Range: $y \geq 0$") + rangeMsg.move_to(self.graph_origin+2*YTD*UP+5*XTD*LEFT) + rangeMsg.scale(0.5) + rangeMsg.set_color(YELLOW) + + domainline1 = Line(self.graph_origin+0.6*YTD*DOWN+1.2*XTD*LEFT, self.graph_origin+0.6*YTD*DOWN + 4*XTD*LEFT) + domainline2 = Arrow(self.graph_origin+0.6*YTD*DOWN+1.1*XTD*RIGHT, self.graph_origin+0.6*YTD*DOWN + 5.3*XTD*RIGHT) + domainline1.set_color(PINK) + domainline2.set_color(PINK) + + domainMsg = TextMobject(r"Domain: $x \geq -4$") + domainMsg.move_to(self.graph_origin+0.6*YTD*DOWN) + domainMsg.scale(0.5) + domainMsg.set_color(GREEN) + + + + + self.play(ShowCreation(graphobj)) + self.play(ShowCreation(graph_lab)) + self.wait(1) + self.play(GrowArrow(rangeline1)) + self.play(GrowArrow(rangeline2)) + self.play(Write(rangeMsg)) + self.wait(1) + self.play(GrowArrow(domainline1)) + self.play(GrowArrow(domainline2)) + self.play(Write(domainMsg)) + self.wait(3) + + self.wait(2) + + + + +class PlotSineGraphs(GraphScene): + CONFIG = { + "x_min": -8, + "x_max": 8, + "y_min": -1, + "y_max": 1, + "graph_origin": ORIGIN, + "x_labeled_nums": list(range(-8, 9)), + "y_labeled_nums": list(range(-1, 2)), + } + 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) + + self.setup_axes(animate = True) + + sineobj = self.get_graph(lambda x : np.sin(x), x_min = -7, x_max = 8) + sine_lab = self.get_graph_label(sineobj, label = "\\sin(x)") + + + rangeline1 = Line(8*XTD*LEFT,1*YTD*UP+8*XTD*LEFT) + rangeline2 = Line(8*XTD*LEFT,1*YTD*DOWN+8*XTD*LEFT) + rangeline1.set_color(RED) + rangeline2.set_color(RED) + + rangeMsg = TextMobject(r"Range: $-1 \leq y \leq 1$") + rangeMsg.move_to(1.1*YTD*UP+8.5*XTD*LEFT) + rangeMsg.scale(0.5) + rangeMsg.set_color(YELLOW) + + + domainline1 = Arrow(1.1*YTD*DOWN+2*XTD*LEFT, 1.1*YTD*DOWN + 8.5*XTD*LEFT) + domainline2 = Arrow(1.1*YTD*DOWN+2*XTD*RIGHT, 1.1*YTD*DOWN + 8.5*XTD*RIGHT) + domainline1.set_color(PINK) + domainline2.set_color(PINK) + + domainMsg = TextMobject(r"Domain: $[-\infty, \infty]$") + domainMsg.move_to(1.1*YTD*DOWN) + domainMsg.scale(0.5) + domainMsg.set_color(GREEN) + + + + self.play(ShowCreation(sineobj)) + self.play(ShowCreation(sine_lab)) + self.wait(1) + self.play(GrowArrow(rangeline1)) + self.play(GrowArrow(rangeline2)) + self.play(Write(rangeMsg)) + self.wait(1) + self.play(GrowArrow(domainline1)) + self.play(GrowArrow(domainline2)) + self.play(Write(domainMsg)) + self.wait(3) + + + \ No newline at end of file diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_level_curves.mp4 b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_level_curves.mp4 new file mode 100644 index 0000000..6af2670 Binary files /dev/null and b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_level_curves.mp4 differ diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_level_curves2.mp4 b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_level_curves2.mp4 new file mode 100644 index 0000000..b21ae25 Binary files /dev/null and b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_level_curves2.mp4 differ diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_neural_nets.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_neural_nets.py new file mode 100644 index 0000000..eb6bf45 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_neural_nets.py @@ -0,0 +1,177 @@ +from manimlib.imports import * + +class SigmoidFunc(GraphScene): + CONFIG = { + "x_min": -4, + "x_max": 4, + "y_min": -1, + "y_max": 1, + "graph_origin": ORIGIN + 0.8*DOWN, + "x_labeled_nums": list(range(-4, 5)), + "y_labeled_nums": list(range(-1, 2)), + "y_axis_height": 4.5, + } + 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) + + topic = TextMobject("Sigmoid Function") + topic.move_to(3.2*UP) + topic.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE) + + self.setup_axes(animate = True) + sigmoid_func = self.get_graph(lambda x : (1/(1 + np.exp(-x))), x_min = -4, x_max = 4) + sigmoid_lab = self.get_graph_label(sigmoid_func, label = r"\frac{1}{1 + e^{-z}}") + + + + + self.play(ShowCreation(sigmoid_func),Write(sigmoid_lab)) + self.play(Write(topic)) + self.wait(2) + self.play(FadeOut(sigmoid_func), FadeOut(sigmoid_lab)) + self.wait(1) + + + +class NeuralNet(GraphScene): + def construct(self): + + sigmoid_exp = TextMobject(r"g(z) = g($\theta^T$ X) = $\frac{1}{1 + e^{-z}}$") + sigmoid_exp.move_to(3*UP + 4*LEFT) + sigmoid_exp.scale(0.8) + sigmoid_exp.set_color(BLUE) + sigmoid_exp1 = TextMobject(r"Predict: 'y = 1'",r"When g(z) $\geq$ 0.5, z $\geq$ 0, $\theta^T$ X $\geq$ 0") + sigmoid_exp2 = TextMobject(r"Predict: 'y = 0'", r"When g(z) $\leq$ 0.5, z $\leq$ 0, $\theta^T$ X $\leq$ 0") + sigmoid_exp1.scale(0.5) + sigmoid_exp2.scale(0.5) + sigmoid_exp1.set_color(PURPLE) + sigmoid_exp2.set_color(PURPLE) + + sigmoid_exp1[0].next_to(sigmoid_exp, 1.5*DOWN) + sigmoid_exp1[1].next_to(sigmoid_exp1[0], DOWN) + sigmoid_exp2[0].next_to(sigmoid_exp1[1], 1.5*DOWN) + sigmoid_exp2[1].next_to(sigmoid_exp2[0], DOWN) + + + self.play(Write(sigmoid_exp)) + self.play(Write(sigmoid_exp1[0]), Write(sigmoid_exp1[1])) + self.play(Write(sigmoid_exp2[0]), Write(sigmoid_exp2[1])) + self.wait(2) + + + neuron1 = Circle() + neuron1.set_fill(YELLOW_A, opacity = 0.5) + + neuron2 = Circle() + neuron2.set_fill(ORANGE, opacity = 0.5) + + neuron3 = Circle() + neuron3.set_fill(GREEN_E, opacity = 0.5) + + neuron1.move_to(2*UP+RIGHT) + neuron2.move_to(2*DOWN+RIGHT) + neuron3.move_to(4*RIGHT) + + arrow1 = Arrow(neuron1.get_right(),neuron3.get_left(),buff=0.1) + arrow1.set_color(RED) + arrow2 = Arrow(neuron2.get_right(),neuron3.get_left(),buff=0.1) + arrow2.set_color(RED) + + arrow3 = Arrow(neuron3.get_right(),7*RIGHT,buff=0.1) + arrow3.set_color(RED) + + + sign1 = TextMobject("+1") + sign1.move_to(2*UP+RIGHT) + sign1.scale(2) + sign2 = TextMobject(r"$x_1$") + sign2.move_to(2*DOWN+RIGHT) + sign2.scale(2) + sign3 = TextMobject(r"$h_{\theta}(x)$") + sign3.move_to(6*RIGHT+0.4*DOWN) + sign3.scale(0.7) + sign4 = TextMobject(r"$= g(10 - 20x_1)$") + sign4.next_to(sign3,DOWN) + sign4.scale(0.5) + sign5 = TextMobject(r"$= g(10 - 20x_1)$") + sign5.next_to(sign3,DOWN) + sign5.scale(0.5) + sign6 = TextMobject(r"$= g(10 - 20x_1)$") + sign6.next_to(sign3,DOWN) + sign6.scale(0.5) + + + weight1 = TextMobject("10") + weight1.next_to(arrow1,UP) + weight2 = TextMobject("-20") + weight2.next_to(arrow2,DOWN) + + gate = TextMobject("NOT GATE") + gate.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE) + gate.scale(1.5) + gate.move_to(3*RIGHT+3.5*UP) + + + + truth_table = TextMobject(r"\begin{displaymath}\begin{array}{|c|c|} x & y\\ \hline 1 & 0 \\0 & 1 \\\end{array}\end{displaymath}") + truth_table.next_to(sigmoid_exp2[1], 3*DOWN) + + values = TextMobject("1", "0") + values.scale(2) + + sign4_trans1 = TextMobject(r"$= g(10 - 20(1))$") + sign4_trans2 = TextMobject(r"$= g(10 - 20(0))$") + sign4_trans1.next_to(sign3,DOWN) + sign4_trans2.next_to(sign3,DOWN) + sign4_trans1.scale(0.5) + sign4_trans2.scale(0.5) + + + + output1 = TextMobject("y = 0") + output2 = TextMobject("y = 1") + output1.next_to(sign4,DOWN) + output2.next_to(sign4,DOWN) + output1.scale(1.5) + output2.scale(1.5) + + + + self.play(ShowCreation(neuron1),ShowCreation(neuron2)) + self.play(ShowCreation(neuron3)) + self.play(ShowCreation(sign1),ShowCreation(sign2)) + self.wait(1) + + self.play(GrowArrow(arrow1)) + self.play(GrowArrow(arrow2)) + self.play(ShowCreation(weight1),ShowCreation(weight2)) + + + + self.play(GrowArrow(arrow3)) + self.play(Write(sign3),Write(sign4)) + + self.play(Write(gate)) + self.play(ShowCreation(truth_table)) + + self.play(ApplyMethod(values[0].move_to, 2*DOWN+RIGHT)) + self.play(FadeOut(values[0])) + self.play(Transform(sign4,sign4_trans1)) + self.play(Write(output1)) + self.wait(1) + self.play(FadeOut(output1)) + self.play(Transform(sign4, sign5)) + + + self.play(ApplyMethod(values[1].move_to, 2*DOWN+RIGHT)) + self.play(FadeOut(values[1])) + self.play(Transform(sign4,sign4_trans2)) + self.play(Write(output2)) + self.wait(1) + self.play(FadeOut(output2)) + self.play(Transform(sign4, sign6)) + + self.wait(2) + + diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_parabola_example.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_parabola_example.py new file mode 100644 index 0000000..74dc063 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_parabola_example.py @@ -0,0 +1,35 @@ +from manimlib.imports import * + +class Parabola(ThreeDScene): + def construct(self): + axes = ThreeDAxes() # creates a 3D Axis + + paraboloid = ParametricSurface( + lambda u, v: np.array([ + 2*np.cosh(u)*np.cos(v), + 2*np.cosh(u)*np.sin(v), + 2*np.sinh(u) + ]),v_min=0,v_max=TAU,u_min=0,u_max=2,checkerboard_colors=[YELLOW_D, YELLOW_E], + resolution=(15, 32)) + + text3d = TextMobject(r"Plot of $f: \mathbb{R}^2 \rightarrow \mathbb{R}$", "z = f(x,y)") + self.add_fixed_in_frame_mobjects(text3d) + text3d[0].move_to(4*LEFT+2*DOWN) + text3d[1].next_to(text3d[0], DOWN) + text3d[0].set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE) + text3d[1].set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE) + + #self.set_camera_orientation(phi=0 * DEGREES,theta=270*DEGREES) + self.move_camera(phi=110* DEGREES,theta=45*DEGREES) + self.add(axes) + self.play(ShowCreation(paraboloid)) + self.play(Write(text3d[0])) + self.play(Write(text3d[1])) + self.begin_ambient_camera_rotation(rate=0.2) + self.wait(3) + self.move_camera(phi=0 * DEGREES,theta=180*DEGREES,run_time=3) + self.wait(3) + self.move_camera(phi=110* DEGREES,theta=90*DEGREES,run_time=3) + self.wait(3) + + \ No newline at end of file -- cgit From 9c45f041b4702c28767117c129ce3a09ae1863ac Mon Sep 17 00:00:00 2001 From: nishanpoojary Date: Sun, 24 May 2020 17:44:29 +0530 Subject: Added Multivariable Function folder --- .../multivariable_func_derivative_vectorvf.py | 247 +++++++++++++++++++++ .../multivariable_func_examples.py | 69 ++++++ .../multivariable_func_plot_sphere.py | 42 ++++ .../multivariable_func_respresntation.py | 80 +++++++ .../multivariable_func_vectorvf_sine.py | 91 ++++++++ 5 files changed, 529 insertions(+) create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_derivative_vectorvf.py create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_examples.py create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_plot_sphere.py create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_respresntation.py create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_vectorvf_sine.py (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives') diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_derivative_vectorvf.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_derivative_vectorvf.py new file mode 100644 index 0000000..466e389 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_derivative_vectorvf.py @@ -0,0 +1,247 @@ +from manimlib.imports import * + +class Derivative(GraphScene): + CONFIG = { + "x_min": 0, + "x_max": 3, + "y_min": 0, + "y_max": 5, + "graph_origin": ORIGIN+6*LEFT+3*DOWN, + "x_axis_width": 6, + "x_labeled_nums": list(range(0, 4)), + "y_labeled_nums": list(range(0, 6)), + } + 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) + + self.setup_axes(animate = True) + + graph = self.get_graph(lambda x : x*x, x_min = 0.5, x_max = 2, color = GREEN) + + point1 = Dot().shift(self.graph_origin+0.25*YTD*UP + 0.5*XTD*RIGHT) + point1_lab = TextMobject(r"$t = a$") + point1_lab.scale(0.7) + point1_lab.next_to(point1, RIGHT) + + point2 = Dot().shift(self.graph_origin+2*XTD*RIGHT+4*YTD*UP) + point2_lab = TextMobject(r"$t = b$") + point2_lab.scale(0.7) + point2_lab.next_to(point2, RIGHT) + + + vector1 = Arrow(self.graph_origin, self.graph_origin+1*YTD*UP + 1*XTD*RIGHT, buff=0.02, color = RED) + vector1_lab = TextMobject(r"$\vec r(t)$", color = RED) + vector1_lab.move_to(self.graph_origin+1.2*XTD*RIGHT+ 0.75*YTD*UP) + vector1_lab.scale(0.8) + + vector2 = Arrow(self.graph_origin, self.graph_origin+2.25*YTD*UP + 1.5*XTD*RIGHT, buff=0.02, color = YELLOW_C) + vector2_lab = TextMobject(r"$\vec r(t + h)$", color = YELLOW_C) + vector2_lab.move_to(self.graph_origin+0.5*XTD*RIGHT+ 2*YTD*UP) + vector2_lab.scale(0.8) + + vector3 = Arrow(self.graph_origin+1*YTD*UP + 1*XTD*RIGHT, self.graph_origin+2.25*YTD*UP + 1.5*XTD*RIGHT, buff=0.02, color = PINK) + vector3_lab = TextMobject(r"$\vec r(t + h) - \vec r(t)$", color = PINK) + vector3_lab.move_to(self.graph_origin+2*XTD*RIGHT+ 1.5*YTD*UP) + vector3_lab.scale(0.8) + + + self.play(ShowCreation(graph)) + self.play(ShowCreation(point1), Write(point1_lab)) + self.play(ShowCreation(point2), Write(point2_lab)) + + self.play(GrowArrow(vector1),Write(vector1_lab)) + self.play(GrowArrow(vector2),Write(vector2_lab)) + self.play(GrowArrow(vector3),Write(vector3_lab)) + self.wait(1) + + self.display_text() + + self.play(ApplyMethod(vector3_lab.move_to,(self.graph_origin+2.3*XTD*RIGHT+ 2.2*YTD*UP))) + + vector4 = Arrow(self.graph_origin+1*YTD*UP + 1*XTD*RIGHT, self.graph_origin+1*YTD*UP + 1.5*XTD*RIGHT, buff=0.02, color = PURPLE) + vector4_lab = TextMobject(r"$dx$", color = PURPLE) + vector4_lab.move_to(self.graph_origin+1.7*XTD*RIGHT+ 0.8*YTD*UP) + vector4_lab.scale(0.7) + + vector5 = Arrow(self.graph_origin+1*YTD*UP + 1.5*XTD*RIGHT, self.graph_origin+2.25*YTD*UP + 1.5*XTD*RIGHT, buff=0.02, color = ORANGE) + vector5_lab = TextMobject(r"$dy$", color = ORANGE) + vector5_lab.move_to(self.graph_origin+1.7*XTD*RIGHT+ 1.4*YTD*UP) + vector5_lab.scale(0.7) + + self.play(GrowArrow(vector4),Write(vector4_lab)) + self.play(GrowArrow(vector5),Write(vector5_lab)) + self.wait(2) + + + + def display_text(self): + text1 = TextMobject(r"$\vec r(t)$",r"+", r"$\vec r(t + h) - \vec r(t)$") + text1[0].set_color(RED) + text1[2].set_color(PINK) + text1.scale(0.7) + + text2 = TextMobject(r"$\vec r(t + h)$", color = YELLOW_C) + text2.scale(0.7) + + text3 = TextMobject(r"$ \vec r(t + h) - \vec r(t)$", color = PINK) + text3.scale(0.7) + + text4 = TextMobject(r"[", r"$x(t+h)$", r"$\vec i$", r"+", r"$y(t+h)$", r"$\vec j$", r"$] - [$", r"$x(t)$", r"$\vec i$", r"+", r"y(t)", r"$\vec j$", r"]") + text4.set_color_by_tex(r"\vec i", BLUE) + text4.set_color_by_tex(r"\vec j", GREEN) + text4[1].set_color(YELLOW_C) + text4[4].set_color(YELLOW_C) + text4[-6].set_color(RED) + text4[-3].set_color(RED) + text4.scale(0.7) + + text5 = TextMobject(r"$[x(t+h) - x(t)]$", r"$\vec i$", r"+", r"$[y(t+h) + y(t)]$", r"$\vec j$") + text5.set_color_by_tex(r"\vec i", BLUE) + text5.set_color_by_tex(r"\vec j", GREEN) + text5[0].set_color(PURPLE) + text5[3].set_color(ORANGE) + text5.scale(0.7) + + text6 = TextMobject(r"$\frac{[\vec r(t + h) - \vec r(t)]}{h}$", r"=", r"$\frac{[x(t+h) - x(t)]}{h}$", r"$\vec i$", r"+", r"$\frac{[y(t+h) + y(t)]}{h}$", r"$\vec j$") + text6.set_color_by_tex(r"\vec i", BLUE) + text6.set_color_by_tex(r"\vec j", GREEN) + text6[0].set_color(PINK) + text6[2].set_color(PURPLE) + text6[-2].set_color(ORANGE) + text6.scale(0.8) + + text7 = TextMobject(r"$\lim_{h \rightarrow 0}$", r"$\frac{[\vec r(t + h) - \vec r(t)]}{h}$", r"=", r"$\lim_{h \rightarrow 0}$", r"$\frac{[x(t+h) - x(t)]}{h}$", r"$\vec i$", r"+", r"$\lim_{h \rightarrow 0}$", r"$\frac{[y(t+h) + y(t)]}{h}$", r"$\vec j$") + text7.set_color_by_tex(r"\vec i", BLUE) + text7.set_color_by_tex(r"\vec j", GREEN) + text7[1].set_color(PINK) + text7[4].set_color(PURPLE) + text7[-2].set_color(ORANGE) + text7.scale(0.6) + + text8 = TextMobject(r"$\vec r'(t)$", r"=",r"$\vec x'(t)$", r"$\vec i$", r"+", r"$\vec y'(t)$", r"$\vec j$") + text8.set_color_by_tex(r"\vec i", BLUE) + text8.set_color_by_tex(r"\vec j", GREEN) + text8[0].set_color(PINK) + text8[2].set_color(PURPLE) + text8[5].set_color(ORANGE) + text8.scale(0.7) + + text9 = TextMobject(r"$\frac{d \vec r}{dt}$", r"=", r"$\frac{d \vec x}{dt}$", r"$\vec i$", r"+", r"$\frac{d \vec y}{dt}$", r"$\vec j$") + text9.set_color_by_tex(r"\vec i", BLUE) + text9.set_color_by_tex(r"\vec j", GREEN) + text9[0].set_color(PINK) + text9[2].set_color(PURPLE) + text9[5].set_color(ORANGE) + text9.scale(0.7) + + + text10 = TextMobject(r"$d \vec r$", r"=", r"$\frac{d \vec x}{dt}dt$", r"$\vec i$", r"+", r"$\frac{d \vec y}{dt}dt$", r"$\vec j$") + text10.set_color_by_tex(r"\vec i", BLUE) + text10.set_color_by_tex(r"\vec j", GREEN) + text10[0].set_color(PINK) + text10[2].set_color(PURPLE) + text10[5].set_color(ORANGE) + text10.scale(0.7) + + text11 = TextMobject(r"$d \vec r$", r"=", r"$x'(t)dt$", r"$\vec i$", r"+", r"$y'(t)dt$", r"$\vec j$") + text11.set_color_by_tex(r"\vec i", BLUE) + text11.set_color_by_tex(r"\vec j", GREEN) + text11[0].set_color(PINK) + text11[2].set_color(PURPLE) + text11[5].set_color(ORANGE) + text11.scale(0.7) + + text12 = TextMobject(r"$d \vec r$", r"=", r"$dx$", r"$\vec i$", r"+", r"$dy$", r"$\vec j$") + text12.set_color_by_tex(r"\vec i", BLUE) + text12.set_color_by_tex(r"\vec j", GREEN) + text12[0].set_color(PINK) + text12[2].set_color(PURPLE) + text12[5].set_color(ORANGE) + text12.scale(0.7) + + + text1.move_to(1*UP+2.7*RIGHT) + text2.move_to(1*UP+2.7*RIGHT) + text3.move_to(1*UP+2.7*RIGHT) + text4.move_to(1*UP+2.7*RIGHT) + text5.move_to(1*UP+2.7*RIGHT) + text6.move_to(1*UP+2.7*RIGHT) + text7.move_to(1*UP+2.5*RIGHT) + text8.move_to(1*UP+2.7*RIGHT) + text9.move_to(1*UP+2.7*RIGHT) + text10.move_to(1*UP+2.7*RIGHT) + text11.move_to(1*UP+2.7*RIGHT) + text12.move_to(1*UP+2.7*RIGHT) + + brace1 = Brace(text7[0:2], DOWN, buff = SMALL_BUFF) + brace2 = Brace(text7[3:6], UP, buff = SMALL_BUFF) + brace3 = Brace(text7[7:], DOWN, buff = SMALL_BUFF) + t1 = brace1.get_text(r"$\vec r'(t)$") + t1.set_color(PINK) + + t2 = brace2.get_text(r"$\vec x'(t)$") + t2.set_color(PURPLE) + + t3 = brace3.get_text(r"$\vec y'(t)$") + t3.set_color(ORANGE) + + + self.play(Write(text1)) + self.play(Transform(text1, text2)) + self.wait(1) + + self.play(Transform(text1, text3)) + self.wait(1) + + self.play(Transform(text1, text4)) + self.wait(1) + + self.play(Transform(text1, text5)) + self.wait(1) + + self.play(Transform(text1, text6)) + self.wait(1) + + self.play(Transform(text1, text7)) + self.wait(1) + + self.play( + GrowFromCenter(brace1), + FadeIn(t1), + ) + self.wait() + self.play( + ReplacementTransform(brace1.copy(),brace2), + ReplacementTransform(t1.copy(),t2) + ) + self.wait() + self.play( + ReplacementTransform(brace2.copy(),brace3), + ReplacementTransform(t2.copy(),t3) + ) + self.wait() + + self.play(FadeOut(brace1), FadeOut(t1), FadeOut(brace2), FadeOut(t2), FadeOut(brace3), FadeOut(t3),) + self.wait() + + self.play(Transform(text1, text8)) + self.wait(1) + + self.play(Transform(text1, text9)) + self.wait(1) + + self.play(Transform(text1, text10)) + self.wait(1) + + self.play(Transform(text1, text11)) + self.wait(1) + + self.play(Transform(text1, text12)) + self.wait(1) + + + + + diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_examples.