From dec03b51ad54f9a869a5db0a0bdad2f5b1d2313a Mon Sep 17 00:00:00 2001
From: stayaryan
Date: Mon, 20 Jul 2020 17:38:44 +0530
Subject: pull request
---
.../intro-to-calculus/gabriels-horn/gabriel1.py | 67 +++++++++++++++++++
.../intro-to-calculus/gabriels-horn/gabriel2.py | 43 ++++++++++++
.../intro-to-calculus/gabrielshorn/gabriel1.py | 67 -------------------
.../intro-to-calculus/gabrielshorn/gabriel2.py | 43 ------------
.../intro-to-derivative/derivative1.py | 55 +++++++++++++++
.../intro-to-derivative/derivative2.py | 78 ++++++++++++++++++++++
.../intro-to-derivative/derivative3.py | 57 ++++++++++++++++
.../introderivative/derivative1.py | 55 ---------------
.../introderivative/derivative2.py | 78 ----------------------
.../introderivative/derivative3.py | 57 ----------------
.../calculus/intro-to-calculus/limit/limitdef.py | 73 --------------------
.../calculus/intro-to-calculus/limit/limitfin1.py | 76 +++++++++++++++++++++
.../calculus/intro-to-calculus/limit/limitfin2.py | 70 +++++++++++++++++++
.../intro-to-calculus/riemann-integrals/README.md | 18 +++++
.../RiemannRectanglesAnimation.py | 66 ++++++++++++++++++
.../intro-to-calculus/riemann-integrals/mimi.py | 53 +++++++++++++++
.../riemann-integrals/rierect1.py | 31 +++++++++
.../riemann-integrals/rierect2.py | 31 +++++++++
.../riemann-integrals/rierect3.py | 31 +++++++++
.../intro-to-calculus/riemannintegrals/README.md | 18 -----
.../riemannintegrals/RiemannRectanglesAnimation.py | 66 ------------------
.../intro-to-calculus/riemannintegrals/mimi.py | 53 ---------------
.../intro-to-calculus/riemannintegrals/rierect1.py | 31 ---------
.../intro-to-calculus/riemannintegrals/rierect2.py | 31 ---------
.../intro-to-calculus/riemannintegrals/rierect3.py | 31 ---------
25 files changed, 676 insertions(+), 603 deletions(-)
create mode 100644 FSF-2020/calculus/intro-to-calculus/gabriels-horn/gabriel1.py
create mode 100644 FSF-2020/calculus/intro-to-calculus/gabriels-horn/gabriel2.py
delete mode 100644 FSF-2020/calculus/intro-to-calculus/gabrielshorn/gabriel1.py
delete mode 100644 FSF-2020/calculus/intro-to-calculus/gabrielshorn/gabriel2.py
create mode 100644 FSF-2020/calculus/intro-to-calculus/intro-to-derivative/derivative1.py
create mode 100644 FSF-2020/calculus/intro-to-calculus/intro-to-derivative/derivative2.py
create mode 100644 FSF-2020/calculus/intro-to-calculus/intro-to-derivative/derivative3.py
delete mode 100644 FSF-2020/calculus/intro-to-calculus/introderivative/derivative1.py
delete mode 100644 FSF-2020/calculus/intro-to-calculus/introderivative/derivative2.py
delete mode 100644 FSF-2020/calculus/intro-to-calculus/introderivative/derivative3.py
delete mode 100644 FSF-2020/calculus/intro-to-calculus/limit/limitdef.py
create mode 100644 FSF-2020/calculus/intro-to-calculus/limit/limitfin1.py
create mode 100644 FSF-2020/calculus/intro-to-calculus/limit/limitfin2.py
create mode 100644 FSF-2020/calculus/intro-to-calculus/riemann-integrals/README.md
create mode 100644 FSF-2020/calculus/intro-to-calculus/riemann-integrals/RiemannRectanglesAnimation.py
create mode 100644 FSF-2020/calculus/intro-to-calculus/riemann-integrals/mimi.py
create mode 100644 FSF-2020/calculus/intro-to-calculus/riemann-integrals/rierect1.py
