diff options
Diffstat (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions')
9 files changed, 0 insertions, 248 deletions
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/Limits_and_Continuity_of_Multivariable_Function_Quiz.pdf b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/Limits_and_Continuity_of_Multivariable_Function_Quiz.pdf Binary files differdeleted file mode 100644 index 99918e5..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/Limits_and_Continuity_of_Multivariable_Function_Quiz.pdf +++ /dev/null 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 deleted file mode 100644 index 63b6165..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file1_epsilon_delta_defn.py +++ /dev/null @@ -1,120 +0,0 @@ -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 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/file2_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 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 deleted file mode 100644 index 02e00e8..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file3_limit_func.py +++ /dev/null @@ -1,30 +0,0 @@ -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 deleted file mode 100644 index 551c8a8..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file4_continuity_func.py +++ /dev/null @@ -1,32 +0,0 @@ -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 diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file1_epsilon_delta_defn.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file1_epsilon_delta_defn.gif Binary files differdeleted file mode 100644 index 68f637e..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file1_epsilon_delta_defn.gif +++ /dev/null diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file2_limit_approach_point.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file2_limit_approach_point.gif Binary files differdeleted file mode 100644 index 830b6f1..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file2_limit_approach_point.gif +++ /dev/null diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file3_limit_func.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file3_limit_func.gif Binary files differdeleted file mode 100644 index 07b23be..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file3_limit_func.gif +++ /dev/null diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file4_continuity_func.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file4_continuity_func.gif Binary files differdeleted file mode 100644 index 560e0f1..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file4_continuity_func.gif +++ /dev/null |