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_examples.py new file mode 100644 index 0000000..7322e47 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_examples.py @@ -0,0 +1,69 @@ +from manimlib.imports import * + +class Examples(GraphScene): + def construct(self): + + rectangle = Rectangle(height = 3, width = 4, color = GREEN) + square = Square(side_length = 5, color = PURPLE) + circle = Circle(radius = 2, color = PINK) + radius = Line(ORIGIN,2*RIGHT) + + radius.set_color(RED) + + rectangle_area_func = TextMobject(r"$Area = f(Length, Breadth)$") + rectangle_area_func.scale(0.6) + square_area_func = TextMobject(r"$Area = f(Length)$") + circle_area_func = TextMobject(r"$Area = f(r)$") + + + rectangle_area = TextMobject(r"$Area = Length \times Breadth$") + rectangle_area.scale(0.6) + square_area = TextMobject(r"$Area = Length^2$") + circle_area = TextMobject(r"$Area = \pi r^2$") + + braces_rect1 = Brace(rectangle, LEFT) + eq_text1 = braces_rect1.get_text("Length") + braces_rect2 = Brace(rectangle, UP) + eq_text2 = braces_rect2.get_text("Breadth") + + braces_square = Brace(square, LEFT) + braces_square_text = braces_square.get_text("Length") + + radius_text = TextMobject("r") + radius_text.next_to(radius,UP) + + + + self.play(ShowCreation(rectangle)) + self.wait(1) + self.play(GrowFromCenter(braces_rect1),Write(eq_text1),GrowFromCenter(braces_rect2),Write(eq_text2)) + self.wait(1) + self.play(Write(rectangle_area_func)) + self.wait(1) + self.play(Transform(rectangle_area_func, rectangle_area)) + self.wait(1) + self.play(FadeOut(braces_rect1),FadeOut(eq_text1),FadeOut(braces_rect2),FadeOut(eq_text2),FadeOut(rectangle_area_func)) + + + self.play(Transform(rectangle, square)) + self.wait(1) + self.play(GrowFromCenter(braces_square),Write(braces_square_text)) + self.wait(1) + self.play(Write(square_area_func)) + self.wait(1) + self.play(Transform(square_area_func, square_area)) + self.wait(1) + self.play(FadeOut(braces_square),FadeOut(braces_square_text),FadeOut(square_area_func)) + + + self.play(Transform(rectangle, circle)) + self.wait(1) + self.play(ShowCreation(radius),Write(radius_text)) + self.wait(1) + self.play(FadeOut(radius_text),FadeOut(radius)) + self.wait(1) + self.play(Write(circle_area_func)) + self.wait(1) + self.play(Transform(circle_area_func, circle_area)) + self.wait(1) + self.play(FadeOut(circle_area_func)) \ No newline at end of file diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_plot_sphere.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_plot_sphere.py new file mode 100644 index 0000000..baf08b1 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_plot_sphere.py @@ -0,0 +1,42 @@ +from manimlib.imports import * + +class Sphere(ThreeDScene): + def construct(self): + axes = ThreeDAxes() # creates a 3D Axis + + sphere = ParametricSurface( + lambda u, v: np.array([ + np.sin(u)*np.cos(v), + np.sin(u)*np.sin(v), + np.cos(u) + ]),u_min=0,u_max=PI,v_min=0,v_max=2*PI,checkerboard_colors=[RED_D, RED_E], + resolution=(15, 32)).scale(2) + + + + #self.set_camera_orientation(phi=0 * DEGREES,theta=270*DEGREES) + + text3d = TextMobject(r"$f(x,y) \rightarrow Point(x,y,z)$") + text3d1 = TextMobject(r"$f(x,y) \rightarrow Point(x,y, 1 - x^2 - y^2)$") + self.add_fixed_in_frame_mobjects(text3d) + text3d.scale(0.7) + text3d1.scale(0.7) + text3d.to_corner(UL) + text3d1.to_corner(UL) + text3d.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE) + text3d1.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE) + self.play(Write(text3d)) + self.wait(1) + + self.play(Transform(text3d,text3d1)) + self.add_fixed_in_frame_mobjects(text3d1) + self.play(FadeOut(text3d)) + + + self.set_camera_orientation(phi=75 * DEGREES) + self.begin_ambient_camera_rotation(rate=0.3) + + + self.add(axes) + self.play(Write(sphere)) + self.wait(5) \ No newline at end of file diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_respresntation.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_respresntation.py new file mode 100644 index 0000000..4bfcf21 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_respresntation.py @@ -0,0 +1,80 @@ +from manimlib.imports import * + +class MultivariableFunc(Scene): + def construct(self): + + topic = TextMobject("Multivariable Functions") + topic.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE) + topic.scale(2) + + self.play(Write(topic)) + self.wait(1) + self.play(FadeOut(topic)) + + + circle = Circle() + circle.scale(3) + + eqn1 = TextMobject(r"f(x,y) = $x^2y$") + eqn1.set_color(YELLOW) + + + + number1 = TextMobject("(2,1)") + number1.move_to(3*UP+ 3*LEFT) + number1.scale(1.2) + number1.set_color(GREEN) + + output1 = TextMobject("4") + output1.scale(1.5) + output1.set_color(BLUE) + + eqn1_1 = TextMobject(r"f(2,1) = $2^2(1)$") + eqn1_1.set_color(YELLOW) + + + self.play(ShowCreation(circle),Write(eqn1)) + self.wait(1) + self.play(ApplyMethod(number1.move_to, 0.6*LEFT)) + self.play(FadeOut(number1)) + self.play(Transform(eqn1, eqn1_1)) + self.wait(1) + self.play(ApplyMethod(output1.move_to, 3*DOWN+4*RIGHT)) + self.wait(1) + self.play(FadeOut(output1)) + + + eqn2 = TextMobject(r"f(x,y,z) = $x^2y+2yz$") + eqn2.set_color(YELLOW) + + number2 = TextMobject("(2,1,3)") + number2.move_to(3*UP+ 3*LEFT) + number2.scale(1.2) + number2.set_color(GREEN) + + output2 = TextMobject("8") + output2.scale(1.5) + output2.set_color(BLUE) + + eqn2_1 = TextMobject(r"f(2,1,3) = $2^2(1) + 2(1)(3)$") + eqn2_1.set_color(YELLOW) + + eqn2_2 = TextMobject(r"f(2,1,3) = $2 + 6$") + eqn2_2.set_color(YELLOW) + + + + self.play(FadeOut(eqn1)) + self.play(Write(eqn2)) + + self.wait(1) + self.play(ApplyMethod(number2.move_to, 1.2*LEFT)) + self.play(FadeOut(number2)) + self.play(Transform(eqn2, eqn2_1)) + self.wait(1) + self.play(Transform(eqn2, eqn2_2)) + self.wait(1) + self.play(ApplyMethod(output2.move_to, 3*DOWN+4*RIGHT)) + self.wait(1) + self.play(FadeOut(output2),FadeOut(eqn2),FadeOut(circle)) + self.wait(2) \ No newline at end of file diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_vectorvf_sine.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_vectorvf_sine.py new file mode 100644 index 0000000..06e225e --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_vectorvf_sine.py @@ -0,0 +1,91 @@ +from manimlib.imports import * + +class SineVectors(GraphScene): + CONFIG = { + "x_min": 0, + "x_max": 10, + "y_min": -1, + "y_max": 1, + "graph_origin": ORIGIN+4*LEFT, + #"x_labeled_nums": list(range(-5, 6)), + #"y_labeled_nums": list(range(0, 5)), + } + 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) + + self.setup_axes(animate = True) + + + sine1 = self.get_graph(lambda x : np.sin(x), x_min = 0, x_max = 1.575, color = GREEN) + + point1 = Dot().shift(self.graph_origin+1*YTD*UP + 1.575*XTD*RIGHT) + point1_lab = TextMobject(r"$t = (\frac{\pi}{2})$") + point1_lab.scale(0.7) + point1_lab.next_to(point1, UP) + + vector1 = Arrow(self.graph_origin, self.graph_origin+1*YTD*UP + 1.575*XTD*RIGHT, buff=0.1, color = RED) + vector1_lab = TextMobject(r"$r(\frac{\pi}{2})$", color = RED) + vector1_lab.move_to(self.graph_origin+1.5*XTD*RIGHT+ 0.5*YTD*UP) + + self.play(GrowArrow(vector1),Write(vector1_lab)) + self.play(ShowCreation(point1), Write(point1_lab)) + self.play(ShowCreation(sine1)) + self.wait(1) + + + sine2 = self.get_graph(lambda x : np.sin(x), x_min = 1.575, x_max = 3.15, color = GREEN) + + point2 = Dot().shift(self.graph_origin+3.15*XTD*RIGHT) + point2_lab = TextMobject(r"$t = (\pi)$") + point2_lab.scale(0.7) + point2_lab.next_to(point2, UP+RIGHT) + + vector2 = Arrow(self.graph_origin, self.graph_origin+3.15*XTD*RIGHT, buff=0.1, color = BLUE) + vector2_lab = TextMobject(r"$r(\pi)$", color = BLUE) + vector2_lab.move_to(self.graph_origin+1.5*XTD*RIGHT+ 0.15*YTD*UP) + + self.play(GrowArrow(vector2),Write(vector2_lab)) + self.play(ShowCreation(point2), Write(point2_lab)) + self.play(ShowCreation(sine2)) + self.wait(1) + + + sine3 = self.get_graph(lambda x : np.sin(x), x_min = 3.15, x_max = 4.725, color = GREEN) + + point3 = Dot().shift(self.graph_origin+1*YTD*DOWN + 4.725*XTD*RIGHT) + point3_lab = TextMobject(r"$t = (\frac{3\pi}{2})$") + point3_lab.scale(0.7) + point3_lab.next_to(point3, DOWN) + + vector3 = Arrow(self.graph_origin, self.graph_origin+1*YTD*DOWN + 4.725*XTD*RIGHT, buff=0.1, color = YELLOW_C) + vector3_lab = TextMobject(r"$r(\frac{3\pi}{2})$", color = YELLOW_C) + vector3_lab.move_to(self.graph_origin+2*XTD*RIGHT+ 0.7*YTD*DOWN) + + self.play(GrowArrow(vector3),Write(vector3_lab)) + self.play(ShowCreation(point3), Write(point3_lab)) + self.play(ShowCreation(sine3)) + self.wait(1) + + + sine4 = self.get_graph(lambda x : np.sin(x), x_min = 4.725, x_max = 6.3, color = GREEN) + + point4 = Dot().shift(self.graph_origin+6.3*XTD*RIGHT) + point4_lab = TextMobject(r"$t = (2\pi)$") + point4_lab.scale(0.7) + point4_lab.next_to(point4, UP+RIGHT) + + vector4 = Arrow(self.graph_origin, self.graph_origin+6.3*XTD*RIGHT, buff=0.1, color = PURPLE) + vector4_lab = TextMobject(r"$r(2\pi)$", color = PURPLE) + vector4_lab.move_to(self.graph_origin+4.5*XTD*RIGHT+ 0.15*YTD*DOWN) + + self.play(GrowArrow(vector4),Write(vector4_lab)) + self.play(ShowCreation(point4), Write(point4_lab)) + self.play(ShowCreation(sine4)) + self.wait(3) + -- cgit From bb9e15afaafe5305d27e3037530831e33a3e254c Mon Sep 17 00:00:00 2001 From: nishanpoojary Date: Sun, 24 May 2020 17:45:13 +0530 Subject: Added Limits and Continuity Folder --- .../limit_approach_point.py | 66 ++++++++++++++++++++++ 1 file changed, 66 insertions(+) create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Limits and Continuity of Multivariable Functions/limit_approach_point.py (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives') diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Limits and Continuity of Multivariable Functions/limit_approach_point.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Limits and Continuity of Multivariable Functions/limit_approach_point.py new file mode 100644 index 0000000..57d1d45 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Limits and Continuity of Multivariable Functions/limit_approach_point.py @@ -0,0 +1,66 @@ +from manimlib.imports import * + +class Limit(GraphScene): + CONFIG = { + "x_min": 0, + "x_max": 4, + "y_min": 0, + "y_max": 4, + "graph_origin": ORIGIN + 3* DOWN+4*LEFT, + "x_labeled_nums": list(range(0, 4)), + "y_labeled_nums": list(range(0, 5)), + } + def construct(self): + topic = TextMobject("Different paths of approach to limit point") + topic.scale(1.5) + topic.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE) + self.play(Write(topic)) + self.wait(1) + self.play(FadeOut(topic)) + + + + XTD = self.x_axis_width/(self.x_max- self.x_min) + YTD = self.y_axis_height/(self.y_max- self.y_min) + + self.setup_axes(animate = True) + + y_x = self.get_graph(lambda x : x, x_min = -1, x_max = 4) + y_x_lab = self.get_graph_label(y_x, label = r"y = x") + + y_xsquare = self.get_graph(lambda x : x*x, x_min = -1, x_max = 4) + y_xsquare_lab = self.get_graph_label(y_xsquare, label = r"y = x^2") + + y_1 = self.get_graph(lambda x : 1, x_min = -1, x_max = 4) + y_1_lab = self.get_graph_label(y_1, label = r"y = 1") + + y_2minusx = self.get_graph(lambda x : 2 - x, x_min = -1, x_max = 4, color = RED) + y_2minusx_lab = self.get_graph_label(y_2minusx, label = r"y = 2 - x") + + limit_point = Dot().shift(self.graph_origin+1*XTD*RIGHT+1*YTD*UP) + limit_point_lab = TextMobject(r"(1,1)") + limit_point_lab.next_to(limit_point, DOWN) + + self.play(ShowCreation(limit_point)) + self.play(Write(limit_point_lab)) + self.wait(1) + + self.play(ShowCreation(y_x)) + self.play(Write(y_x_lab)) + self.wait(1) + + self.play(ShowCreation(y_xsquare)) + self.play(Write(y_xsquare_lab)) + self.wait(1) + + self.play(ShowCreation(y_1)) + self.play(Write(y_1_lab)) + self.wait(1) + + self.play(ShowCreation(y_2minusx)) + self.play(Write(y_2minusx_lab)) + self.wait(1) + + + + \ No newline at end of file -- cgit From ab5f5c2d48794961ace6716a1b0405c24495e9e1 Mon Sep 17 00:00:00 2001 From: nishanpoojary Date: Sun, 24 May 2020 17:46:00 +0530 Subject: Delete scalar_function_level_curves.mp4 --- .../Scalar Functions/scalar_function_level_curves.mp4 | Bin 726339 -> 0 bytes 1 file changed, 0 insertions(+), 0 deletions(-) delete mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_level_curves.mp4 (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives') diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_level_curves.mp4 b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_level_curves.mp4 deleted file mode 100644 index 6af2670..0000000 Binary files a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_level_curves.mp4 and /dev/null differ -- cgit From d5f72078a32cd6196b34778ccc4ae8cf299b2d22 Mon Sep 17 00:00:00 2001 From: nishanpoojary Date: Sun, 24 May 2020 17:46:10 +0530 Subject: Delete scalar_function_level_curves2.mp4 --- .../scalar_function_level_curves2.mp4 | Bin 2088849 -> 0 bytes 1 file changed, 0 insertions(+), 0 deletions(-) delete mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_level_curves2.mp4 (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives') diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_level_curves2.mp4 b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_level_curves2.mp4 deleted file mode 100644 index b21ae25..0000000 Binary files a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_level_curves2.mp4 and /dev/null differ -- cgit From b705303069a5fd14c5f8bde6fdb7d42454103782 Mon Sep 17 00:00:00 2001 From: nishanpoojary Date: Sun, 24 May 2020 17:46:53 +0530 Subject: Add files via upload --- .../Scalar Functions/Scalar_Function_Quiz.pdf | Bin 0 -> 87455 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/Scalar_Function_Quiz.pdf (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives') diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/Scalar_Function_Quiz.pdf b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/Scalar_Function_Quiz.pdf new file mode 100644 index 0000000..6d94a2c Binary files /dev/null and b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/Scalar_Function_Quiz.pdf differ -- cgit From 00cf8aab6f8073ad4fd14cffabf90bf55a70d5eb Mon Sep 17 00:00:00 2001 From: nishanpoojary Date: Sun, 24 May 2020 17:47:31 +0530 Subject: Add files via upload --- .../Multivariable_Functions_Quiz.pdf | Bin 0 -> 109631 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/Multivariable_Functions_Quiz.pdf (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives') diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/Multivariable_Functions_Quiz.pdf b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/Multivariable_Functions_Quiz.pdf new file mode 100644 index 0000000..7895843 Binary files /dev/null and b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/Multivariable_Functions_Quiz.pdf differ -- cgit From fed36d85239ebc725f0eabc50c67394ea32f203f Mon Sep 17 00:00:00 2001 From: nishanpoojary Date: Sun, 24 May 2020 17:55:13 +0530 Subject: Updated Readme.md --- .../multivariable-functions-and-paritial-derivatives/README.md | 9 +++++++++ 1 file changed, 9 insertions(+) (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives') diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/README.md b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/README.md index e69de29..b50200d 100644 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/README.md +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/README.md @@ -0,0 +1,9 @@ +# Contributer: Nishan Poojary +Github Account : nishanpoojary +