create mode 100644 FSF-2020/calculus/intro-to-calculus/riemann-integrals/rierect2.py
create mode 100644 FSF-2020/calculus/intro-to-calculus/riemann-integrals/rierect3.py
delete mode 100644 FSF-2020/calculus/intro-to-calculus/riemannintegrals/README.md
delete mode 100644 FSF-2020/calculus/intro-to-calculus/riemannintegrals/RiemannRectanglesAnimation.py
delete mode 100644 FSF-2020/calculus/intro-to-calculus/riemannintegrals/mimi.py
delete mode 100644 FSF-2020/calculus/intro-to-calculus/riemannintegrals/rierect1.py
delete mode 100644 FSF-2020/calculus/intro-to-calculus/riemannintegrals/rierect2.py
delete mode 100644 FSF-2020/calculus/intro-to-calculus/riemannintegrals/rierect3.py
(limited to 'FSF-2020/calculus')
diff --git a/FSF-2020/calculus/intro-to-calculus/gabriels-horn/gabriel1.py b/FSF-2020/calculus/intro-to-calculus/gabriels-horn/gabriel1.py
new file mode 100644
index 0000000..3596c88
--- /dev/null
+++ b/FSF-2020/calculus/intro-to-calculus/gabriels-horn/gabriel1.py
@@ -0,0 +1,67 @@
+from manimlib.imports import *
+class sphere(GraphScene, ThreeDScene):
+ CONFIG = {
+ 'x_min': 0,
+ 'x_max': 10,
+ 'y_min': -3,
+ 'y_max': 3,
+ 'graph_origin': ORIGIN,
+ "x_axis_width": 10,
+ "y_axis_height": 10,
+ "default_graph_style": {
+ "stroke_width": 2,
+ "stroke_color": WHITE,
+ }
+ }
+ 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)
+
+ text1 = TexMobject(r"y=\frac { 1 }{ x }").move_to(np.array([3,2,0]))
+ text1a = TexMobject(r"y=\frac { 1 }{ x }, x \ge 1").move_to(np.array([3,2,0]))
+ text2 = TexMobject(r"y=\frac { 1 }{ x }", r"\text{ is rotated in 3-dimensions}").to_corner(UL)
+ text3 = TextMobject("For calculating volume, consider a disc as shown").to_corner(UL)
+ text4 = TextMobject("Imagine the disc to move along the length of the horn").to_corner(UL)
+ text5 = TextMobject("In this way complete volume is covered").to_corner(UL)
+ arrow = Vector(np.array([0, np.sin(60*DEGREES), np.cos(60*DEGREES)])).shift(1*RIGHT)
+ text6 = TexMobject(r"\text{Area of circle is }", r"\pi {r}^{2}").to_corner(UL)
+ text7 = TextMobject("The disc moves along the length of hyperbolic curve").to_corner(UL)
+
+ axes = ThreeDAxes(**self.CONFIG)
+ self.setup_axes()
+ graph1 = self.get_graph(lambda x : 1/x, x_min = 1, x_max = 10)
+ graph2 = self.get_graph(lambda x : 1/x, x_min = 0.1, x_max = 10)
+ self.play(FadeIn(self.axes))
+ self.play(ShowCreation(graph2), FadeIn(text1))
+ self.wait(3)
+ self.play(Transform(graph2, graph1), ReplacementTransform(text1, text1a))
+ axes = ThreeDAxes(**self.CONFIG)
+ self.move_camera(phi = 90*DEGREES, theta=0*DEGREES,distance = 200, run_time=5)
+ horn2 = ParametricSurface(lambda u, v : np.array([1*u, (1*np.cos(TAU*v))/u,(1*np.sin(TAU*v))/u]), u_min = 1, v_min = 0.001, u_max = 10, fill_opacity = 0.1)
+ self.play(Transform(graph2, horn2), FadeOut(text1), FadeOut(graph2), ShowCreation(text2), FadeOut(text1a))
+ self.wait(2)
+ self.play(FadeOut(text2))
+ self.add_fixed_in_frame_mobjects(text3)
+ self.wait(1)
+ disc = ParametricSurface(lambda u, v : np.array([0, 1*v*np.sin(TAU*u), 1*v*np.cos(TAU*u)]), fill_opacity = 1, fill_color = PINK).shift(1*RIGHT)
+ self.play(ShowCreation(disc), ShowCreation(arrow))
+ self.play(FadeOut(text3))
+ self.add_fixed_in_frame_mobjects(text6)
+ self.wait(3)
+ self.play(FadeOut(text6))
