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| -rw-r--r-- | FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file1_epsilon_delta_defn.py | 120 |
1 files changed, 120 insertions, 0 deletions
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)
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