+## Sub-Topics Covered: ++ Scalar Functions ++ Multivariable Functions ++ Limits and continuity of Multivariable Function ++ Partial Derivatives ++ Directonal Derivatives -- cgit From cf3141c14d109277d01fe7fcbd4bee5171390d1a Mon Sep 17 00:00:00 2001 From: nishanpoojary Date: Sun, 24 May 2020 18:02:15 +0530 Subject: Add files via upload --- .../Scalar Functions/gifs/domain_range.gif | Bin 0 -> 19837 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/gifs/domain_range.gif (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives') diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/gifs/domain_range.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/gifs/domain_range.gif new file mode 100644 index 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a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/gifs/scalar_function_neural_nets.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/gifs/scalar_function_neural_nets.gif new file mode 100644 index 0000000..9d24688 Binary files /dev/null and b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/gifs/scalar_function_neural_nets.gif differ diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/gifs/scalar_function_parabola_example.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/gifs/scalar_function_parabola_example.gif new file mode 100644 index 0000000..3fdecf4 Binary files /dev/null and b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar 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create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/gifs/multivariable_func_plot_sphere.gif create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/gifs/multivariable_func_respresntation.gif create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/gifs/multivariable_func_vectorvf_sine.gif (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives') diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/gifs/multivariable_func_derivative_vectorvf.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/gifs/multivariable_func_derivative_vectorvf.gif new file mode 100644 index 0000000..a94de90 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a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/gifs/multivariable_func_vectorvf_sine.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/gifs/multivariable_func_vectorvf_sine.gif new file mode 100644 index 0000000..4f6b931 Binary files /dev/null and b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/gifs/multivariable_func_vectorvf_sine.gif differ -- cgit From 4e99a40878f7ba614e0c693ba22de3ae21b1ffd7 Mon Sep 17 00:00:00 2001 From: nishanpoojary Date: Sun, 24 May 2020 18:27:40 +0530 Subject: Added gif to Limits and Continuity Folder --- .../gifs/limit_approach_point.gif | Bin 0 -> 47411 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Limits and Continuity of Multivariable Functions/gifs/limit_approach_point.gif (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives') diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Limits and Continuity of Multivariable Functions/gifs/limit_approach_point.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Limits and Continuity of Multivariable Functions/gifs/limit_approach_point.gif new file mode 100644 index 0000000..830b6f1 Binary files /dev/null and b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Limits and Continuity of Multivariable Functions/gifs/limit_approach_point.gif differ -- cgit From b6de789e96b766e899195c8915017f76698380fa Mon Sep 17 00:00:00 2001 From: nishanpoojary Date: Tue, 26 May 2020 12:17:06 +0530 Subject: Delete scalar_function_parabola_example.py --- .../scalar_function_parabola_example.py | 35 ---------------------- 1 file changed, 35 deletions(-) delete mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_parabola_example.py (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives') diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_parabola_example.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_parabola_example.py deleted file mode 100644 index 74dc063..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_parabola_example.py +++ /dev/null @@ -1,35 +0,0 @@ -from manimlib.imports import * - -class Parabola(ThreeDScene): - def construct(self): - axes = ThreeDAxes() # creates a 3D Axis - - paraboloid = ParametricSurface( - lambda u, v: np.array([ - 2*np.cosh(u)*np.cos(v), - 2*np.cosh(u)*np.sin(v), - 2*np.sinh(u) - ]),v_min=0,v_max=TAU,u_min=0,u_max=2,checkerboard_colors=[YELLOW_D, YELLOW_E], - resolution=(15, 32)) - - text3d = TextMobject(r"Plot of $f: \mathbb{R}^2 \rightarrow \mathbb{R}$", "z = f(x,y)") - self.add_fixed_in_frame_mobjects(text3d) - text3d[0].move_to(4*LEFT+2*DOWN) - text3d[1].next_to(text3d[0], DOWN) - text3d[0].set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE) - text3d[1].set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE) - - #self.set_camera_orientation(phi=0 * DEGREES,theta=270*DEGREES) - self.move_camera(phi=110* DEGREES,theta=45*DEGREES) - self.add(axes) - self.play(ShowCreation(paraboloid)) - self.play(Write(text3d[0])) - self.play(Write(text3d[1])) - self.begin_ambient_camera_rotation(rate=0.2) - self.wait(3) - self.move_camera(phi=0 * DEGREES,theta=180*DEGREES,run_time=3) - self.wait(3) - self.move_camera(phi=110* DEGREES,theta=90*DEGREES,run_time=3) - self.wait(3) - - \ No newline at end of file -- cgit From d6f6012145d9b00b1a4b9c569e7dcffb92eb9d56 Mon Sep 17 00:00:00 2001 From: nishanpoojary Date: Tue, 26 May 2020 12:17:16 +0530 Subject: Delete scalar_function_neural_nets.py --- .../scalar_function_neural_nets.py | 177 --------------------- 1 file changed, 177 deletions(-) delete mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_neural_nets.py (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives') diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_neural_nets.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_neural_nets.py deleted file mode 100644 index eb6bf45..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_neural_nets.py +++ /dev/null @@ -1,177 +0,0 @@ -from manimlib.imports import * - -class SigmoidFunc(GraphScene): - CONFIG = { - "x_min": -4, - "x_max": 4, - "y_min": -1, - "y_max": 1, - "graph_origin": ORIGIN + 0.8*DOWN, - "x_labeled_nums": list(range(-4, 5)), - "y_labeled_nums": list(range(-1, 2)), - "y_axis_height": 4.5, - } - 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) - - topic = TextMobject("Sigmoid Function") - topic.move_to(3.2*UP) - topic.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE) - - self.setup_axes(animate = True) - sigmoid_func = self.get_graph(lambda x : (1/(1 + np.exp(-x))), x_min = -4, x_max = 4) - sigmoid_lab = self.get_graph_label(sigmoid_func, label = r"\frac{1}{1 + e^{-z}}") - - - - - self.play(ShowCreation(sigmoid_func),Write(sigmoid_lab)) - self.play(Write(topic)) - self.wait(2) - self.play(FadeOut(sigmoid_func), FadeOut(sigmoid_lab)) - self.wait(1) - - - -class NeuralNet(GraphScene): - def construct(self): - - sigmoid_exp = TextMobject(r"g(z) = g($\theta^T$ X) = $\frac{1}{1 + e^{-z}}$") - sigmoid_exp.move_to(3*UP + 4*LEFT) - sigmoid_exp.scale(0.8) - sigmoid_exp.set_color(BLUE) - sigmoid_exp1 = TextMobject(r"Predict: 'y = 1'",r"When g(z) $\geq$ 0.5, z $\geq$ 0, $\theta^T$ X $\geq$ 0") - sigmoid_exp2 = TextMobject(r"Predict: 'y = 0'", r"When g(z) $\leq$ 0.5, z $\leq$ 0, $\theta^T$ X $\leq$ 0") - sigmoid_exp1.scale(0.5) - sigmoid_exp2.scale(0.5) - sigmoid_exp1.set_color(PURPLE) - sigmoid_exp2.set_color(PURPLE) - - sigmoid_exp1[0].next_to(sigmoid_exp, 1.5*DOWN) - sigmoid_exp1[1].next_to(sigmoid_exp1[0], DOWN) - sigmoid_exp2[0].next_to(sigmoid_exp1[1], 1.5*DOWN) - sigmoid_exp2[1].next_to(sigmoid_exp2[0], DOWN) - - - self.play(Write(sigmoid_exp)) - self.play(Write(sigmoid_exp1[0]), Write(sigmoid_exp1[1])) - self.play(Write(sigmoid_exp2[0]), Write(sigmoid_exp2[1])) - self.wait(2) - - - neuron1 = Circle() - neuron1.set_fill(YELLOW_A, opacity = 0.5) - - neuron2 = Circle() - neuron2.set_fill(ORANGE, opacity = 0.5) - - neuron3 = Circle() - neuron3.set_fill(GREEN_E, opacity = 0.5) - - neuron1.move_to(2*UP+RIGHT) - neuron2.move_to(2*DOWN+RIGHT) - neuron3.move_to(4*RIGHT) - - arrow1 = Arrow(neuron1.get_right(),neuron3.get_left(),buff=0.1) - arrow1.set_color(RED) - arrow2 = Arrow(neuron2.get_right(),neuron3.get_left(),buff=0.1) - arrow2.set_color(RED) - - arrow3 = Arrow(neuron3.get_right(),7*RIGHT,buff=0.1) - arrow3.set_color(RED) - - - sign1 = TextMobject("+1") - sign1.move_to(2*UP+RIGHT) - sign1.scale(2) - sign2 = TextMobject(r"$x_1$") - sign2.move_to(2*DOWN+RIGHT) - sign2.scale(2) - sign3 = TextMobject(r"$h_{\theta}(x)$") - sign3.move_to(6*RIGHT+0.4*DOWN) - sign3.scale(0.7) - sign4 = TextMobject(r"$= g(10 - 20x_1)$") - sign4.next_to(sign3,DOWN) - sign4.scale(0.5) - sign5 = TextMobject(r"$= g(10 - 20x_1)$") - sign5.next_to(sign3,DOWN) - sign5.scale(0.5) - sign6 = TextMobject(r"$= g(10 - 20x_1)$") - sign6.next_to(sign3,DOWN) - sign6.scale(0.5) - - - weight1 = TextMobject("10") - weight1.next_to(arrow1,UP) - weight2 = TextMobject("-20") - weight2.next_to(arrow2,DOWN) - - gate = TextMobject("NOT GATE") - gate.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE) - gate.scale(1.5) - gate.move_to(3*RIGHT+3.5*UP) - - - - truth_table = TextMobject(r"\begin{displaymath}\begin{array}{|c|c|} x & y\\ \hline 1 & 0 \\0 & 1 \\\end{array}\end{displaymath}") - truth_table.next_to(sigmoid_exp2[1], 3*DOWN) - - values = TextMobject("1", "0") - values.scale(2) - - sign4_trans1 = TextMobject(r"$= g(10 - 20(1))$") - sign4_trans2 = TextMobject(r"$= g(10 - 20(0))$") - sign4_trans1.next_to(sign3,DOWN) - sign4_trans2.next_to(sign3,DOWN) - sign4_trans1.scale(0.5) - sign4_trans2.scale(0.5) - - - - output1 = TextMobject("y = 0") - output2 = TextMobject("y = 1") - output1.next_to(sign4,DOWN) - output2.next_to(sign4,DOWN) - output1.scale(1.5) - output2.scale(1.5) - - - - self.play(ShowCreation(neuron1),ShowCreation(neuron2)) - self.play(ShowCreation(neuron3)) - self.play(ShowCreation(sign1),ShowCreation(sign2)) - self.wait(1) - - self.play(GrowArrow(arrow1)) - self.play(GrowArrow(arrow2)) - self.play(ShowCreation(weight1),ShowCreation(weight2)) - - - - self.play(GrowArrow(arrow3)) - self.play(Write(sign3),Write(sign4)) - - self.play(Write(gate)) - self.play(ShowCreation(truth_table)) - - self.play(ApplyMethod(values[0].move_to, 2*DOWN+RIGHT)) - self.play(FadeOut(values[0])) - self.play(Transform(sign4,sign4_trans1)) - self.play(Write(output1)) - self.wait(1) - self.play(FadeOut(output1)) - self.play(Transform(sign4, sign5)) - - - self.play(ApplyMethod(values[1].move_to, 2*DOWN+RIGHT)) - self.play(FadeOut(values[1])) - self.play(Transform(sign4,sign4_trans2)) - self.play(Write(output2)) - self.wait(1) - self.play(FadeOut(output2)) - self.play(Transform(sign4, sign6)) - - self.wait(2) - - -- cgit From 8bbc08351b26bff772c5a7b3e17aec3ee0d3392e Mon Sep 17 00:00:00 2001 From: nishanpoojary Date: Tue, 26 May 2020 12:17:24 +0530 Subject: Delete scalar_function_domain_range.py --- .../scalar_function_domain_range.py | 132 --------------------- 1 file changed, 132 deletions(-) delete mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_domain_range.py (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives') diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_domain_range.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_domain_range.py deleted file mode 100644 index 9b1ca7b..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_domain_range.py +++ /dev/null @@ -1,132 +0,0 @@ -# Plotting Graphs -from manimlib.imports import * - -class PlotGraphs(GraphScene): - CONFIG = { - "x_min": -5, - "x_max": 5, - "y_min": 0, - "y_max": 4, - "graph_origin": ORIGIN + 2.5* DOWN, - "x_labeled_nums": list(range(-5, 6)), - "y_labeled_nums": list(range(0, 5)), - } - def construct(self): - - topic = TextMobject("Domain and Range") - topic.scale(2) - topic.set_color(YELLOW) - self.play(Write(topic)) - self.play(FadeOut(topic)) - self.wait(1) - - - XTD = self.x_axis_width/(self.x_max- self.x_min) - YTD = self.y_axis_height/(self.y_max- self.y_min) - - self.setup_axes(animate = True) - - graphobj = self.get_graph(lambda x : np.sqrt(x + 4), x_min = -4, x_max = 5) - graph_lab = self.get_graph_label(graphobj, label = r"\sqrt{x + 4}") - - - rangeline1 = Arrow(self.graph_origin+2.2*YTD*UP+5*XTD*LEFT, self.graph_origin+4.1*YTD*UP+5*XTD*LEFT) - rangeline2 = Arrow(self.graph_origin+1.7*YTD*UP+5*XTD*LEFT, self.graph_origin+5*XTD*LEFT) - rangeline1.set_color(RED) - rangeline2.set_color(RED) - - rangeMsg = TextMobject(r"Range: $y \geq 0$") - rangeMsg.move_to(self.graph_origin+2*YTD*UP+5*XTD*LEFT) - rangeMsg.scale(0.5) - rangeMsg.set_color(YELLOW) - - domainline1 = Line(self.graph_origin+0.6*YTD*DOWN+1.2*XTD*LEFT, self.graph_origin+0.6*YTD*DOWN + 4*XTD*LEFT) - domainline2 = Arrow(self.graph_origin+0.6*YTD*DOWN+1.1*XTD*RIGHT, self.graph_origin+0.6*YTD*DOWN + 5.3*XTD*RIGHT) - domainline1.set_color(PINK) - domainline2.set_color(PINK) - - domainMsg = TextMobject(r"Domain: $x \geq -4$") - domainMsg.move_to(self.graph_origin+0.6*YTD*DOWN) - domainMsg.scale(0.5) - domainMsg.set_color(GREEN) - - - - - self.play(ShowCreation(graphobj)) - self.play(ShowCreation(graph_lab)) - self.wait(1) - self.play(GrowArrow(rangeline1)) - self.play(GrowArrow(rangeline2)) - self.play(Write(rangeMsg)) - self.wait(1) - self.play(GrowArrow(domainline1)) - self.play(GrowArrow(domainline2)) - self.play(Write(domainMsg)) - self.wait(3) - - self.wait(2) - - - - -class PlotSineGraphs(GraphScene): - CONFIG = { - "x_min": -8, - "x_max": 8, - "y_min": -1, - "y_max": 1, - "graph_origin": ORIGIN, - "x_labeled_nums": list(range(-8, 9)), - "y_labeled_nums": list(range(-1, 2)), - } - 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) - - self.setup_axes(animate = True) - - sineobj = self.get_graph(lambda x : np.sin(x), x_min = -7, x_max = 8) - sine_lab = self.get_graph_label(sineobj, label = "\\sin(x)") - - - rangeline1 = Line(8*XTD*LEFT,1*YTD*UP+8*XTD*LEFT) - rangeline2 = Line(8*XTD*LEFT,1*YTD*DOWN+8*XTD*LEFT) - rangeline1.set_color(RED) - rangeline2.set_color(RED) - - rangeMsg = TextMobject(r"Range: $-1 \leq y \leq 1$") - rangeMsg.move_to(1.1*YTD*UP+8.5*XTD*LEFT) - rangeMsg.scale(0.5) - rangeMsg.set_color(YELLOW) - - - domainline1 = Arrow(1.1*YTD*DOWN+2*XTD*LEFT, 1.1*YTD*DOWN + 8.5*XTD*LEFT) - domainline2 = Arrow(1.1*YTD*DOWN+2*XTD*RIGHT, 1.1*YTD*DOWN + 8.5*XTD*RIGHT) - domainline1.set_color(PINK) - domainline2.set_color(PINK) - - domainMsg = TextMobject(r"Domain: $[-\infty, \infty]$") - domainMsg.move_to(1.1*YTD*DOWN) - domainMsg.scale(0.5) - domainMsg.set_color(GREEN) - - - - self.play(ShowCreation(sineobj)) - self.play(ShowCreation(sine_lab)) - self.wait(1) - self.play(GrowArrow(rangeline1)) - self.play(GrowArrow(rangeline2)) - self.play(Write(rangeMsg)) - self.wait(1) - self.play(GrowArrow(domainline1)) - self.play(GrowArrow(domainline2)) - self.play(Write(domainMsg)) - self.wait(3) - - - \ No newline at end of file -- cgit From 54f1ced7c719db38c5f0801a097e360c459d1637 Mon Sep 17 00:00:00 2001 From: nishanpoojary Date: Tue, 26 May 2020 12:17:32 +0530 Subject: Delete scalar_function_application.py --- .../scalar_function_application.py | 129 --------------------- 1 file changed, 129 deletions(-) delete mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_application.py (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives') diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_application.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_application.py deleted file mode 100644 index 56b3e53..