+ self.add_fixed_in_frame_mobjects(text7)
+ self.wait(2)
+ self.move_camera(phi = 60*DEGREES, theta= -45*DEGREES, distance = 200, run_time=5)
+ #self.play(FadeOut(text6))
+ #self.add_fixed_in_frame_mobjects(text7)
+ k=0
+ while k<9:
+ disc1 = ParametricSurface(lambda u, v : np.array([0, (1/(1+k))*v*np.sin(TAU*u), (1/(1+k))*v*np.cos(TAU*u)]), fill_opacity = 0.5, fill_color = PINK).shift((1+k)*RIGHT)
+ self.play(FadeIn(disc1), run_time = 0.1)
+ k = k+0.1
+ self.play(FadeOut(text7))
+ self.add_fixed_in_frame_mobjects(text5)
+ self.wait(2)
+ self.begin_ambient_camera_rotation(rate = 0.4)
+ self.wait(10)
+ self.stop_ambient_camera_rotation()
\ No newline at end of file
diff --git a/FSF-2020/calculus/intro-to-calculus/gabriels-horn/gabriel2.py b/FSF-2020/calculus/intro-to-calculus/gabriels-horn/gabriel2.py
new file mode 100644
index 0000000..1e2a820
--- /dev/null
+++ b/FSF-2020/calculus/intro-to-calculus/gabriels-horn/gabriel2.py
@@ -0,0 +1,43 @@
+from manimlib.imports import *
+class surface(GraphScene, ThreeDScene):
+ CONFIG = {
+ 'x_min': 0,
+ 'x_max': 10,
+ 'y_min': -3,
+ 'y_max': 3,
+ 'graph_origin': ORIGIN,
+ "x_axis_width": 10,
+ "y_axis_height": 10,
+ "default_graph_style": {
+ "stroke_width": 2,
+ "stroke_color": RED,
+ }
+ }
+ 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()
+ text1 = TexMobject(r"y=\frac { 1 }{ x }").move_to(np.array([3,2,0]))
+ text2 = TexMobject(r"\int _{ 1 }^{ \infty }{ \frac { 1 }{ x } dx }", r"\text{ diverges}").to_corner(UL)
+ text3 = TexMobject(r"\text{Hence }", r"\int _{ 1 }^{ \infty }{ \frac { 1 }{ x } dx=\infty }").to_corner(UL)
+ text4 = TextMobject("Which means surface area is infinity").to_corner(UL)
+ graph1 = self.get_graph(lambda x : 1/x, x_min = 1, x_max = 10)
+ self.play(FadeIn(self.axes))
+ self.play(ShowCreation(graph1), FadeIn(text1))
+ self.wait(5)
+ axes = ThreeDAxes(**self.CONFIG)
+ self.move_camera(phi = 60*DEGREES, theta=45*DEGREES,distance = 200, run_time=5)
+ horn2 = ParametricSurface(lambda u, v : np.array([1*u, (1*np.cos(TAU*v))/u,(1*np.sin(TAU*v))/u]), u_min = 1, v_min = 0.001, u_max = 10, fill_opacity = 0.1)
+ horn3 = ParametricSurface(lambda u, v : np.array([1*u, (1*np.cos(TAU*v))/u,(1*np.sin(TAU*v))/u]), u_min = 1, v_min = 0.001, u_max = 10, fill_opacity = 1)
+ self.play(Transform(graph1, horn2))
+ self.play(FadeOut(text1))
+ self.add_fixed_in_frame_mobjects(text2)
+ self.wait(3)
+ self.play(FadeOut(text2))
+ self.add_fixed_in_frame_mobjects(text3)
+ self.wait(3)
+ self.play(ShowCreation(horn3))
+ self.play(FadeOut(text3))
+ self.add_fixed_in_frame_mobjects(text4)
+ self.wait(5)
\ No newline at end of file
diff --git a/FSF-2020/calculus/intro-to-calculus/gabrielshorn/gabriel1.py b/FSF-2020/calculus/intro-to-calculus/gabrielshorn/gabriel1.py
deleted file mode 100644
index 3596c88..0000000
--- a/FSF-2020/calculus/intro-to-calculus/gabrielshorn/gabriel1.py
+++ /dev/null
@@ -1,67 +0,0 @@
-from manimlib.imports import *
-class sphere(GraphScene, ThreeDScene):
- CONFIG = {
- 'x_min': 0,
- 'x_max': 10,
- 'y_min': -3,
- 'y_max': 3,
- 'graph_origin': ORIGIN,
- "x_axis_width": 10,
- "y_axis_height": 10,
- "default_graph_style": {
- "stroke_width": 2,
- "stroke_color": WHITE,
- }
- }
- 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)
