From ac83cc7b152273a6f6bd823028e7dec75a6f9fd1 Mon Sep 17 00:00:00 2001 From: nishanpoojary Date: Wed, 1 Jul 2020 11:56:42 +0530 Subject: Added updated multivariable-limits-and-continuity folder --- .../file1_epsilon_delta_defn.py | 179 +++++++++++++++++++++ 1 file changed, 179 insertions(+) create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file1_epsilon_delta_defn.py (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file1_epsilon_delta_defn.py') diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file1_epsilon_delta_defn.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file1_epsilon_delta_defn.py new file mode 100644 index 0000000..803c122 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file1_epsilon_delta_defn.py @@ -0,0 +1,179 @@ +from manimlib.imports import * + +class EpsilonDelta(ThreeDScene): + def construct(self): + axes = ThreeDAxes() # creates a 3D Axis + + + sphere = ParametricSurface( + lambda u, v: np.array([ + 3*np.sin(u)*np.cos(v), + 3*np.sin(u)*np.sin(v), + 3*np.cos(u) + ]),u_min=0,u_max=PI/4,v_min=PI/2,v_max=PI,checkerboard_colors=[RED_D, RED_E], + resolution=(15, 32)).scale(1) + + + cylinder_z = ParametricSurface( + lambda u, v: np.array([ + 0.25*np.cos(TAU * v), + 1.8* (1 - u), + 0.25*np.sin(TAU * v) + + ]), + checkerboard_colors=[YELLOW_C, YELLOW_E], resolution=(6, 32)).fade(0.2).rotate(PI/4).move_to(np.array([-0.65,0.65,2.54])) + + + cylinder_x = ParametricSurface( + lambda u, v: np.array([ + 0.3*np.cos(TAU * v)-1, + 0.3*np.sin(TAU * v)+1, + 2.6*(1 - u) + ]), + checkerboard_colors=[BLUE_C, BLUE_E], resolution=(6, 32)).fade(0.2) + + + delta_circle = Circle(radius= 0.3, color = BLACK).shift(1*LEFT+1*UP).set_fill(GREEN_E, opacity = 0.5) + + epsilon_circle = [np.array([0.25*np.cos(i*DEGREES),0,0.25*np.sin(i*DEGREES)]) for i in range(361)] + + epsilon_circle_polygon = Polygon(*epsilon_circle, color = RED_E, fill_color = RED_E, fill_opacity = 0.5).rotate(PI/4).move_to(np.array([0,0,2.54])) + + + dot_circle = Dot().move_to(np.array([-1,1,0])).set_fill("#000080") + + dot_surface = Dot().rotate(-PI/4).scale(1.5).move_to(np.array([-1.2,1.2,2.7])).set_fill("#000080") + + dot_L_epsilon1 = Polygon(*[np.array([0.05*np.cos(i*DEGREES),0,0.05*np.sin(i*DEGREES)]) for i in range(361)], color = "#000080", fill_color = "#000080", fill_opacity = 1).rotate(PI/4).move_to(np.array([0,0,2.3])) + + dot_L_epsilon2 = Polygon(*[np.array([0.05*np.cos(i*DEGREES),0,0.05*np.sin(i*DEGREES)]) for i in range(361)], color = "#000080", fill_color = "#000080", fill_opacity = 1).rotate(PI/4).move_to(np.array([0,0,2.8])) + + dot_L = Polygon(*[np.array([0.05*np.cos(i*DEGREES),0,0.05*np.sin(i*DEGREES)]) for i in range(361)], color = "#006400", fill_color = "#006400", fill_opacity = 1).rotate(PI/4).move_to(np.array([0,0,2.54])) + + + + self.add(axes) + + axis = TextMobject(r"X",r"Y",r"Z") + axis[0].move_to(6*RIGHT) + axis[1].move_to(6*UP) + axis[2].move_to(np.array([0,0,3.7])) + + self.add_fixed_orientation_mobjects(axis[2]) + self.add_fixed_orientation_mobjects(axis[0]) + self.add_fixed_orientation_mobjects(axis[1]) + + self.set_camera_orientation(phi=75*DEGREES,theta=135*DEGREES) + #self.set_camera_orientation(phi=80*DEGREES,theta=45*DEGREES) + + + self.play(ShowCreation(sphere),ShowCreation(delta_circle), ShowCreation(dot_circle)) + + temp_circle_center = TextMobject(r"$(a,b,0)$").scale(0.6).set_color(BLUE_C).move_to(1.7*LEFT+1.1*UP) + self.add_fixed_orientation_mobjects(temp_circle_center) + self.wait() + + delta_lab = TextMobject(r"$\delta$", r"$-$", "disk").scale(0.5).move_to(0.6*LEFT+1.7*UP) + delta_lab[0].set_color(PINK).scale(1.3) + delta_lab[1].set_color(ORANGE) + delta_lab[2].set_color(GREEN_E) + + self.add_fixed_orientation_mobjects(delta_lab) + + self.play(ShowCreation(dot_surface)) + + temp_curve_circle_center = TextMobject(r"$(a,b,L)$").scale(0.6).set_color("#006400").move_to(np.array([-2,1,2.7])) + self.add_fixed_orientation_mobjects(temp_curve_circle_center) + + + self.wait() + self.play(ShowCreation(cylinder_x), FadeOut(dot_surface)) + self.wait() + + self.move_camera(phi=0* DEGREES,theta=135*DEGREES) + self.wait() + + self.move_camera(phi=80* DEGREES,theta=225*DEGREES) + self.wait() + + self.play(FadeOut(delta_lab), ShowCreation(cylinder_z)) + self.wait() + + self.play(FadeOut(temp_circle_center), FadeOut(temp_curve_circle_center),ShowCreation(epsilon_circle_polygon)) + + self.move_camera(phi=80* DEGREES,theta=325*DEGREES) + + dot_L_epsilon1_lab = TextMobject(r"$L$", r"$-$", r"$\epsilon$").scale(0.6).move_to(np.array([-0.4,-0.4,2.3])) + dot_L_epsilon1_lab[0].set_color("#D4108A") + dot_L_epsilon1_lab[1].set_color("#006400") + dot_L_epsilon1_lab[2].set_color("#4DC8A1").scale(1.5) + + dot_L_epsilon2_lab = TextMobject(r"$L$", r"$+$", r"$\epsilon$").scale(0.6).move_to(np.array([-0.4,-0.4,2.8])) + dot_L_epsilon2_lab[0].set_color("#D4108A") + dot_L_epsilon2_lab[1].set_color("#006400") + dot_L_epsilon2_lab[2].set_color("#4DC8A1").scale(1.5) + + dot_L_lab = TextMobject(r"$L$").scale(0.6).set_color("#D4108A").move_to(np.array([-0.4,-0.4,2.54])) + + + self.play(ShowCreation(dot_L_epsilon1), ShowCreation(dot_L), ShowCreation(dot_L_epsilon2)) + self.add_fixed_orientation_mobjects(dot_L_epsilon1_lab, dot_L_epsilon2_lab, dot_L_lab) + self.wait(4) + + self.move_camera(phi=80* DEGREES,theta=45*DEGREES) + self.wait(2) + + + + + + + + + + + + + + + ''' + + + + + + + + + + + + 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(ShowCreation(circle), ShowCreation(line1), ShowCreation(line2)) + self.play(ShowCreation(line3), ShowCreation(line4)) + self.wait(8) + ''' \ No newline at end of file -- cgit