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/scalar_function_application.py +++ /dev/null @@ -1,129 +0,0 @@ -from manimlib.imports import * - -class ScalarApplication(ThreeDScene): - def construct(self): - axes = ThreeDAxes() # creates a 3D Axis - - cube = Cube() - cube.set_fill(YELLOW_E, opacity = 0.1) - cube.scale(2) - self.set_camera_orientation(phi=0 * DEGREES,theta=270*DEGREES) - self.play(ShowCreation(cube),ShowCreation(axes)) - - dot = Sphere() - dot.scale(0.1) - dot.move_to(np.array([1,0.5,1])) - dot.set_fill(RED) - - #dot = Dot(np.array([1,0.5,1]), color = RED) - temp_func = TextMobject("T(x,y,z)") - temp_func.next_to(dot,RIGHT) - temp_func.set_color(RED) - temp_func_trans = TextMobject("T(1,0.5,1)") - temp_func_trans.next_to(dot,RIGHT) - temp_func_trans.set_color(RED) - temp = TextMobject(r"$36 ^\circ$") - temp.next_to(dot,RIGHT) - temp.set_color(RED_E) - - - self.play(ShowCreation(dot)) - self.play(ShowCreation(temp_func)) - self.play(Transform(temp_func, temp_func_trans)) - self.wait(1) - self.play(Transform(temp_func, temp)) - - - - - dot1 = Sphere() - dot1.scale(0.1) - dot1.move_to(np.array([-1,-0.8,-1.5])) - dot1.set_fill(BLUE_E) - #dot1 = Dot(np.array([-1,-0.8,-1.5]), color = BLUE) - temp_func1 = TextMobject("T(x,y,z)") - temp_func1.next_to(dot1,LEFT) - temp_func1.set_color(BLUE) - temp_func_trans1 = TextMobject("T(-1,-0.8,-1.5)") - temp_func_trans1.next_to(dot1,LEFT) - temp_func_trans1.set_color(BLUE) - temp1 = TextMobject(r"$24 ^\circ$") - temp1.next_to(dot1,LEFT) - temp1.set_color(BLUE) - - self.play(ShowCreation(dot1)) - self.play(ShowCreation(temp_func1)) - self.play(Transform(temp_func1, temp_func_trans1)) - self.wait(1) - self.play(Transform(temp_func1, temp1)) - - self.play(FadeOut(temp_func)) - self.play(FadeOut(temp_func1)) - - - self.move_camera(phi=80* DEGREES,theta=45*DEGREES,run_time=3) - - self.begin_ambient_camera_rotation(rate=0.2) - self.wait(4) - self.stop_ambient_camera_rotation() - self.wait(2) - - - - -class AddTempScale(Scene): - def construct(self): - temp_scale = ImageMobject("tempscale.png") - temp_scale.scale(4) - temp_scale.move_to(2*RIGHT) - self.play(ShowCreation(temp_scale)) - - - temp_func = TextMobject("T(x,y,z)") - temp_func.move_to(3*UP +2*LEFT) - temp_func.set_color(RED) - temp_func_trans = TextMobject("T(1,0.5,1)") - temp_func_trans.move_to(3*UP +2*LEFT) - temp_func_trans.set_color(RED) - temp = TextMobject(r"$36 ^\circ$") - temp.set_color(RED) - temp.move_to(3*UP +2*LEFT) - temp.scale(0.7) - - self.play(ShowCreation(temp_func)) - self.play(Transform(temp_func, temp_func_trans)) - self.wait(1) - self.play(Transform(temp_func, temp)) - self.play(ApplyMethod(temp_func.move_to, 1.8*UP +1.8*RIGHT)) - - - temp_func1 = TextMobject("T(x,y,z)") - temp_func1.move_to(2*UP +2*LEFT) - temp_func1.set_color(BLUE) - temp_func_trans1 = TextMobject("T(-1,-0.8,-1.5)") - temp_func_trans1.move_to(2*UP +2*LEFT) - temp_func_trans1.set_color(BLUE) - temp1 = TextMobject(r"$24 ^\circ$") - temp1.set_color(BLUE) - temp1.move_to(2*UP +2*LEFT) - temp1.scale(0.7) - - self.play(ShowCreation(temp_func1)) - self.play(Transform(temp_func1, temp_func_trans1)) - self.wait(1) - self.play(Transform(temp_func1, temp1)) - self.play(ApplyMethod(temp_func1.move_to, 0.6*UP +1.8*RIGHT)) - - - - transtext = TextMobject("Scalar Function Transform:") - transtext.set_color(GREEN) - transtext1 = TextMobject(r"$\mathbb{R}^3 \rightarrow \mathbb{R}$") - transtext1.set_color(YELLOW_E) - transtext.move_to(3*UP +3*LEFT) - transtext1.next_to(transtext,DOWN) - self.play(Write(transtext)) - self.play(Write(transtext1)) - self.wait(2) - - -- cgit From 58ddbb958fc1ac480567f2350ecbdecc63a3fd95 Mon Sep 17 00:00:00 2001 From: nishanpoojary Date: Tue, 26 May 2020 12:17:40 +0530 Subject: Delete Scalar_Function_Quiz.pdf --- .../Scalar Functions/Scalar_Function_Quiz.pdf | Bin 87455 -> 0 bytes 1 file changed, 0 insertions(+), 0 deletions(-) delete mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/Scalar_Function_Quiz.pdf (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives') diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/Scalar_Function_Quiz.pdf b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/Scalar_Function_Quiz.pdf deleted file mode 100644 index 6d94a2c..0000000 Binary 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-> 0 bytes 1 file changed, 0 insertions(+), 0 deletions(-) delete mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/gifs/domain_range.gif (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives') diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/gifs/domain_range.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/gifs/domain_range.gif deleted file mode 100644 index d0351e5..0000000 Binary files a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Scalar Functions/gifs/domain_range.gif and /dev/null differ -- cgit From 80dd36e43b3f884b7b352af7e0cebb9cb5275452 Mon Sep 17 00:00:00 2001 From: nishanpoojary Date: Tue, 26 May 2020 12:19:07 +0530 Subject: Delete multivariable_func_vectorvf_sine.py --- .../multivariable_func_vectorvf_sine.py | 91 ---------------------- 1 file changed, 91 deletions(-) delete mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_vectorvf_sine.py (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives') diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_vectorvf_sine.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_vectorvf_sine.py deleted file mode 100644 index 06e225e..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_vectorvf_sine.py +++ /dev/null @@ -1,91 +0,0 @@ -from manimlib.imports import * - -class SineVectors(GraphScene): - CONFIG = { - "x_min": 0, - "x_max": 10, - "y_min": -1, - "y_max": 1, - "graph_origin": ORIGIN+4*LEFT, - #"x_labeled_nums": list(range(-5, 6)), - #"y_labeled_nums": list(range(0, 5)), - } - 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) - - self.setup_axes(animate = True) - - - sine1 = self.get_graph(lambda x : np.sin(x), x_min = 0, x_max = 1.575, color = GREEN) - - point1 = Dot().shift(self.graph_origin+1*YTD*UP + 1.575*XTD*RIGHT) - point1_lab = TextMobject(r"$t = (\frac{\pi}{2})$") - point1_lab.scale(0.7) - point1_lab.next_to(point1, UP) - - vector1 = Arrow(self.graph_origin, self.graph_origin+1*YTD*UP + 1.575*XTD*RIGHT, buff=0.1, color = RED) - vector1_lab = TextMobject(r"$r(\frac{\pi}{2})$", color = RED) - vector1_lab.move_to(self.graph_origin+1.5*XTD*RIGHT+ 0.5*YTD*UP) - - self.play(GrowArrow(vector1),Write(vector1_lab)) - self.play(ShowCreation(point1), Write(point1_lab)) - self.play(ShowCreation(sine1)) - self.wait(1) - - - sine2 = self.get_graph(lambda x : np.sin(x), x_min = 1.575, x_max = 3.15, color = GREEN) - - point2 = Dot().shift(self.graph_origin+3.15*XTD*RIGHT) - point2_lab = TextMobject(r"$t = (\pi)$") - point2_lab.scale(0.7) - point2_lab.next_to(point2, UP+RIGHT) - - vector2 = Arrow(self.graph_origin, self.graph_origin+3.15*XTD*RIGHT, buff=0.1, color = BLUE) - vector2_lab = TextMobject(r"$r(\pi)$", color = BLUE) - vector2_lab.move_to(self.graph_origin+1.5*XTD*RIGHT+ 0.15*YTD*UP) - - self.play(GrowArrow(vector2),Write(vector2_lab)) - self.play(ShowCreation(point2), Write(point2_lab)) - self.play(ShowCreation(sine2)) - self.wait(1) - - - sine3 = self.get_graph(lambda x : np.sin(x), x_min = 3.15, x_max = 4.725, color = GREEN) - - point3 = Dot().shift(self.graph_origin+1*YTD*DOWN + 4.725*XTD*RIGHT) - point3_lab = TextMobject(r"$t = (\frac{3\pi}{2})$") - point3_lab.scale(0.7) - point3_lab.next_to(point3, DOWN) - - vector3 = Arrow(self.graph_origin, self.graph_origin+1*YTD*DOWN + 4.725*XTD*RIGHT, buff=0.1, color = YELLOW_C) - vector3_lab = TextMobject(r"$r(\frac{3\pi}{2})$", color = YELLOW_C) - vector3_lab.move_to(self.graph_origin+2*XTD*RIGHT+ 0.7*YTD*DOWN) - - self.play(GrowArrow(vector3),Write(vector3_lab)) - self.play(ShowCreation(point3), Write(point3_lab)) - self.play(ShowCreation(sine3)) - self.wait(1) - - - sine4 = self.get_graph(lambda x : np.sin(x), x_min = 4.725, x_max = 6.3, color = GREEN) - - point4 = Dot().shift(self.graph_origin+6.3*XTD*RIGHT) - point4_lab = TextMobject(r"$t = (2\pi)$") - point4_lab.scale(0.7) - point4_lab.next_to(point4, UP+RIGHT) - - vector4 = Arrow(self.graph_origin, self.graph_origin+6.3*XTD*RIGHT, buff=0.1, color = PURPLE) - vector4_lab = TextMobject(r"$r(2\pi)$", color = PURPLE) - vector4_lab.move_to(self.graph_origin+4.5*XTD*RIGHT+ 0.15*YTD*DOWN) - - self.play(GrowArrow(vector4),Write(vector4_lab)) - self.play(ShowCreation(point4), Write(point4_lab)) - self.play(ShowCreation(sine4)) - self.wait(3) - -- cgit From b1d37a71c5b9d80a9487092aaa548082929657ad Mon Sep 17 00:00:00 2001 From: nishanpoojary Date: Tue, 26 May 2020 12:19:16 +0530 Subject: Delete multivariable_func_respresntation.py --- .../multivariable_func_respresntation.py | 80 ---------------------- 1 file changed, 80 deletions(-) delete mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_respresntation.py (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives') diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_respresntation.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_respresntation.py deleted file mode 100644 index 4bfcf21..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_respresntation.py +++ /dev/null @@ -1,80 +0,0 @@ -from manimlib.imports import * - -class MultivariableFunc(Scene): - def construct(self): - - topic = TextMobject("Multivariable Functions") - topic.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE) - topic.scale(2) - - self.play(Write(topic)) - self.wait(1) - self.play(FadeOut(topic)) - - - circle = Circle() - circle.scale(3) - - eqn1 = TextMobject(r"f(x,y) = $x^2y$") - eqn1.set_color(YELLOW) - - - - number1 = TextMobject("(2,1)") - number1.move_to(3*UP+ 3*LEFT) - number1.scale(1.2) - number1.set_color(GREEN) - - output1 = TextMobject("4") - output1.scale(1.5) - output1.set_color(BLUE) - - eqn1_1 = TextMobject(r"f(2,1) = $2^2(1)$") - eqn1_1.set_color(YELLOW) - - - self.play(ShowCreation(circle),Write(eqn1)) - self.wait(1) - self.play(ApplyMethod(number1.move_to, 0.6*LEFT)) - self.play(FadeOut(number1)) - self.play(Transform(eqn1, eqn1_1)) - self.wait(1) - self.play(ApplyMethod(output1.move_to, 3*DOWN+4*RIGHT)) - self.wait(1) - self.play(FadeOut(output1)) - - - eqn2 = TextMobject(r"f(x,y,z) = $x^2y+2yz$") - eqn2.set_color(YELLOW) - - number2 = TextMobject("(2,1,3)") - number2.move_to(3*UP+ 3*LEFT) - number2.scale(1.2) - number2.set_color(GREEN) - - output2 = TextMobject("8") - output2.scale(1.5) - output2.set_color(BLUE) - - eqn2_1 = TextMobject(r"f(2,1,3) = $2^2(1) + 2(1)(3)$") - eqn2_1.set_color(YELLOW) - - eqn2_2 = TextMobject(r"f(2,1,3) = $2 + 6$") - eqn2_2.set_color(YELLOW) - - - - self.play(FadeOut(eqn1)) - self.play(Write(eqn2)) - - self.wait(1) - self.play(ApplyMethod(number2.move_to, 1.2*LEFT)) - self.play(FadeOut(number2)) - self.play(Transform(eqn2, eqn2_1)) - self.wait(1) - self.play(Transform(eqn2, eqn2_2)) - self.wait(1) - self.play(ApplyMethod(output2.move_to, 3*DOWN+4*RIGHT)) - self.wait(1) - self.play(FadeOut(output2),FadeOut(eqn2),FadeOut(circle)) - self.wait(2) \ No newline at end of file -- cgit From 4f83639077a36f1775c3c063f0b6be1c40097247 Mon Sep 17 00:00:00 2001 From: nishanpoojary Date: Tue, 26 May 2020 12:19:24 +0530 Subject: Delete multivariable_func_plot_sphere.py --- .../multivariable_func_plot_sphere.py | 42 ---------------------- 1 file changed, 42 deletions(-) delete mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_plot_sphere.py (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives') diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_plot_sphere.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_plot_sphere.py deleted file mode 100644 index baf08b1..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_plot_sphere.py +++ /dev/null @@ -1,42 +0,0 @@ -from manimlib.imports import * - -class Sphere(ThreeDScene): - def construct(self): - axes = ThreeDAxes() # creates a 3D Axis - - sphere = ParametricSurface( - lambda u, v: np.array([ - np.sin(u)*np.cos(v), - np.sin(u)*np.sin(v), - np.cos(u) - ]),u_min=0,u_max=PI,v_min=0,v_max=2*PI,checkerboard_colors=[RED_D, RED_E], - resolution=(15, 32)).scale(2) - - - - #self.set_camera_orientation(phi=0 * DEGREES,theta=270*DEGREES) - - text3d = TextMobject(r"$f(x,y) \rightarrow Point(x,y,z)$") - text3d1 = TextMobject(r"$f(x,y) \rightarrow Point(x,y, 1 - x^2 - y^2)$") - self.add_fixed_in_frame_mobjects(text3d) - text3d.scale(0.7) - text3d1.scale(0.7) - text3d.to_corner(UL) - text3d1.to_corner(UL) - text3d.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE) - text3d1.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE) - self.play(Write(text3d)) - self.wait(1) - - self.play(Transform(text3d,text3d1)) - self.add_fixed_in_frame_mobjects(text3d1) - self.play(FadeOut(text3d)) - - - self.set_camera_orientation(phi=75 * DEGREES) - self.begin_ambient_camera_rotation(rate=0.3) - - - self.add(axes) - self.play(Write(sphere)) - self.wait(5) \ No newline at end of file -- cgit From 9046a816f265c4f1e99c65a919d2d8240f4118a0 Mon Sep 17 00:00:00 2001 From: nishanpoojary Date: Tue, 26 May 2020 12:19:32 +0530 Subject: Delete multivariable_func_examples.py --- .../multivariable_func_examples.py | 69 ---------------------- 1 file changed, 69 deletions(-) delete mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_examples.py (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives') diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_examples.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_examples.py deleted file mode 100644 index 7322e47..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_examples.py +++ /dev/null @@ -1,69 +0,0 @@ -from manimlib.imports import * - -class Examples(GraphScene): - def construct(self): - - rectangle = Rectangle(height = 3, width = 4, color = GREEN) - square = Square(side_length = 5, color = PURPLE) - circle = Circle(radius = 2, color = PINK) - radius = Line(ORIGIN,2*RIGHT) - - radius.set_color(RED) - - rectangle_area_func = TextMobject(r"$Area = f(Length, Breadth)$") - rectangle_area_func.scale(0.6) - square_area_func = TextMobject(r"$Area = f(Length)$") - circle_area_func = TextMobject(r"$Area = f(r)$") - - - rectangle_area = TextMobject(r"$Area = Length \times Breadth$") - rectangle_area.scale(0.6) - square_area = TextMobject(r"$Area = Length^2$") - circle_area = TextMobject(r"$Area = \pi r^2$") - - braces_rect1 = Brace(rectangle, LEFT) - eq_text1 = braces_rect1.get_text("Length") - braces_rect2 = Brace(rectangle, UP) - eq_text2 = braces_rect2.get_text("Breadth") - - braces_square = Brace(square, LEFT) - braces_square_text = braces_square.get_text("Length") - - radius_text = TextMobject("r") - radius_text.next_to(radius,UP) - - - - self.play(ShowCreation(rectangle)) - self.wait(1) - self.play(GrowFromCenter(braces_rect1),Write(eq_text1),GrowFromCenter(braces_rect2),Write(eq_text2)) - self.wait(1) - self.play(Write(rectangle_area_func)) - self.wait(1) - self.play(Transform(rectangle_area_func, rectangle_area)) - self.wait(1) - self.play(FadeOut(braces_rect1),FadeOut(eq_text1),FadeOut(braces_rect2),FadeOut(eq_text2),FadeOut(rectangle_area_func)) - - - self.play(Transform(rectangle, square)) - self.wait(1) - self.play(GrowFromCenter(braces_square),Write(braces_square_text)) - self.wait(1) - self.play(Write(square_area_func)) - self.wait(1) - self.play(Transform(square_area_func, square_area)) - self.wait(1) - self.play(FadeOut(braces_square),FadeOut(braces_square_text),FadeOut(square_area_func)) - - - self.play(Transform(rectangle, circle)) - self.wait(1) - self.play(ShowCreation(radius),Write(radius_text)) - self.wait(1) - self.play(FadeOut(radius_text),FadeOut(radius)) - self.wait(1) - self.play(Write(circle_area_func)) - self.wait(1) - self.play(Transform(circle_area_func, circle_area)) - self.wait(1) - self.play(FadeOut(circle_area_func)) \ No newline at end of file -- cgit From ae89b51ed274c28c5351113b9a37beb0eeb0c487 Mon Sep 17 00:00:00 2001 From: nishanpoojary Date: Tue, 26 May 2020 12:19:40 +0530 Subject: Delete multivariable_func_derivative_vectorvf.py --- .../multivariable_func_derivative_vectorvf.py | 247 --------------------- 1 file changed, 247 deletions(-) delete mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_derivative_vectorvf.py (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives') diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_derivative_vectorvf.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_derivative_vectorvf.py deleted file mode 100644 index 466e389..