-
- text1 = TexMobject(r"y=\frac { 1 }{ x }").move_to(np.array([3,2,0]))
- text1a = TexMobject(r"y=\frac { 1 }{ x }, x \ge 1").move_to(np.array([3,2,0]))
- text2 = TexMobject(r"y=\frac { 1 }{ x }", r"\text{ is rotated in 3-dimensions}").to_corner(UL)
- text3 = TextMobject("For calculating volume, consider a disc as shown").to_corner(UL)
- text4 = TextMobject("Imagine the disc to move along the length of the horn").to_corner(UL)
- text5 = TextMobject("In this way complete volume is covered").to_corner(UL)
- arrow = Vector(np.array([0, np.sin(60*DEGREES), np.cos(60*DEGREES)])).shift(1*RIGHT)
- text6 = TexMobject(r"\text{Area of circle is }", r"\pi {r}^{2}").to_corner(UL)
- text7 = TextMobject("The disc moves along the length of hyperbolic curve").to_corner(UL)
-
- axes = ThreeDAxes(**self.CONFIG)
- self.setup_axes()
- graph1 = self.get_graph(lambda x : 1/x, x_min = 1, x_max = 10)
- graph2 = self.get_graph(lambda x : 1/x, x_min = 0.1, x_max = 10)
- self.play(FadeIn(self.axes))
- self.play(ShowCreation(graph2), FadeIn(text1))
- self.wait(3)
- self.play(Transform(graph2, graph1), ReplacementTransform(text1, text1a))
- axes = ThreeDAxes(**self.CONFIG)
- self.move_camera(phi = 90*DEGREES, theta=0*DEGREES,distance = 200, run_time=5)
- horn2 = ParametricSurface(lambda u, v : np.array([1*u, (1*np.cos(TAU*v))/u,(1*np.sin(TAU*v))/u]), u_min = 1, v_min = 0.001, u_max = 10, fill_opacity = 0.1)
- self.play(Transform(graph2, horn2), FadeOut(text1), FadeOut(graph2), ShowCreation(text2), FadeOut(text1a))
- self.wait(2)
- self.play(FadeOut(text2))
- self.add_fixed_in_frame_mobjects(text3)
- self.wait(1)
- disc = ParametricSurface(lambda u, v : np.array([0, 1*v*np.sin(TAU*u), 1*v*np.cos(TAU*u)]), fill_opacity = 1, fill_color = PINK).shift(1*RIGHT)
- self.play(ShowCreation(disc), ShowCreation(arrow))
- self.play(FadeOut(text3))
- self.add_fixed_in_frame_mobjects(text6)
- self.wait(3)
- self.play(FadeOut(text6))
- self.add_fixed_in_frame_mobjects(text7)
- self.wait(2)
- self.move_camera(phi = 60*DEGREES, theta= -45*DEGREES, distance = 200, run_time=5)
- #self.play(FadeOut(text6))
- #self.add_fixed_in_frame_mobjects(text7)
- k=0
- while k<9:
- disc1 = ParametricSurface(lambda u, v : np.array([0, (1/(1+k))*v*np.sin(TAU*u), (1/(1+k))*v*np.cos(TAU*u)]), fill_opacity = 0.5, fill_color = PINK).shift((1+k)*RIGHT)
- self.play(FadeIn(disc1), run_time = 0.1)
- k = k+0.1
- self.play(FadeOut(text7))
- self.add_fixed_in_frame_mobjects(text5)
- self.wait(2)
- self.begin_ambient_camera_rotation(rate = 0.4)
- self.wait(10)
- self.stop_ambient_camera_rotation()
\ No newline at end of file
diff --git a/FSF-2020/calculus/intro-to-calculus/gabrielshorn/gabriel2.py b/FSF-2020/calculus/intro-to-calculus/gabrielshorn/gabriel2.py
deleted file mode 100644
index 1e2a820..0000000
--- a/FSF-2020/calculus/intro-to-calculus/gabrielshorn/gabriel2.py
+++ /dev/null
@@ -1,43 +0,0 @@
-from manimlib.imports import *
-class surface(GraphScene, ThreeDScene):
- CONFIG = {
- 'x_min': 0,
- 'x_max': 10,
- 'y_min': -3,
- 'y_max': 3,
- 'graph_origin': ORIGIN,
- "x_axis_width": 10,
- "y_axis_height": 10,
- "default_graph_style": {
- "stroke_width": 2,
- "stroke_color": RED,
- }
- }
- 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()