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_derivative_vectorvf.py +++ /dev/null @@ -1,247 +0,0 @@ -from manimlib.imports import * - -class Derivative(GraphScene): - CONFIG = { - "x_min": 0, - "x_max": 3, - "y_min": 0, - "y_max": 5, - "graph_origin": ORIGIN+6*LEFT+3*DOWN, - "x_axis_width": 6, - "x_labeled_nums": list(range(0, 4)), - "y_labeled_nums": list(range(0, 6)), - } - 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) - - self.setup_axes(animate = True) - - graph = self.get_graph(lambda x : x*x, x_min = 0.5, x_max = 2, color = GREEN) - - point1 = Dot().shift(self.graph_origin+0.25*YTD*UP + 0.5*XTD*RIGHT) - point1_lab = TextMobject(r"$t = a$") - point1_lab.scale(0.7) - point1_lab.next_to(point1, RIGHT) - - point2 = Dot().shift(self.graph_origin+2*XTD*RIGHT+4*YTD*UP) - point2_lab = TextMobject(r"$t = b$") - point2_lab.scale(0.7) - point2_lab.next_to(point2, RIGHT) - - - vector1 = Arrow(self.graph_origin, self.graph_origin+1*YTD*UP + 1*XTD*RIGHT, buff=0.02, color = RED) - vector1_lab = TextMobject(r"$\vec r(t)$", color = RED) - vector1_lab.move_to(self.graph_origin+1.2*XTD*RIGHT+ 0.75*YTD*UP) - vector1_lab.scale(0.8) - - vector2 = Arrow(self.graph_origin, self.graph_origin+2.25*YTD*UP + 1.5*XTD*RIGHT, buff=0.02, color = YELLOW_C) - vector2_lab = TextMobject(r"$\vec r(t + h)$", color = YELLOW_C) - vector2_lab.move_to(self.graph_origin+0.5*XTD*RIGHT+ 2*YTD*UP) - vector2_lab.scale(0.8) - - vector3 = Arrow(self.graph_origin+1*YTD*UP + 1*XTD*RIGHT, self.graph_origin+2.25*YTD*UP + 1.5*XTD*RIGHT, buff=0.02, color = PINK) - vector3_lab = TextMobject(r"$\vec r(t + h) - \vec r(t)$", color = PINK) - vector3_lab.move_to(self.graph_origin+2*XTD*RIGHT+ 1.5*YTD*UP) - vector3_lab.scale(0.8) - - - self.play(ShowCreation(graph)) - self.play(ShowCreation(point1), Write(point1_lab)) - self.play(ShowCreation(point2), Write(point2_lab)) - - self.play(GrowArrow(vector1),Write(vector1_lab)) - self.play(GrowArrow(vector2),Write(vector2_lab)) - self.play(GrowArrow(vector3),Write(vector3_lab)) - self.wait(1) - - self.display_text() - - self.play(ApplyMethod(vector3_lab.move_to,(self.graph_origin+2.3*XTD*RIGHT+ 2.2*YTD*UP))) - - vector4 = Arrow(self.graph_origin+1*YTD*UP + 1*XTD*RIGHT, self.graph_origin+1*YTD*UP + 1.5*XTD*RIGHT, buff=0.02, color = PURPLE) - vector4_lab = TextMobject(r"$dx$", color = PURPLE) - vector4_lab.move_to(self.graph_origin+1.7*XTD*RIGHT+ 0.8*YTD*UP) - vector4_lab.scale(0.7) - - vector5 = Arrow(self.graph_origin+1*YTD*UP + 1.5*XTD*RIGHT, self.graph_origin+2.25*YTD*UP + 1.5*XTD*RIGHT, buff=0.02, color = ORANGE) - vector5_lab = TextMobject(r"$dy$", color = ORANGE) - vector5_lab.move_to(self.graph_origin+1.7*XTD*RIGHT+ 1.4*YTD*UP) - vector5_lab.scale(0.7) - - self.play(GrowArrow(vector4),Write(vector4_lab)) - self.play(GrowArrow(vector5),Write(vector5_lab)) - self.wait(2) - - - - def display_text(self): - text1 = TextMobject(r"$\vec r(t)$",r"+", r"$\vec r(t + h) - \vec r(t)$") - text1[0].set_color(RED) - text1[2].set_color(PINK) - text1.scale(0.7) - - text2 = TextMobject(r"$\vec r(t + h)$", color = YELLOW_C) - text2.scale(0.7) - - text3 = TextMobject(r"$ \vec r(t + h) - \vec r(t)$", color = PINK) - text3.scale(0.7) - - text4 = TextMobject(r"[", r"$x(t+h)$", r"$\vec i$", r"+", r"$y(t+h)$", r"$\vec j$", r"$] - [$", r"$x(t)$", r"$\vec i$", r"+", r"y(t)", r"$\vec j$", r"]") - text4.set_color_by_tex(r"\vec i", BLUE) - text4.set_color_by_tex(r"\vec j", GREEN) - text4[1].set_color(YELLOW_C) - text4[4].set_color(YELLOW_C) - text4[-6].set_color(RED) - text4[-3].set_color(RED) - text4.scale(0.7) - - text5 = TextMobject(r"$[x(t+h) - x(t)]$", r"$\vec i$", r"+", r"$[y(t+h) + y(t)]$", r"$\vec j$") - text5.set_color_by_tex(r"\vec i", BLUE) - text5.set_color_by_tex(r"\vec j", GREEN) - text5[0].set_color(PURPLE) - text5[3].set_color(ORANGE) - text5.scale(0.7) - - text6 = TextMobject(r"$\frac{[\vec r(t + h) - \vec r(t)]}{h}$", r"=", r"$\frac{[x(t+h) - x(t)]}{h}$", r"$\vec i$", r"+", r"$\frac{[y(t+h) + y(t)]}{h}$", r"$\vec j$") - text6.set_color_by_tex(r"\vec i", BLUE) - text6.set_color_by_tex(r"\vec j", GREEN) - text6[0].set_color(PINK) - text6[2].set_color(PURPLE) - text6[-2].set_color(ORANGE) - text6.scale(0.8) - - text7 = TextMobject(r"$\lim_{h \rightarrow 0}$", r"$\frac{[\vec r(t + h) - \vec r(t)]}{h}$", r"=", r"$\lim_{h \rightarrow 0}$", r"$\frac{[x(t+h) - x(t)]}{h}$", r"$\vec i$", r"+", r"$\lim_{h \rightarrow 0}$", r"$\frac{[y(t+h) + y(t)]}{h}$", r"$\vec j$") - text7.set_color_by_tex(r"\vec i", BLUE) - text7.set_color_by_tex(r"\vec j", GREEN) - text7[1].set_color(PINK) - text7[4].set_color(PURPLE) - text7[-2].set_color(ORANGE) - text7.scale(0.6) - - text8 = TextMobject(r"$\vec r'(t)$", r"=",r"$\vec x'(t)$", r"$\vec i$", r"+", r"$\vec y'(t)$", r"$\vec j$") - text8.set_color_by_tex(r"\vec i", BLUE) - text8.set_color_by_tex(r"\vec j", GREEN) - text8[0].set_color(PINK) - text8[2].set_color(PURPLE) - text8[5].set_color(ORANGE) - text8.scale(0.7) - - text9 = TextMobject(r"$\frac{d \vec r}{dt}$", r"=", r"$\frac{d \vec x}{dt}$", r"$\vec i$", r"+", r"$\frac{d \vec y}{dt}$", r"$\vec j$") - text9.set_color_by_tex(r"\vec i", BLUE) - text9.set_color_by_tex(r"\vec j", GREEN) - text9[0].set_color(PINK) - text9[2].set_color(PURPLE) - text9[5].set_color(ORANGE) - text9.scale(0.7) - - - text10 = TextMobject(r"$d \vec r$", r"=", r"$\frac{d \vec x}{dt}dt$", r"$\vec i$", r"+", r"$\frac{d \vec y}{dt}dt$", r"$\vec j$") - text10.set_color_by_tex(r"\vec i", BLUE) - text10.set_color_by_tex(r"\vec j", GREEN) - text10[0].set_color(PINK) - text10[2].set_color(PURPLE) - text10[5].set_color(ORANGE) - text10.scale(0.7) - - text11 = TextMobject(r"$d \vec r$", r"=", r"$x'(t)dt$", r"$\vec i$", r"+", r"$y'(t)dt$", r"$\vec j$") - text11.set_color_by_tex(r"\vec i", BLUE) - text11.set_color_by_tex(r"\vec j", GREEN) - text11[0].set_color(PINK) - text11[2].set_color(PURPLE) - text11[5].set_color(ORANGE) - text11.scale(0.7) - - text12 = TextMobject(r"$d \vec r$", r"=", r"$dx$", r"$\vec i$", r"+", r"$dy$", r"$\vec j$") - text12.set_color_by_tex(r"\vec i", BLUE) - text12.set_color_by_tex(r"\vec j", GREEN) - text12[0].set_color(PINK) - text12[2].set_color(PURPLE) - text12[5].set_color(ORANGE) - text12.scale(0.7) - - - text1.move_to(1*UP+2.7*RIGHT) - text2.move_to(1*UP+2.7*RIGHT) - text3.move_to(1*UP+2.7*RIGHT) - text4.move_to(1*UP+2.7*RIGHT) - text5.move_to(1*UP+2.7*RIGHT) - text6.move_to(1*UP+2.7*RIGHT) - text7.move_to(1*UP+2.5*RIGHT) - text8.move_to(1*UP+2.7*RIGHT) - text9.move_to(1*UP+2.7*RIGHT) - text10.move_to(1*UP+2.7*RIGHT) - text11.move_to(1*UP+2.7*RIGHT) - text12.move_to(1*UP+2.7*RIGHT) - - brace1 = Brace(text7[0:2], DOWN, buff = SMALL_BUFF) - brace2 = Brace(text7[3:6], UP, buff = SMALL_BUFF) - brace3 = Brace(text7[7:], DOWN, buff = SMALL_BUFF) - t1 = brace1.get_text(r"$\vec r'(t)$") - t1.set_color(PINK) - - t2 = brace2.get_text(r"$\vec x'(t)$") - t2.set_color(PURPLE) - - t3 = brace3.get_text(r"$\vec y'(t)$") - t3.set_color(ORANGE) - - - self.play(Write(text1)) - self.play(Transform(text1, text2)) - self.wait(1) - - self.play(Transform(text1, text3)) - self.wait(1) - - self.play(Transform(text1, text4)) - self.wait(1) - - self.play(Transform(text1, text5)) - self.wait(1) - - self.play(Transform(text1, text6)) - self.wait(1) - - self.play(Transform(text1, text7)) - self.wait(1) - - self.play( - GrowFromCenter(brace1), - FadeIn(t1), - ) - self.wait() - self.play( - ReplacementTransform(brace1.copy(),brace2), - ReplacementTransform(t1.copy(),t2) - ) - self.wait() - self.play( - ReplacementTransform(brace2.copy(),brace3), - ReplacementTransform(t2.copy(),t3) - ) - self.wait() - - self.play(FadeOut(brace1), FadeOut(t1), FadeOut(brace2), FadeOut(t2), FadeOut(brace3), FadeOut(t3),) - self.wait() - - self.play(Transform(text1, text8)) - self.wait(1) - - self.play(Transform(text1, text9)) - self.wait(1) - - self.play(Transform(text1, text10)) - self.wait(1) - - self.play(Transform(text1, text11)) - self.wait(1) - - self.play(Transform(text1, text12)) - self.wait(1) - - - - - -- cgit From 8efa8b48786fdad5b4041239584fb561bcc6e09e Mon Sep 17 00:00:00 2001 From: nishanpoojary Date: Tue, 26 May 2020 12:19:48 +0530 Subject: Delete Multivariable_Functions_Quiz.pdf --- .../Multivariable_Functions_Quiz.pdf | Bin 109631 -> 0 bytes 1 file changed, 0 insertions(+), 0 deletions(-) delete mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/Multivariable_Functions_Quiz.pdf (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives') diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/Multivariable_Functions_Quiz.pdf b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/Multivariable_Functions_Quiz.pdf deleted file mode 100644 index 7895843..0000000 Binary files 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multivariable_func_derivative_vectorvf.gif --- .../gifs/multivariable_func_derivative_vectorvf.gif | Bin 117597 -> 0 bytes 1 file changed, 0 insertions(+), 0 deletions(-) delete mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/gifs/multivariable_func_derivative_vectorvf.gif (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives') diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/gifs/multivariable_func_derivative_vectorvf.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/gifs/multivariable_func_derivative_vectorvf.gif deleted file mode 100644 index a94de90..0000000 Binary files a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/gifs/multivariable_func_derivative_vectorvf.gif and /dev/null differ -- cgit From 5d91fddefadc72abbdfe9961cd38b48c77b60abd Mon Sep 17 00:00:00 2001 From: nishanpoojary Date: Tue, 26 May 2020 12:20:46 +0530 Subject: Delete limit_approach_point.py --- .../limit_approach_point.py | 66 ---------------------- 1 file changed, 66 deletions(-) delete mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Limits and Continuity of Multivariable Functions/limit_approach_point.py (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives') diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Limits and Continuity of Multivariable Functions/limit_approach_point.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Limits and Continuity of Multivariable Functions/limit_approach_point.py deleted file mode 100644 index 57d1d45..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Limits and Continuity of Multivariable Functions/limit_approach_point.py +++ /dev/null @@ -1,66 +0,0 @@ -from manimlib.imports import * - -class Limit(GraphScene): - CONFIG = { - "x_min": 0, - "x_max": 4, - "y_min": 0, - "y_max": 4, - "graph_origin": ORIGIN + 3* DOWN+4*LEFT, - "x_labeled_nums": list(range(0, 4)), - "y_labeled_nums": list(range(0, 5)), - } - def construct(self): - topic = TextMobject("Different paths of approach to limit point") - topic.scale(1.5) - topic.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE) - self.play(Write(topic)) - self.wait(1) - self.play(FadeOut(topic)) - - - - XTD = self.x_axis_width/(self.x_max- self.x_min) - YTD = self.y_axis_height/(self.y_max- self.y_min) - - self.setup_axes(animate = True) - - y_x = self.get_graph(lambda x : x, x_min = -1, x_max = 4) - y_x_lab = self.get_graph_label(y_x, label = r"y = x") - - y_xsquare = self.get_graph(lambda x : x*x, x_min = -1, x_max = 4) - y_xsquare_lab = self.get_graph_label(y_xsquare, label = r"y = x^2") - - y_1 = self.get_graph(lambda x : 1, x_min = -1, x_max = 4) - y_1_lab = self.get_graph_label(y_1, label = r"y = 1") - - y_2minusx = self.get_graph(lambda x : 2 - x, x_min = -1, x_max = 4, color = RED) - y_2minusx_lab = self.get_graph_label(y_2minusx, label = r"y = 2 - x") - - limit_point = Dot().shift(self.graph_origin+1*XTD*RIGHT+1*YTD*UP) - limit_point_lab = TextMobject(r"(1,1)") - limit_point_lab.next_to(limit_point, DOWN) - - self.play(ShowCreation(limit_point)) - self.play(Write(limit_point_lab)) - self.wait(1) - - self.play(ShowCreation(y_x)) - self.play(Write(y_x_lab)) - self.wait(1) - - self.play(ShowCreation(y_xsquare)) - self.play(Write(y_xsquare_lab)) - self.wait(1) - - self.play(ShowCreation(y_1)) - self.play(Write(y_1_lab)) - self.wait(1) - - self.play(ShowCreation(y_2minusx)) - self.play(Write(y_2minusx_lab)) - self.wait(1) - - - - \ No newline at end of file -- cgit From dcf9888ff648234c364a6b0733aeadc48e855e8b Mon Sep 17 00:00:00 2001 From: nishanpoojary Date: Tue, 26 May 2020 12:20:56 +0530 Subject: Delete limit_approach_point.gif --- .../gifs/limit_approach_point.gif | Bin 47411 -> 0 bytes 1 file changed, 0 insertions(+), 0 deletions(-) delete mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Limits and Continuity of Multivariable Functions/gifs/limit_approach_point.gif (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives') diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Limits and Continuity of Multivariable Functions/gifs/limit_approach_point.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Limits and Continuity of Multivariable Functions/gifs/limit_approach_point.gif deleted file mode 100644 index 830b6f1..0000000 Binary files a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Limits and Continuity of Multivariable Functions/gifs/limit_approach_point.gif and /dev/null differ -- cgit From e92c84ba37bd991b5a7f093fbc411280568ea380 Mon Sep 17 00:00:00 2001 From: nishanpoojary Date: Tue, 26 May 2020 12:34:24 +0530 Subject: Upload scalar-functions Folder --- .../scalar-functions/Scalar_Function_Quiz.pdf | Bin 0 -> 87455 bytes .../scalar-functions/file1_domain_range.py | 132 +++++++++++++++ .../file2_scalar_function_application.py | 129 +++++++++++++++ .../scalar-functions/file3_parabola_example.py | 35 ++++ .../scalar-functions/file4_neural_nets.py | 177 +++++++++++++++++++++ .../scalar-functions/gifs/file1_domain_range.gif | Bin 0 -> 74879 bytes .../gifs/file2_scalar_function_application.gif | Bin 0 -> 225144 bytes .../gifs/file3_parabola_example.gif | Bin 0 -> 905534 bytes .../scalar-functions/gifs/file4_neural_nets.gif | Bin 0 -> 95828 bytes 9 files changed, 473 insertions(+) create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/Scalar_Function_Quiz.pdf create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file1_domain_range.py create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file2_scalar_function_application.py create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file3_parabola_example.py create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file4_neural_nets.py create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file1_domain_range.gif create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file2_scalar_function_application.gif create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file3_parabola_example.gif create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file4_neural_nets.gif (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives') diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/Scalar_Function_Quiz.pdf b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/Scalar_Function_Quiz.pdf new file mode 100644 index 0000000..6d94a2c Binary files /dev/null and b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/Scalar_Function_Quiz.pdf differ diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file1_domain_range.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file1_domain_range.py new file mode 100644 index 0000000..9b1ca7b --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file1_domain_range.py @@ -0,0 +1,132 @@ +# Plotting Graphs +from manimlib.imports import * + +class PlotGraphs(GraphScene): + CONFIG = { + "x_min": -5, + "x_max": 5, + "y_min": 0, + "y_max": 4, + "graph_origin": ORIGIN + 2.5* DOWN, + "x_labeled_nums": list(range(-5, 6)), + "y_labeled_nums": list(range(0, 5)), + } + def construct(self): + + topic = TextMobject("Domain and Range") + topic.scale(2) + topic.set_color(YELLOW) + self.play(Write(topic)) + self.play(FadeOut(topic)) + self.wait(1) + + + XTD = self.x_axis_width/(self.x_max- self.x_min) + YTD = self.y_axis_height/(self.y_max- self.y_min) + + self.setup_axes(animate = True) + + graphobj = self.get_graph(lambda x : np.sqrt(x + 4), x_min = -4, x_max = 5) + graph_lab = self.get_graph_label(graphobj, label = r"\sqrt{x + 4}") + + + rangeline1 = Arrow(self.graph_origin+2.2*YTD*UP+5*XTD*LEFT, self.graph_origin+4.1*YTD*UP+5*XTD*LEFT) + rangeline2 = Arrow(self.graph_origin+1.7*YTD*UP+5*XTD*LEFT, self.graph_origin+5*XTD*LEFT) + rangeline1.set_color(RED) + rangeline2.set_color(RED) + + rangeMsg = TextMobject(r"Range: $y \geq 0$") + rangeMsg.move_to(self.graph_origin+2*YTD*UP+5*XTD*LEFT) + rangeMsg.scale(0.5) + rangeMsg.set_color(YELLOW) + + domainline1 = Line(self.graph_origin+0.6*YTD*DOWN+1.2*XTD*LEFT, self.graph_origin+0.6*YTD*DOWN + 4*XTD*LEFT) + domainline2 = Arrow(self.graph_origin+0.6*YTD*DOWN+1.1*XTD*RIGHT, self.graph_origin+0.6*YTD*DOWN + 5.3*XTD*RIGHT) + domainline1.set_color(PINK) + domainline2.set_color(PINK) + + domainMsg = TextMobject(r"Domain: $x \geq -4$") + domainMsg.move_to(self.graph_origin+0.6*YTD*DOWN) + domainMsg.scale(0.5) + domainMsg.set_color(GREEN) + + + + + self.play(ShowCreation(graphobj)) + self.play(ShowCreation(graph_lab)) + self.wait(1) + self.play(GrowArrow(rangeline1)) + self.play(GrowArrow(rangeline2)) + self.play(Write(rangeMsg)) + self.wait(1) + self.play(GrowArrow(domainline1)) + self.play(GrowArrow(domainline2)) + self.play(Write(domainMsg)) + self.wait(3) + + self.wait(2) + + + + +class PlotSineGraphs(GraphScene): + CONFIG = { + "x_min": -8, + "x_max": 8, + "y_min": -1, + "y_max": 1, + "graph_origin": ORIGIN, + "x_labeled_nums": list(range(-8, 9)), + "y_labeled_nums": list(range(-1, 2)), + } + 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) + + self.setup_axes(animate = True) + + sineobj = self.get_graph(lambda x : np.sin(x), x_min = -7, x_max = 8) + sine_lab = self.get_graph_label(sineobj, label = "\\sin(x)") + + + rangeline1 = Line(8*XTD*LEFT,1*YTD*UP+8*XTD*LEFT) + rangeline2 = Line(8*XTD*LEFT,1*YTD*DOWN+8*XTD*LEFT) + rangeline1.set_color(RED) + rangeline2.set_color(RED) + + rangeMsg = TextMobject(r"Range: $-1 \leq y \leq 1$") + rangeMsg.move_to(1.1*YTD*UP+8.5*XTD*LEFT) + rangeMsg.scale(0.5) + rangeMsg.set_color(YELLOW) + + + domainline1 = Arrow(1.1*YTD*DOWN+2*XTD*LEFT, 1.1*YTD*DOWN + 8.5*XTD*LEFT) + domainline2 = Arrow(1.1*YTD*DOWN+2*XTD*RIGHT, 1.1*YTD*DOWN + 8.5*XTD*RIGHT) + domainline1.set_color(PINK) + domainline2.set_color(PINK) + + domainMsg = TextMobject(r"Domain: $[-\infty, \infty]$") + domainMsg.move_to(1.1*YTD*DOWN) + domainMsg.scale(0.5) + domainMsg.set_color(GREEN) + + + + self.play(ShowCreation(sineobj)) + self.play(ShowCreation(sine_lab)) + self.wait(1) + self.play(GrowArrow(rangeline1)) + self.play(GrowArrow(rangeline2)) + self.play(Write(rangeMsg)) + self.wait(1) + self.play(GrowArrow(domainline1)) + self.play(GrowArrow(domainline2)) + self.play(Write(domainMsg)) + self.wait(3) + + + \ No newline at end of file diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file2_scalar_function_application.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file2_scalar_function_application.py new file mode 100644 index 0000000..56b3e53 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file2_scalar_function_application.py @@ -0,0 +1,129 @@ +from manimlib.imports import * + +class ScalarApplication(ThreeDScene): + def construct(self): + axes = ThreeDAxes() # creates a 3D Axis + + cube = Cube() + cube.set_fill(YELLOW_E, opacity = 0.1) + cube.scale(2) + self.set_camera_orientation(phi=0 * DEGREES,theta=270*DEGREES) + self.play(ShowCreation(cube),ShowCreation(axes)) + + dot = Sphere() + dot.scale(0.1) + dot.move_to(np.array([1,0.5,1])) + dot.set_fill(RED) + + #dot = Dot(np.array([1,0.5,1]), color = RED) + temp_func = TextMobject("T(x,y,z)") + temp_func.next_to(dot,RIGHT) + temp_func.set_color(RED) + temp_func_trans = TextMobject("T(1,0.5,1)") + temp_func_trans.next_to(dot,RIGHT) + temp_func_trans.set_color(RED) + temp = TextMobject(r"$36 ^\circ$") + temp.next_to(dot,RIGHT) + temp.set_color(RED_E) + + + self.play(ShowCreation(dot)) + self.play(ShowCreation(temp_func)) + self.play(Transform(temp_func, temp_func_trans)) + self.wait(1) + self.play(Transform(temp_func, temp)) + + + + + dot1 = Sphere() + dot1.scale(0.1) + dot1.move_to(np.array([-1,-0.8,-1.5])) + dot1.set_fill(BLUE_E) + #dot1 = Dot(np.array([-1,-0.8,-1.5]), color = BLUE) + temp_func1 = TextMobject("T(x,y,z)") + temp_func1.next_to(dot1,LEFT) + temp_func1.set_color(BLUE) + temp_func_trans1 = TextMobject("T(-1,-0.8,-1.5)") + temp_func_trans1.next_to(dot1,LEFT) + temp_func_trans1.set_color(BLUE) + temp1 = TextMobject(r"$24 ^\circ$") + temp1.next_to(dot1,LEFT) + temp1.set_color(BLUE) + + self.play(ShowCreation(dot1)) + self.play(ShowCreation(temp_func1)) + self.play(Transform(temp_func1, temp_func_trans1)) + self.wait(1) + self.play(Transform(temp_func1, temp1)) + + self.play(FadeOut(temp_func)) + self.play(FadeOut(temp_func1)) + + + self.move_camera(phi=80* DEGREES,theta=45*DEGREES,run_time=3) + + self.begin_ambient_camera_rotation(rate=0.2) + self.wait(4) + self.stop_ambient_camera_rotation() + self.wait(2) + + + + +class AddTempScale(Scene): + def construct(self): + temp_scale = ImageMobject("tempscale.png") + temp_scale.scale(4) + temp_scale.move_to(2*RIGHT) + self.play(ShowCreation(temp_scale)) + + + temp_func = TextMobject("T(x,y,z)") + temp_func.move_to(3*UP +2*LEFT) + temp_func.set_color(RED) + temp_func_trans = TextMobject("T(1,0.5,1)") + temp_func_trans.move_to(3*UP +2*LEFT) + temp_func_trans.set_color(RED) + temp = TextMobject(r"$36 ^\circ$") + temp.set_color(RED) + temp.move_to(3*UP +2*LEFT) + temp.scale(0.7) + + self.play(ShowCreation(temp_func)) + self.play(Transform(temp_func, temp_func_trans)) + self.wait(1) + self.play(Transform(temp_func, temp)) + self.play(ApplyMethod(temp_func.move_to, 1.8*UP +1.8*RIGHT)) + + + temp_func1 = TextMobject("T(x,y,z)") + temp_func1.move_to(2*UP +2*LEFT) + temp_func1.set_color(BLUE) + temp_func_trans1 = TextMobject("T(-1,-0.8,-1.5)") + temp_func_trans1.move_to(2*UP +2*LEFT) + temp_func_trans1.set_color(BLUE) + temp1 = TextMobject(r"$24 ^\circ$") + temp1.set_color(BLUE) + temp1.move_to(2*UP +2*LEFT) + temp1.scale(0.7) + + self.play(ShowCreation(temp_func1)) + self.play(Transform(temp_func1, temp_func_trans1)) + self.wait(1) + self.play(Transform(temp_func1, temp1)) + self.play(ApplyMethod(temp_func1.move_to, 0.6*UP +1.8*RIGHT)) + + + + transtext = TextMobject("Scalar Function Transform:") + transtext.set_color(GREEN) + transtext1 = TextMobject(r"$\mathbb{R}^3 \rightarrow \mathbb{R}$") + transtext1.set_color(YELLOW_E) + transtext.move_to(3*UP +3*LEFT) + transtext1.next_to(transtext,DOWN) + self.play(Write(transtext)) + self.play(Write(transtext1)) + self.wait(2) + + diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file3_parabola_example.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file3_parabola_example.py new file mode 100644 index 0000000..74dc063 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file3_parabola_example.py @@ -0,0 +1,35 @@ +from manimlib.imports import * + +class Parabola(ThreeDScene): + def construct(self): + axes = ThreeDAxes() # creates a 3D Axis + + paraboloid = ParametricSurface( + lambda u, v: np.array([ + 2*np.cosh(u)*np.cos(v), + 2*np.cosh(u)*np.sin(v), + 2*np.sinh(u) + ]),v_min=0,v_max=TAU,u_min=0,u_max=2,checkerboard_colors=[YELLOW_D, YELLOW_E], + resolution=(15, 32)) + + text3d = TextMobject(r"Plot of $f: \mathbb{R}^2 \rightarrow \mathbb{R}$", "z = f(x,y)") + self.add_fixed_in_frame_mobjects(text3d) + text3d[0].move_to(4*LEFT+2*DOWN) + text3d[1].next_to(text3d[0], DOWN) + text3d[0].set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE) + text3d[1].set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE) + + #self.set_camera_orientation(phi=0 * DEGREES,theta=270*DEGREES) + self.move_camera(phi=110* DEGREES,theta=45*DEGREES) + self.add(axes) + self.play(ShowCreation(paraboloid)) + self.play(Write(text3d[0])) + self.play(Write(text3d[1])) + self.begin_ambient_camera_rotation(rate=0.2) + self.wait(3) + self.move_camera(phi=0 * DEGREES,theta=180*DEGREES,run_time=3) + self.wait(3) + self.move_camera(phi=110* DEGREES,theta=90*DEGREES,run_time=3) + self.wait(3) + + \ No newline at end of file diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file4_neural_nets.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file4_neural_nets.py new file mode 100644 index 0000000..eb6bf45 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file4_neural_nets.py @@ -0,0 +1,177 @@ +from manimlib.imports import * + +class SigmoidFunc(GraphScene): + CONFIG = { + "x_min": -4, + "x_max": 4, + "y_min": -1, + "y_max": 1, + "graph_origin": ORIGIN + 0.8*DOWN, + "x_labeled_nums": list(range(-4, 5)), + "y_labeled_nums": list(range(-1, 2)), + "y_axis_height": 4.5, + } + 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) + + topic = TextMobject("Sigmoid Function") + topic.move_to(3.2*UP) + topic.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE) + + self.setup_axes(animate = True) + sigmoid_func = self.get_graph(lambda x : (1/(1 + np.exp(-x))), x_min = -4, x_max = 4) + sigmoid_lab = self.get_graph_label(sigmoid_func, label = r"\frac{1}{1 + e^{-z}}") + + + + + self.play(ShowCreation(sigmoid_func),Write(sigmoid_lab)) + self.play(Write(topic)) + self.wait(2) + self.play(FadeOut(sigmoid_func), FadeOut(sigmoid_lab)) + self.wait(1) + + + +class NeuralNet(GraphScene): + def construct(self): + + sigmoid_exp = TextMobject(r"g(z) = g($\theta^T$ X) = $\frac{1}{1 + e^{-z}}$") + sigmoid_exp.move_to(3*UP + 4*LEFT) + sigmoid_exp.scale(0.8) + sigmoid_exp.set_color(BLUE) + sigmoid_exp1 = TextMobject(r"Predict: 'y = 1'",r"When g(z) $\geq$ 0.5, z $\geq$ 0, $\theta^T$ X $\geq$ 0") + sigmoid_exp2 = TextMobject(r"Predict: 'y = 0'", r"When g(z) $\leq$ 0.5, z $\leq$ 0, $\theta^T$ X $\leq$ 0") + sigmoid_exp1.scale(0.5) + sigmoid_exp2.scale(0.5) + sigmoid_exp1.set_color(PURPLE) + sigmoid_exp2.set_color(PURPLE) + + sigmoid_exp1[0].next_to(sigmoid_exp, 1.5*DOWN) + sigmoid_exp1[1].next_to(sigmoid_exp1[0], DOWN) + sigmoid_exp2[0].next_to(sigmoid_exp1[1], 1.5*DOWN) + sigmoid_exp2[1].next_to(sigmoid_exp2[0], DOWN) + + + self.play(Write(sigmoid_exp)) + self.play(Write(sigmoid_exp1[0]), Write(sigmoid_exp1[1])) + self.play(Write(sigmoid_exp2[0]), Write(sigmoid_exp2[1])) + self.wait(2) + + + neuron1 = Circle() + neuron1.set_fill(YELLOW_A, opacity = 0.5) + + neuron2 = Circle() + neuron2.set_fill(ORANGE, opacity = 0.5) + + neuron3 = Circle() + neuron3.set_fill(GREEN_E, opacity = 0.5) + + neuron1.move_to(2*UP+RIGHT) + neuron2.move_to(2*DOWN+RIGHT) + neuron3.move_to(4*RIGHT) + + arrow1 = Arrow(neuron1.get_right(),neuron3.get_left(),buff=0.1) + arrow1.set_color(RED) + arrow2 = Arrow(neuron2.get_right(),neuron3.get_left(),buff=0.1) + arrow2.set_color(RED) + + arrow3 = Arrow(neuron3.get_right(),7*RIGHT,buff=0.1) + arrow3.set_color(RED) + + + sign1 = TextMobject("+1") + sign1.move_to(2*UP+RIGHT) + sign1.scale(2) + sign2 = TextMobject(r"$x_1$") + sign2.move_to(2*DOWN+RIGHT) + sign2.scale(2) + sign3 = TextMobject(r"$h_{\theta}(x)$") + sign3.move_to(6*RIGHT+0.4*DOWN) + sign3.scale(0.7) + sign4 = TextMobject(r"$= g(10 - 20x_1)$") + sign4.next_to(sign3,DOWN) + sign4.scale(0.5) + sign5 = TextMobject(r"$= g(10 - 20x_1)$") + sign5.next_to(sign3,DOWN) + sign5.scale(0.5) + sign6 = TextMobject(r"$= g(10 - 20x_1)$") + sign6.next_to(sign3,DOWN) + sign6.scale(0.5) + + + weight1 = TextMobject("10") + weight1.next_to(arrow1,UP) + weight2 = TextMobject("-20") + weight2.next_to(arrow2,DOWN) + + gate = TextMobject("NOT GATE") + gate.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE) + gate.scale(1.5) + gate.move_to(3*RIGHT+3.5*UP) + + + + truth_table = TextMobject(r"\begin{displaymath}\begin{array}{|c|c|} x & y\\ \hline 1 & 0 \\0 & 1 \\\end{array}\end{displaymath}") + truth_table.next_to(sigmoid_exp2[1], 3*DOWN) + + values = TextMobject("1", "0") + values.scale(2) + + sign4_trans1 = TextMobject(r"$= g(10 - 20(1))$") + sign4_trans2 = TextMobject(r"$= g(10 - 20(0))$") + sign4_trans1.next_to(sign3,DOWN) + sign4_trans2.next_to(sign3,DOWN) + sign4_trans1.scale(0.5) + sign4_trans2.scale(0.5) + + + + output1 = TextMobject("y = 0") + output2 = TextMobject("y = 1") + output1.next_to(sign4,DOWN) + output2.next_to(sign4,DOWN) + output1.scale(1.5) + output2.scale(1.5) + + + + self.play(ShowCreation(neuron1),ShowCreation(neuron2)) + self.play(ShowCreation(neuron3)) + self.play(ShowCreation(sign1),ShowCreation(sign2)) + self.wait(1) + + self.play(GrowArrow(arrow1)) + self.play(GrowArrow(arrow2)) + self.play(ShowCreation(weight1),ShowCreation(weight2)) + + + + self.play(GrowArrow(arrow3)) + self.play(Write(sign3),Write(sign4)) + + self.play(Write(gate)) + self.play(ShowCreation(truth_table)) + + self.play(ApplyMethod(values[0].move_to, 2*DOWN+RIGHT)) + self.play(FadeOut(values[0])) + self.play(Transform(sign4,sign4_trans1)) + self.play(Write(output1)) + self.wait(1) + self.play(FadeOut(output1)) + self.play(Transform(sign4, sign5)) + + + self.play(ApplyMethod(values[1].move_to, 2*DOWN+RIGHT)) + self.play(FadeOut(values[1])) + self.play(Transform(sign4,sign4_trans2)) + self.play(Write(output2)) + self.wait(1) + self.play(FadeOut(output2)) + self.play(Transform(sign4, sign6)) + + self.wait(2) + + diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file1_domain_range.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file1_domain_range.gif new file mode 100644 index 0000000..d0351e5 Binary files /dev/null and b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file1_domain_range.gif differ diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file2_scalar_function_application.gif 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a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file4_neural_nets.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file4_neural_nets.gif new file mode 100644 index 0000000..9d24688 Binary files /dev/null and b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file4_neural_nets.gif differ -- cgit From 7557884e36f721156f4a6f0eb8dd9997d9c25805 Mon Sep 17 00:00:00 2001 From: nishanpoojary Date: Tue, 26 May 2020 12:35:30 +0530 Subject: Uploaded multivariable-functions Folder --- .../Multivariable_Functions_Quiz.pdf | Bin 0 -> 109631 bytes .../file1_multivariable_func_respresentation.py | 80 +++++++ .../file2_multivariable_func_examples.py | 69 ++++++ .../multivariable-functions/file3_plot_sphere.py | 42 ++++ .../multivariable-functions/file4_vectorvf_sine.py | 91 ++++++++ .../file5_derivative_vectorvf.py | 247 +++++++++++++++++++++ .../file1_multivariable_func_respresentation.gif | Bin 0 -> 73055 bytes .../gifs/file2_multivariable_func_examples.gif | Bin 0 -> 57945 bytes .../gifs/file3_plot_sphere.gif | Bin 0 -> 198324 bytes .../gifs/file4_vectorvf_sine.gif | Bin 0 -> 29814 bytes .../gifs/file5_derivative_vectorvf.gif | Bin 0 -> 117597 bytes 11 files changed, 529 insertions(+) create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/Multivariable_Functions_Quiz.pdf create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file1_multivariable_func_respresentation.py create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file2_multivariable_func_examples.py create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file3_plot_sphere.py create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file4_vectorvf_sine.py create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file5_derivative_vectorvf.py create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file1_multivariable_func_respresentation.gif create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file2_multivariable_func_examples.gif create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file3_plot_sphere.gif create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file4_vectorvf_sine.gif create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file5_derivative_vectorvf.gif (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives') diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/Multivariable_Functions_Quiz.pdf b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/Multivariable_Functions_Quiz.pdf new file mode 100644 index 0000000..7895843 Binary files /dev/null and b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/Multivariable_Functions_Quiz.pdf differ diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file1_multivariable_func_respresentation.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file1_multivariable_func_respresentation.py new file mode 100644 index 0000000..4bfcf21 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file1_multivariable_func_respresentation.py @@ -0,0 +1,80 @@ +from manimlib.imports import * + +class MultivariableFunc(Scene): + def construct(self): + + topic = TextMobject("Multivariable Functions") + topic.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE) + topic.scale(2) + + self.play(Write(topic)) + self.wait(1) + self.play(FadeOut(topic)) + + + circle = Circle() + circle.scale(3) + + eqn1 = TextMobject(r"f(x,y) = $x^2y$") + eqn1.set_color(YELLOW) + + + + number1 = TextMobject("(2,1)") + number1.move_to(3*UP+ 3*LEFT) + number1.scale(1.2) + number1.set_color(GREEN) + + output1 = TextMobject("4") + output1.scale(1.5) + output1.set_color(BLUE) + + eqn1_1 = TextMobject(r"f(2,1) = $2^2(1)$") + eqn1_1.set_color(YELLOW) + + + self.play(ShowCreation(circle),Write(eqn1)) + self.wait(1) + self.play(ApplyMethod(number1.move_to, 0.6*LEFT)) + self.play(FadeOut(number1)) + self.play(Transform(eqn1, eqn1_1)) + self.wait(1) + self.play(ApplyMethod(output1.move_to, 3*DOWN+4*RIGHT)) + self.wait(1) + self.play(FadeOut(output1)) + + + eqn2 = TextMobject(r"f(x,y,z) = $x^2y+2yz$") + eqn2.set_color(YELLOW) + + number2 = TextMobject("(2,1,3)") + number2.move_to(3*UP+ 3*LEFT) + number2.scale(1.2) + number2.set_color(GREEN) + + output2 = TextMobject("8") + output2.scale(1.5) + output2.set_color(BLUE) + + eqn2_1 = TextMobject(r"f(2,1,3) = $2^2(1) + 2(1)(3)$") + eqn2_1.set_color(YELLOW) + + eqn2_2 = TextMobject(r"f(2,1,3) = $2 + 6$") + eqn2_2.set_color(YELLOW) + + + + self.play(FadeOut(eqn1)) + self.play(Write(eqn2)) + + self.wait(1) + self.play(ApplyMethod(number2.move_to, 1.2*LEFT)) + self.play(FadeOut(number2)) + self.play(Transform(eqn2, eqn2_1)) + self.wait(1) + self.play(Transform(eqn2, eqn2_2)) + self.wait(1) + self.play(ApplyMethod(output2.move_to, 3*DOWN+4*RIGHT)) + self.wait(1) + self.play(FadeOut(output2),FadeOut(eqn2),FadeOut(circle)) + self.wait(2) \ No newline at end of file diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file2_multivariable_func_examples.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file2_multivariable_func_examples.py new file mode 100644 index 0000000..7322e47 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file2_multivariable_func_examples.py @@ -0,0 +1,69 @@ +from manimlib.imports import * + +class Examples(GraphScene): + def construct(self): + + rectangle = Rectangle(height = 3, width = 4, color = GREEN) + square = Square(side_length = 5, color = PURPLE) + circle = Circle(radius = 2, color = PINK) + radius = Line(ORIGIN,2*RIGHT) + + radius.set_color(RED) + + rectangle_area_func = TextMobject(r"$Area = f(Length, Breadth)$") + rectangle_area_func.scale(0.6) + square_area_func = TextMobject(r"$Area = f(Length)$") + circle_area_func = TextMobject(r"$Area = f(r)$") + + + rectangle_area = TextMobject(r"$Area = Length \times Breadth$") + rectangle_area.scale(0.6) + square_area = TextMobject(r"$Area = Length^2$") + circle_area = TextMobject(r"$Area = \pi r^2$") + + braces_rect1 = Brace(rectangle, LEFT) + eq_text1 = braces_rect1.get_text("Length") + braces_rect2 = Brace(rectangle, UP) + eq_text2 = braces_rect2.get_text("Breadth") + + braces_square = Brace(square, LEFT) + braces_square_text = braces_square.get_text("Length") + + radius_text = TextMobject("r") + radius_text.next_to(radius,UP) + + + + self.play(ShowCreation(rectangle)) + self.wait(1) + self.play(GrowFromCenter(braces_rect1),Write(eq_text1),GrowFromCenter(braces_rect2),Write(eq_text2)) + self.wait(1) + self.play(Write(rectangle_area_func)) + self.wait(1) + self.play(Transform(rectangle_area_func, rectangle_area)) + self.wait(1) + self.play(FadeOut(braces_rect1),FadeOut(eq_text1),FadeOut(braces_rect2),FadeOut(eq_text2),FadeOut(rectangle_area_func)) + + + self.play(Transform(rectangle, square)) + self.wait(1) + self.play(GrowFromCenter(braces_square),Write(braces_square_text)) + self.wait(1) + self.play(Write(square_area_func)) + self.wait(1) + self.play(Transform(square_area_func, square_area)) + self.wait(1) + self.play(FadeOut(braces_square),FadeOut(braces_square_text),FadeOut(square_area_func)) + + + self.play(Transform(rectangle, circle)) + self.wait(1) + self.play(ShowCreation(radius),Write(radius_text)) + self.wait(1) + self.play(FadeOut(radius_text),FadeOut(radius)) + self.wait(1) + self.play(Write(circle_area_func)) + self.wait(1) + self.play(Transform(circle_area_func, circle_area)) + self.wait(1) + self.play(FadeOut(circle_area_func)) \ No newline at end of file diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file3_plot_sphere.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file3_plot_sphere.py new file mode 100644 index 0000000..baf08b1 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file3_plot_sphere.py @@ -0,0 +1,42 @@ +from manimlib.imports import * + +class Sphere(ThreeDScene): + def construct(self): + axes = ThreeDAxes() # creates a 3D Axis + + sphere = ParametricSurface( + lambda u, v: np.array([ + np.sin(u)*np.cos(v), + np.sin(u)*np.sin(v), + np.cos(u) + ]),u_min=0,u_max=PI,v_min=0,v_max=2*PI,checkerboard_colors=[RED_D, RED_E], + resolution=(15, 32)).scale(2) + + + + #self.set_camera_orientation(phi=0 * DEGREES,theta=270*DEGREES) + + text3d = TextMobject(r"$f(x,y) \rightarrow Point(x,y,z)$") + text3d1 = TextMobject(r"$f(x,y) \rightarrow Point(x,y, 1 - x^2 - y^2)$") + self.add_fixed_in_frame_mobjects(text3d) + text3d.scale(0.7) + text3d1.scale(0.7) + text3d.to_corner(UL) + text3d1.to_corner(UL) + text3d.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE) + text3d1.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE) + self.play(Write(text3d)) + self.wait(1) + + self.play(Transform(text3d,text3d1)) + self.add_fixed_in_frame_mobjects(text3d1) + self.play(FadeOut(text3d)) + + + self.set_camera_orientation(phi=75 * DEGREES) + self.begin_ambient_camera_rotation(rate=0.3) + + + self.add(axes) + self.play(Write(sphere)) + self.wait(5) \ No newline at end of file diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file4_vectorvf_sine.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file4_vectorvf_sine.py new file mode 100644 index 0000000..06e225e --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file4_vectorvf_sine.py @@ -0,0 +1,91 @@ +from manimlib.imports import * + +class SineVectors(GraphScene): + CONFIG = { + "x_min": 0, + "x_max": 10, + "y_min": -1, + "y_max": 1, + "graph_origin": ORIGIN+4*LEFT, + #"x_labeled_nums": list(range(-5, 6)), + #"y_labeled_nums": list(range(0, 5)), + } + 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) + + self.setup_axes(animate = True) + + + sine1 = self.get_graph(lambda x : np.sin(x), x_min = 0, x_max = 1.575, color = GREEN) + + point1 = Dot().shift(self.graph_origin+1*YTD*UP + 1.575*XTD*RIGHT) + point1_lab = TextMobject(r"$t = (\frac{\pi}{2})$") + point1_lab.scale(0.7) + point1_lab.next_to(point1, UP) + + vector1 = Arrow(self.graph_origin, self.graph_origin+1*YTD*UP + 1.575*XTD*RIGHT, buff=0.1, color = RED) + vector1_lab = TextMobject(r"$r(\frac{\pi}{2})$", color = RED) + vector1_lab.move_to(self.graph_origin+1.5*XTD*RIGHT+ 0.5*YTD*UP) + + self.play(GrowArrow(vector1),Write(vector1_lab)) + self.play(ShowCreation(point1), Write(point1_lab)) + self.play(ShowCreation(sine1)) + self.wait(1) + + + sine2 = self.get_graph(lambda x : np.sin(x), x_min = 1.575, x_max = 3.15, color = GREEN) + + point2 = Dot().shift(self.graph_origin+3.15*XTD*RIGHT) + point2_lab = TextMobject(r"$t = (\pi)$") + point2_lab.scale(0.7) + point2_lab.next_to(point2, UP+RIGHT) + + vector2 = Arrow(self.graph_origin, self.graph_origin+3.15*XTD*RIGHT, buff=0.1, color = BLUE) + vector2_lab = TextMobject(r"$r(\pi)$", color = BLUE) + vector2_lab.move_to(self.graph_origin+1.5*XTD*RIGHT+ 0.15*YTD*UP) + + self.play(GrowArrow(vector2),Write(vector2_lab)) + self.play(ShowCreation(point2), Write(point2_lab)) + self.play(ShowCreation(sine2)) + self.wait(1) + + + sine3 = self.get_graph(lambda x : np.sin(x), x_min = 3.15, x_max = 4.725, color = GREEN) + + point3 = Dot().shift(self.graph_origin+1*YTD*DOWN + 4.725*XTD*RIGHT) + point3_lab = TextMobject(r"$t = (\frac{3\pi}{2})$") + point3_lab.scale(0.7) + point3_lab.next_to(point3, DOWN) + + vector3 = Arrow(self.graph_origin, self.graph_origin+1*YTD*DOWN + 4.725*XTD*RIGHT, buff=0.1, color = YELLOW_C) + vector3_lab = TextMobject(r"$r(\frac{3\pi}{2})$", color = YELLOW_C) + vector3_lab.move_to(self.graph_origin+2*XTD*RIGHT+ 0.7*YTD*DOWN) + + self.play(GrowArrow(vector3),Write(vector3_lab)) + self.play(ShowCreation(point3), Write(point3_lab)) + self.play(ShowCreation(sine3)) + self.wait(1) + + + sine4 = self.get_graph(lambda x : np.sin(x), x_min = 4.725, x_max = 6.3, color = GREEN) + + point4 = Dot().shift(self.graph_origin+6.3*XTD*RIGHT) + point4_lab = TextMobject(r"$t = (2\pi)$") + point4_lab.scale(0.7) + point4_lab.next_to(point4, UP+RIGHT) + + vector4 = Arrow(self.graph_origin, self.graph_origin+6.3*XTD*RIGHT, buff=0.1, color = PURPLE) + vector4_lab = TextMobject(r"$r(2\pi)$", color = PURPLE) + vector4_lab.move_to(self.graph_origin+4.5*XTD*RIGHT+ 0.15*YTD*DOWN) + + self.play(GrowArrow(vector4),Write(vector4_lab)) + self.play(ShowCreation(point4), Write(point4_lab)) + self.play(ShowCreation(sine4)) + self.wait(3) + diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file5_derivative_vectorvf.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file5_derivative_vectorvf.py new file mode 100644 index 0000000..466e389 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file5_derivative_vectorvf.py @@ -0,0 +1,247 @@ +from manimlib.imports import * + +class Derivative(GraphScene): + CONFIG = { + "x_min": 0, + "x_max": 3, + "y_min": 0, + "y_max": 5, + "graph_origin": ORIGIN+6*LEFT+3*DOWN, + "x_axis_width": 6, + "x_labeled_nums": list(range(0, 4)), + "y_labeled_nums": list(range(0, 6)), + } + 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) + + self.setup_axes(animate = True) + + graph = self.get_graph(lambda x : x*x, x_min = 0.5, x_max = 2, color = GREEN) + + point1 = Dot().shift(self.graph_origin+0.25*YTD*UP + 0.5*XTD*RIGHT) + point1_lab = TextMobject(r"$t = a$") + point1_lab.scale(0.7) + point1_lab.next_to(point1, RIGHT) + + point2 = Dot().shift(self.graph_origin+2*XTD*RIGHT+4*YTD*UP) + point2_lab = TextMobject(r"$t = b$") + point2_lab.scale(0.7) + point2_lab.next_to(point2, RIGHT) + + + vector1 = Arrow(self.graph_origin, self.graph_origin+1*YTD*UP + 1*XTD*RIGHT, buff=0.02, color = RED) + vector1_lab = TextMobject(r"$\vec r(t)$", color = RED) + vector1_lab.move_to(self.graph_origin+1.2*XTD*RIGHT+ 0.75*YTD*UP) + vector1_lab.scale(0.8) + + vector2 = Arrow(self.graph_origin, self.graph_origin+2.25*YTD*UP + 1.5*XTD*RIGHT, buff=0.02, color = YELLOW_C) + vector2_lab = TextMobject(r"$\vec r(t + h)$", color = YELLOW_C) + vector2_lab.move_to(self.graph_origin+0.5*XTD*RIGHT+ 2*YTD*UP) + vector2_lab.scale(0.8) + + vector3 = Arrow(self.graph_origin+1*YTD*UP + 1*XTD*RIGHT, self.graph_origin+2.25*YTD*UP + 1.5*XTD*RIGHT, buff=0.02, color = PINK) + vector3_lab = TextMobject(r"$\vec r(t + h) - \vec r(t)$", color = PINK) + vector3_lab.move_to(self.graph_origin+2*XTD*RIGHT+ 1.5*YTD*UP) + vector3_lab.scale(0.8) + + + self.play(ShowCreation(graph)) + self.play(ShowCreation(point1), Write(point1_lab)) + self.play(ShowCreation(point2), Write(point2_lab)) + + self.play(GrowArrow(vector1),Write(vector1_lab)) + self.play(GrowArrow(vector2),Write(vector2_lab)) + self.play(GrowArrow(vector3),Write(vector3_lab)) + self.wait(1) + + self.display_text() + + self.play(ApplyMethod(vector3_lab.move_to,(self.graph_origin+2.3*XTD*RIGHT+ 2.2*YTD*UP))) + + vector4 = Arrow(self.graph_origin+1*YTD*UP + 1*XTD*RIGHT, self.graph_origin+1*YTD*UP + 1.5*XTD*RIGHT, buff=0.02, color = PURPLE) + vector4_lab = TextMobject(r"$dx$", color = PURPLE) + vector4_lab.move_to(self.graph_origin+1.7*XTD*RIGHT+ 0.8*YTD*UP) + vector4_lab.scale(0.7) + + vector5 = Arrow(self.graph_origin+1*YTD*UP + 1.5*XTD*RIGHT, self.graph_origin+2.25*YTD*UP + 1.5*XTD*RIGHT, buff=0.02, color = ORANGE) + vector5_lab = TextMobject(r"$dy$", color = ORANGE) + vector5_lab.move_to(self.graph_origin+1.7*XTD*RIGHT+ 1.4*YTD*UP) + vector5_lab.scale(0.7) + + self.play(GrowArrow(vector4),Write(vector4_lab)) + self.play(GrowArrow(vector5),Write(vector5_lab)) + self.wait(2) + + + + def display_text(self): + text1 = TextMobject(r"$\vec r(t)$",r"+", r"$\vec r(t + h) - \vec r(t)$") + text1[0].set_color(RED) + text1[2].set_color(PINK) + text1.scale(0.7) + + text2 = TextMobject(r"$\vec r(t + h)$", color = YELLOW_C) + text2.scale(0.7) + + text3 = TextMobject(r"$ \vec r(t + h) - \vec r(t)$", color = PINK) + text3.scale(0.7) + + text4 = TextMobject(r"[", r"$x(t+h)$", r"$\vec i$", r"+", r"$y(t+h)$", r"$\vec j$", r"$] - [$", r"$x(t)$", r"$\vec i$", r"+", r"y(t)", r"$\vec j$", r"]") + text4.set_color_by_tex(r"\vec i", BLUE) + text4.set_color_by_tex(r"\vec j", GREEN) + text4[1].set_color(YELLOW_C) + text4[4].set_color(YELLOW_C) + text4[-6].set_color(RED) + text4[-3].set_color(RED) + text4.scale(0.7) + + text5 = TextMobject(r"$[x(t+h) - x(t)]$", r"$\vec i$", r"+", r"$[y(t+h) + y(t)]$", r"$\vec j$") + text5.set_color_by_tex(r"\vec i", BLUE) + text5.set_color_by_tex(r"\vec j", GREEN) + text5[0].set_color(PURPLE) + text5[3].set_color(ORANGE) + text5.scale(0.7) + + text6 = TextMobject(r"$\frac{[\vec r(t + h) - \vec r(t)]}{h}$", r"=", r"$\frac{[x(t+h) - x(t)]}{h}$", r"$\vec i$", r"+", r"$\frac{[y(t+h) + y(t)]}{h}$", r"$\vec j$") + text6.set_color_by_tex(r"\vec i", BLUE) + text6.set_color_by_tex(r"\vec j", GREEN) + text6[0].set_color(PINK) + text6[2].set_color(PURPLE) + text6[-2].set_color(ORANGE) + text6.scale(0.8) + + text7 = TextMobject(r"$\lim_{h \rightarrow 0}$", r"$\frac{[\vec r(t + h) - \vec r(t)]}{h}$", r"=", r"$\lim_{h \rightarrow 0}$", r"$\frac{[x(t+h) - x(t)]}{h}$", r"$\vec i$", r"+", r"$\lim_{h \rightarrow 0}$", r"$\frac{[y(t+h) + y(t)]}{h}$", r"$\vec j$") + text7.set_color_by_tex(r"\vec i", BLUE) + text7.set_color_by_tex(r"\vec j", GREEN) + text7[1].set_color(PINK) + text7[4].set_color(PURPLE) + text7[-2].set_color(ORANGE) + text7.scale(0.6) + + text8 = TextMobject(r"$\vec r'(t)$", r"=",r"$\vec x'(t)$", r"$\vec i$", r"+", r"$\vec y'(t)$", r"$\vec j$") + text8.set_color_by_tex(r"\vec i", BLUE) + text8.set_color_by_tex(r"\vec j", GREEN) + text8[0].set_color(PINK) + text8[2].set_color(PURPLE) + text8[5].set_color(ORANGE) + text8.scale(0.7) + + text9 = TextMobject(r"$\frac{d \vec r}{dt}$", r"=", r"$\frac{d \vec x}{dt}$", r"$\vec i$", r"+", r"$\frac{d \vec y}{dt}$", r"$\vec j$") + text9.set_color_by_tex(r"\vec i", BLUE) + text9.set_color_by_tex(r"\vec j", GREEN) + text9[0].set_color(PINK) + text9[2].set_color(PURPLE) + text9[5].set_color(ORANGE) + text9.scale(0.7) + + + text10 = TextMobject(r"$d \vec r$", r"=", r"$\frac{d \vec x}{dt}dt$", r"$\vec i$", r"+", r"$\frac{d \vec y}{dt}dt$", r"$\vec j$") + text10.set_color_by_tex(r"\vec i", BLUE) + text10.set_color_by_tex(r"\vec j", GREEN) + text10[0].set_color(PINK) + text10[2].set_color(PURPLE) + text10[5].set_color(ORANGE) + text10.scale(0.7) + + text11 = TextMobject(r"$d \vec r$", r"=", r"$x'(t)dt$", r"$\vec i$", r"+", r"$y'(t)dt$", r"$\vec j$") + text11.set_color_by_tex(r"\vec i", BLUE) + text11.set_color_by_tex(r"\vec j", GREEN) + text11[0].set_color(PINK) + text11[2].set_color(PURPLE) + text11[5].set_color(ORANGE) + text11.scale(0.7) + + text12 = TextMobject(r"$d \vec r$", r"=", r"$dx$", r"$\vec i$", r"+", r"$dy$", r"$\vec j$") + text12.set_color_by_tex(r"\vec i", BLUE) + text12.set_color_by_tex(r"\vec j", GREEN) + text12[0].set_color(PINK) + text12[2].set_color(PURPLE) + text12[5].set_color(ORANGE) + text12.scale(0.7) + + + text1.move_to(1*UP+2.7*RIGHT) + text2.move_to(1*UP+2.7*RIGHT) + text3.move_to(1*UP+2.7*RIGHT) + text4.move_to(1*UP+2.7*RIGHT) + text5.move_to(1*UP+2.7*RIGHT) + text6.move_to(1*UP+2.7*RIGHT) + text7.move_to(1*UP+2.5*RIGHT) + text8.move_to(1*UP+2.7*RIGHT) + text9.move_to(1*UP+2.7*RIGHT) + text10.move_to(1*UP+2.7*RIGHT) + text11.move_to(1*UP+2.7*RIGHT) + text12.move_to(1*UP+2.7*RIGHT) + + brace1 = Brace(text7[0:2], DOWN, buff = SMALL_BUFF) + brace2 = Brace(text7[3:6], UP, buff = SMALL_BUFF) + brace3 = Brace(text7[7:], DOWN, buff = SMALL_BUFF) + t1 = brace1.get_text(r"$\vec r'(t)$") + t1.set_color(PINK) + + t2 = brace2.get_text(r"$\vec x'(t)$") + t2.set_color(PURPLE) + + t3 = brace3.get_text(r"$\vec y'(t)$") + t3.set_color(ORANGE) + + + self.play(Write(text1)) + self.play(Transform(text1, text2)) + self.wait(1) + + self.play(Transform(text1, text3)) + self.wait(1) + + self.play(Transform(text1, text4)) + self.wait(1) + + self.play(Transform(text1, text5)) + self.wait(1) + + self.play(Transform(text1, text6)) + self.wait(1) + + self.play(Transform(text1, text7)) + self.wait(1) + + self.play( + GrowFromCenter(brace1), + FadeIn(t1), + ) + self.wait() + self.play( + ReplacementTransform(brace1.copy(),brace2), + ReplacementTransform(t1.copy(),t2) + ) + self.wait() + self.play( + ReplacementTransform(brace2.copy(),brace3), + ReplacementTransform(t2.copy(),t3) + ) + self.wait() + + self.play(FadeOut(brace1), FadeOut(t1), FadeOut(brace2), FadeOut(t2), FadeOut(brace3), FadeOut(t3),) + self.wait() + + self.play(Transform(text1, text8)) + self.wait(1) + + self.play(Transform(text1, text9)) + self.wait(1) + + self.play(Transform(text1, text10)) + self.wait(1) + + self.play(Transform(text1, text11)) + self.wait(1) + + self.play(Transform(text1, text12)) + self.wait(1) + + + + + diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file1_multivariable_func_respresentation.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file1_multivariable_func_respresentation.gif new file mode 100644 index 0000000..a173bda Binary files /dev/null and b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file1_multivariable_func_respresentation.gif differ diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file2_multivariable_func_examples.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file2_multivariable_func_examples.gif new file mode 100644 index 0000000..11f66f1 Binary files /dev/null and b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file2_multivariable_func_examples.gif differ diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file3_plot_sphere.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file3_plot_sphere.gif new file mode 100644 index 0000000..ad7582c Binary files /dev/null and b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file3_plot_sphere.gif differ diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file4_vectorvf_sine.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file4_vectorvf_sine.gif new file mode 100644 index 0000000..4f6b931 Binary files /dev/null and b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file4_vectorvf_sine.gif differ diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file5_derivative_vectorvf.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file5_derivative_vectorvf.gif new file mode 100644 index 0000000..a94de90 Binary files /dev/null and b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file5_derivative_vectorvf.gif differ -- cgit From 8cf9bc5da64361ce7d5a24a6b3a55443a447a06f Mon Sep 17 00:00:00 2001 From: nishanpoojary Date: Tue, 26 May 2020 12:37:33 +0530 Subject: Uploaded limits-and-continuity-of-multivariable-functions Folder --- .../file1_limit_approach_point.py | 66 +++++++++++++++++++++ .../gifs/file1_limit_approach_point.gif | Bin 0 -> 47411 bytes 2 files changed, 66 insertions(+) create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file1_limit_approach_point.py create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file1_limit_approach_point.gif (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives') diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file1_limit_approach_point.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file1_limit_approach_point.py new file mode 100644 index 0000000..57d1d45 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file1_limit_approach_point.py @@ -0,0 +1,66 @@ +from manimlib.imports import * + +class Limit(GraphScene): + CONFIG = { + "x_min": 0, + "x_max": 4, + "y_min": 0, + "y_max": 4, + "graph_origin": ORIGIN + 3* DOWN+4*LEFT, + "x_labeled_nums": list(range(0, 4)), + "y_labeled_nums": list(range(0, 5)), + } + def construct(self): + topic = TextMobject("Different paths of approach to limit point") + topic.scale(1.5) + topic.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE) + self.play(Write(topic)) + self.wait(1) + self.play(FadeOut(topic)) + + + + XTD = self.x_axis_width/(self.x_max- self.x_min) + YTD = self.y_axis_height/(self.y_max- self.y_min) + + self.setup_axes(animate = True) + + y_x = self.get_graph(lambda x : x, x_min = -1, x_max = 4) + y_x_lab = self.get_graph_label(y_x, label = r"y = x") + + y_xsquare = self.get_graph(lambda x : x*x, x_min = -1, x_max = 4) + y_xsquare_lab = self.get_graph_label(y_xsquare, label = r"y = x^2") + + y_1 = self.get_graph(lambda x : 1, x_min = -1, x_max = 4) + y_1_lab = self.get_graph_label(y_1, label = r"y = 1") + + y_2minusx = self.get_graph(lambda x : 2 - x, x_min = -1, x_max = 4, color = RED) + y_2minusx_lab = self.get_graph_label(y_2minusx, label = r"y = 2 - x") + + limit_point = Dot().shift(self.graph_origin+1*XTD*RIGHT+1*YTD*UP) + limit_point_lab = TextMobject(r"(1,1)") + limit_point_lab.next_to(limit_point, DOWN) + + self.play(ShowCreation(limit_point)) + self.play(Write(limit_point_lab)) + self.wait(1) + + self.play(ShowCreation(y_x)) + self.play(Write(y_x_lab)) + self.wait(1) + + self.play(ShowCreation(y_xsquare)) + self.play(Write(y_xsquare_lab)) + self.wait(1) + + self.play(ShowCreation(y_1)) + self.play(Write(y_1_lab)) + self.wait(1) + + self.play(ShowCreation(y_2minusx)) + self.play(Write(y_2minusx_lab)) + self.wait(1) + + + + \ No newline at end of file diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file1_limit_approach_point.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file1_limit_approach_point.gif new file mode 100644 index 0000000..830b6f1 Binary files /dev/null and b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file1_limit_approach_point.gif differ -- cgit From aa9bcd8cde74b592dd16051809b9f4ce70f63586 Mon Sep 17 00:00:00 2001 From: nishanpoojary Date: Tue, 26 May 2020 12:38:58 +0530 Subject: Update README.md --- .../multivariable-functions-and-paritial-derivatives/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives') diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/README.md b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/README.md index b50200d..6e4d2a8 100644 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/README.md +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/README.md @@ -4,6 +4,6 @@ Github Account : nishanpoojary ## Sub-Topics Covered: + Scalar Functions + Multivariable Functions -+ Limits and continuity of Multivariable Function ++ Limits and Continuity of Multivariable Function + Partial Derivatives + Directonal Derivatives -- cgit From 7cb7a025c6b74c1998739fdae5a84945ff708307 Mon Sep 17 00:00:00 2001 From: nishanpoojary Date: Tue, 26 May 2020 12:39:13 +0530 Subject: Update README.md --- .../multivariable-functions-and-paritial-derivatives/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives') diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/README.md b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/README.md index 6e4d2a8..7ff6b61 100644 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/README.md +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/README.md @@ -4,6 +4,6 @@ Github Account : nishanpoojary ## Sub-Topics Covered: + Scalar Functions + Multivariable Functions -+ Limits and Continuity of Multivariable Function ++ Limits and Continuity of Multivariable Functions + Partial Derivatives + Directonal Derivatives -- cgit From a72c9a676fb98c7ea1cfc8cadae197b2e5098623 Mon Sep 17 00:00:00 2001 From: nishanpoojary Date: Wed, 27 May 2020 18:49:26 +0530 Subject: Uploaded additional files and gifs --- .../file1_epsilon_delta_defn.py | 120 +++++++++++++++++++++ .../file2_limit_approach_point.py | 66 ++++++++++++ .../file3_limit_func.py | 30 ++++++ .../file4_continuity_func.py | 32 ++++++ 4 files changed, 248 insertions(+) create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file1_epsilon_delta_defn.py create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file2_limit_approach_point.py create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file3_limit_func.py create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file4_continuity_func.py (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives') diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file1_epsilon_delta_defn.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file1_epsilon_delta_defn.py new file mode 100644 index 0000000..63b6165 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file1_epsilon_delta_defn.py @@ -0,0 +1,120 @@ +from manimlib.imports import * + +class EpsilonDelta(ThreeDScene): + def construct(self): + axes = ThreeDAxes() # creates a 3D Axis + + + sphere = ParametricSurface( + lambda u, v: np.array([ + 2*np.sin(u)*np.cos(v), + 2*np.sin(u)*np.sin(v), + 2*np.cos(u) + ]),u_min=0,u_max=PI/4,v_min=0,v_max=PI/2,checkerboard_colors=[RED_D, RED_E], + resolution=(15, 32)).scale(2) + #sphere.shift(0.5*RIGHT+0.5*UP) + + #self.set_camera_orientation(phi=0*DEGREES,theta=270*DEGREES) + self.set_camera_orientation(phi=75 * DEGREES) + + + + circle = Circle(radius= 0.4,color = GREEN) + circle.shift(0.5*RIGHT+0.5*UP) + + line1 = DashedLine(np.array([0.5, 0.1,0]), np.array([0.5, 0.1,2.1]), color = BLUE_E) + line2 = DashedLine(np.array([0.5, 0.9,0]), np.array([0.5, 0.9,1.7]), color = BLUE_E) + line3 = DashedLine(np.array([0, 0,2.1]), np.array([0.5, 0.1,2.1]), color = YELLOW_C) + line4 = DashedLine(np.array([0, 0,1.7]), np.array([0.5, 0.9,1.7]), color = YELLOW_C) + + dot1 = Sphere() + dot1.scale(0.01) + dot1.move_to(np.array([0,0,1.9])) + dot1.set_fill(BLUE_E) + + temp_func1 = TextMobject(r"$L$") + temp_func1.scale(0.6) + temp_func1.set_color(BLUE_E) + + dot2 = Sphere() + dot2.scale(0.01) + dot2.move_to(np.array([0,0,1.7])) + dot2.set_fill(PURPLE) + + temp_func2 = TextMobject(r"$L - \epsilon$") + temp_func2.scale(0.6) + temp_func2.set_color(PURPLE) + + dot3 = Sphere() + dot3.scale(0.01) + dot3.move_to(np.array([0,0,2.1])) + dot3.set_fill(PURPLE) + + temp_func3 = TextMobject(r"$L + \epsilon$") + temp_func3.scale(0.6) + temp_func3.set_color(PURPLE) + + self.add(axes) + + self.play(ShowCreation(dot1)) + self.add_fixed_in_frame_mobjects(temp_func1) + temp_func1.move_to(1.9*UP) + self.play(Write(temp_func1)) + + self.play(ShowCreation(dot2)) + self.add_fixed_in_frame_mobjects(temp_func2) + temp_func2.move_to(1.7*UP) + self.play(Write(temp_func2)) + + self.play(ShowCreation(dot3)) + self.add_fixed_in_frame_mobjects(temp_func3) + temp_func3.move_to(2.1*UP) + self.play(Write(temp_func3)) + + + circle_center = Sphere() + circle_center.scale(0.05) + circle_center.move_to(np.array([0.5,0.5,0])) + circle_center.set_fill(GREEN) + + temp_circle_center = TextMobject(r"$(a,b,0)$") + temp_circle_center.scale(0.5) + temp_circle_center.set_color(GREEN) + + curve_circle_center = Sphere() + curve_circle_center.scale(0.05) + curve_circle_center.move_to(np.array([0.5,0.5,1.9])) + curve_circle_center.set_fill(BLUE_E) + + temp_curve_circle_center = TextMobject(r"$(a,b,L)$") + temp_curve_circle_center.scale(0.5) + temp_curve_circle_center.set_color(BLUE) + + delta_lab = TextMobject(r"$\delta - disk$") + delta_lab.scale(0.5) + delta_lab.set_color(PINK) + + self.play(ShowCreation(circle_center)) + self.add_fixed_in_frame_mobjects(temp_circle_center) + temp_circle_center.move_to(1.5*RIGHT) + self.play(Write(temp_circle_center)) + + self.play(ShowCreation(curve_circle_center)) + self.add_fixed_in_frame_mobjects(temp_curve_circle_center) + temp_curve_circle_center.move_to(1.9*UP+1*RIGHT) + self.play(Write(temp_curve_circle_center)) + + + self.add_fixed_in_frame_mobjects(delta_lab) + delta_lab.move_to(0.4*DOWN+1.7*RIGHT) + self.play(Write(delta_lab)) + + + + + + self.begin_ambient_camera_rotation(rate=0.2) + self.play(Write(sphere)) + self.play(ShowCreation(circle), ShowCreation(line1), ShowCreation(line2)) + self.play(ShowCreation(line3), ShowCreation(line4)) + self.wait(8) diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file2_limit_approach_point.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file2_limit_approach_point.py new file mode 100644 index 0000000..57d1d45 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file2_limit_approach_point.py @@ -0,0 +1,66 @@ +from manimlib.imports import * + +class Limit(GraphScene): + CONFIG = { + "x_min": 0, + "x_max": 4, + "y_min": 0, + "y_max": 4, + "graph_origin": ORIGIN + 3* DOWN+4*LEFT, + "x_labeled_nums": list(range(0, 4)), + "y_labeled_nums": list(range(0, 5)), + } + def construct(self): + topic = TextMobject("Different paths of approach to limit point") + topic.scale(1.5) + topic.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE) + self.play(Write(topic)) + self.wait(1) + self.play(FadeOut(topic)) + + + + XTD = self.x_axis_width/(self.x_max- self.x_min) + YTD = self.y_axis_height/(self.y_max- self.y_min) + + self.setup_axes(animate = True) + + y_x = self.get_graph(lambda x : x, x_min = -1, x_max = 4) + y_x_lab = self.get_graph_label(y_x, label = r"y = x") + + y_xsquare = self.get_graph(lambda x : x*x, x_min = -1, x_max = 4) + y_xsquare_lab = self.get_graph_label(y_xsquare, label = r"y = x^2") + + y_1 = self.get_graph(lambda x : 1, x_min = -1, x_max = 4) + y_1_lab = self.get_graph_label(y_1, label = r"y = 1") + + y_2minusx = self.get_graph(lambda x : 2 - x, x_min = -1, x_max = 4, color = RED) + y_2minusx_lab = self.get_graph_label(y_2minusx, label = r"y = 2 - x") + + limit_point = Dot().shift(self.graph_origin+1*XTD*RIGHT+1*YTD*UP) + limit_point_lab = TextMobject(r"(1,1)") + limit_point_lab.next_to(limit_point, DOWN) + + self.play(ShowCreation(limit_point)) + self.play(Write(limit_point_lab)) + self.wait(1) + + self.play(ShowCreation(y_x)) + self.play(Write(y_x_lab)) + self.wait(1) + + self.play(ShowCreation(y_xsquare)) + self.play(Write(y_xsquare_lab)) + self.wait(1) + + self.play(ShowCreation(y_1)) + self.play(Write(y_1_lab)) + self.wait(1) + + self.play(ShowCreation(y_2minusx)) + self.play(Write(y_2minusx_lab)) + self.wait(1) + + + + \ No newline at end of file diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file3_limit_func.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file3_limit_func.py new file mode 100644 index 0000000..02e00e8 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file3_limit_func.py @@ -0,0 +1,30 @@ +from manimlib.imports import * + +class LimitFunc(ThreeDScene): + def construct(self): + axes = ThreeDAxes() + + text3d = TextMobject(r"$f(x,y) = \frac{x^2 - y^2}{x^2 + y^2}$") + self.add_fixed_in_frame_mobjects(text3d) + + text3d.to_corner(UL) + + text3d.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE) + + self.play(Write(text3d)) + self.wait(1) + + limit_func = ParametricSurface( + lambda u, v: np.array([ + u*np.cos(v), + u*np.sin(v), + (np.cos(v)*np.cos(v) - np.sin(v)*np.sin(v))/3 + ]),u_min=-3,u_max=3,v_min=0,v_max=2*PI,checkerboard_colors=[YELLOW_C, YELLOW_E], + resolution=(15, 32)).scale(2) + + self.set_camera_orientation(phi=80 * DEGREES) + self.begin_ambient_camera_rotation(rate=0.3) + + self.add(axes) + self.play(Write(limit_func)) + self.wait(10) \ No newline at end of file diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file4_continuity_func.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file4_continuity_func.py new file mode 100644 index 0000000..551c8a8 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file4_continuity_func.py @@ -0,0 +1,32 @@ +from manimlib.imports import * + +class ContinuityFunc(ThreeDScene): + def construct(self): + axes = ThreeDAxes() + + text3d = TextMobject(r"$f(x,y) = \frac{3x^2y}{x^2 + y^2}$") + self.add_fixed_in_frame_mobjects(text3d) + + text3d.to_corner(UL) + + text3d.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE) + + self.play(Write(text3d)) + self.wait(1) + + continuity_func = ParametricSurface( + lambda u, v: np.array([ + u*np.cos(v), + u*np.sin(v), + 3*u*np.cos(v)*np.cos(v)*np.sin(v) + ]),u_min=-1.5,u_max=1.5,v_min=0,v_max=2*PI,checkerboard_colors=[YELLOW_C, YELLOW_E], + resolution=(15, 32)).scale(2) + + + + self.set_camera_orientation(phi=80 * DEGREES) + self.begin_ambient_camera_rotation(rate=0.3) + + self.add(axes) + self.play(Write(continuity_func)) + self.wait(8) \ No newline at end of file -- cgit From f37fbc5243fd8a60dbd1c1ae6e31536b4c68b2e7 Mon Sep 17 00:00:00 2001 From: nishanpoojary Date: Wed, 27 May 2020 18:56:42 +0530 Subject: Delete file1_limit_approach_point.py --- .../file1_limit_approach_point.py | 66 ---------------------- 1 file changed, 66 deletions(-) delete mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file1_limit_approach_point.py (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives') diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file1_limit_approach_point.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file1_limit_approach_point.py deleted file mode 100644 index 57d1d45..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file1_limit_approach_point.py +++ /dev/null @@ -1,66 +0,0 @@ -from manimlib.imports import * - -class Limit(GraphScene): - CONFIG = { - "x_min": 0, - "x_max": 4, - "y_min": 0, - "y_max": 4, - "graph_origin": ORIGIN + 3* DOWN+4*LEFT, - "x_labeled_nums": list(range(0, 4)), - "y_labeled_nums": list(range(0, 5)), - } - def construct(self): - topic = TextMobject("Different paths of approach to limit point") - topic.scale(1.5) - topic.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE) - self.play(Write(topic)) - self.wait(1) - self.play(FadeOut(topic)) - - - - XTD = self.x_axis_width/(self.x_max- self.x_min) - YTD = self.y_axis_height/(self.y_max- self.y_min) - - self.setup_axes(animate = True) - - y_x = self.get_graph(lambda x : x, x_min = -1, x_max = 4) - y_x_lab = self.get_graph_label(y_x, label = r"y = x") - - y_xsquare = self.get_graph(lambda x : x*x, x_min = -1, x_max = 4) - y_xsquare_lab = self.get_graph_label(y_xsquare, label = r"y = x^2") - - y_1 = self.get_graph(lambda x : 1, x_min = -1, x_max = 4) - y_1_lab = self.get_graph_label(y_1, label = r"y = 1") - - y_2minusx = self.get_graph(lambda x : 2 - x, x_min = -1, x_max = 4, color = RED) - y_2minusx_lab = self.get_graph_label(y_2minusx, label = r"y = 2 - x") - - limit_point = Dot().shift(self.graph_origin+1*XTD*RIGHT+1*YTD*UP) - limit_point_lab = TextMobject(r"(1,1)") - limit_point_lab.next_to(limit_point, DOWN) - - self.play(ShowCreation(limit_point)) - self.play(Write(limit_point_lab)) - self.wait(1) - - self.play(ShowCreation(y_x)) - self.play(Write(y_x_lab)) - self.wait(1) - - self.play(ShowCreation(y_xsquare)) - self.play(Write(y_xsquare_lab)) - self.wait(1) - - self.play(ShowCreation(y_1)) - self.play(Write(y_1_lab)) - self.wait(1) - - self.play(ShowCreation(y_2minusx)) - self.play(Write(y_2minusx_lab)) - self.wait(1) - - - - \ No 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