- text1 = TexMobject(r"y=\frac { 1 }{ x }").move_to(np.array([3,2,0]))
- text2 = TexMobject(r"\int _{ 1 }^{ \infty }{ \frac { 1 }{ x } dx }", r"\text{ diverges}").to_corner(UL)
- text3 = TexMobject(r"\text{Hence }", r"\int _{ 1 }^{ \infty }{ \frac { 1 }{ x } dx=\infty }").to_corner(UL)
- text4 = TextMobject("Which means surface area is infinity").to_corner(UL)
- graph1 = self.get_graph(lambda x : 1/x, x_min = 1, x_max = 10)
- self.play(FadeIn(self.axes))
- self.play(ShowCreation(graph1), FadeIn(text1))
- self.wait(5)
- axes = ThreeDAxes(**self.CONFIG)
- self.move_camera(phi = 60*DEGREES, theta=45*DEGREES,distance = 200, run_time=5)
- horn2 = ParametricSurface(lambda u, v : np.array([1*u, (1*np.cos(TAU*v))/u,(1*np.sin(TAU*v))/u]), u_min = 1, v_min = 0.001, u_max = 10, fill_opacity = 0.1)
- horn3 = ParametricSurface(lambda u, v : np.array([1*u, (1*np.cos(TAU*v))/u,(1*np.sin(TAU*v))/u]), u_min = 1, v_min = 0.001, u_max = 10, fill_opacity = 1)
- self.play(Transform(graph1, horn2))
- self.play(FadeOut(text1))
- self.add_fixed_in_frame_mobjects(text2)
- self.wait(3)
- self.play(FadeOut(text2))
- self.add_fixed_in_frame_mobjects(text3)
- self.wait(3)
- self.play(ShowCreation(horn3))
- self.play(FadeOut(text3))
- self.add_fixed_in_frame_mobjects(text4)
- self.wait(5)
\ No newline at end of file
diff --git a/FSF-2020/calculus/intro-to-calculus/intro-to-derivative/derivative1.py b/FSF-2020/calculus/intro-to-calculus/intro-to-derivative/derivative1.py
new file mode 100644
index 0000000..79a6fc6
--- /dev/null
+++ b/FSF-2020/calculus/intro-to-calculus/intro-to-derivative/derivative1.py
@@ -0,0 +1,55 @@
+from manimlib.imports import *
+class derivative1(GraphScene, Scene):
+ def setup(self):
+ GraphScene.setup(self)
+ CONFIG = {
+ "y_max" : 4,
+ "y_min" : -2,
+ "x_max" : 4,
+ "x_min" : -2,
+ "y_tick_frequency" : 1,
+ "x_tick_frequency" : 1,
+ "axes_color" : WHITE,
+ "num_graph_anchor_points": 3000, #this is the number of points that graph manim
+ "graph_origin" : ORIGIN+2*DOWN+4*LEFT,
+ "x_labeled_nums": list(range(-2,5)),
+ "y_labeled_nums": list(range(-2,5)),
+ "x_axis_label":"$x$",
+ "y_axis_label":r"$f(x)=y= 3-\frac { 3 }{ 2 } x$",
+ "x_axis_width": 5,
+ "y_axis_height": 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)
+
+ text1 = TextMobject("")
+ text2 = TexMobject("{y}_{2}-{y}_{1}")
+ text2 = TexMobject("{x}_{2}-{x}_{1}")
+ text3 = TexMobject(r"m\quad =\frac { { y }_{ 2 }-{ y }_{ 1 } }{ { x }_{ 2 }-{ x }_{ 1 } }").move_to(np.array([3,0,0]))
+ text4 = TexMobject(r"m\quad =\frac { 3 }{ -2 }").move_to(np.array([3,0,0]))
+ text5 = TexMobject(r"m\quad =\quad -1.5").move_to(np.array([3,0,0]))
+ self.setup_axes()
+ graph_1 = self.get_graph(lambda x : 3-1.5*x, color = GREEN_SCREEN, x_min = -1, x_max = 3)
+ graph_2 = self.get_graph(lambda x : 3.1-1.5*x, color = ORANGE, x_min = 0, x_max = 2)
+ dot1 = Dot()
+ dot2 = SmallDot(self.graph_origin+1.7*RIGHT, color = PINK)
+ dot3 = SmallDot(self.graph_origin+2.5*UP, color = RED_B)
+ vec1 = Vector(2.5*DOWN, color = PINK).shift(self.graph_origin+2.5*UP)
+ vec2 = Vector(1.7*RIGHT, color = RED_B).shift(self.graph_origin)
+ brace1 = Brace(vec1, LEFT)
+ brace2 = Brace(vec2, DOWN)
+ br1text = brace1.get_text(r"${y}_{2}-{y}_{1}$").next_to(brace1, LEFT)
+ br2text = brace2.get_text(r"${x}_{2}-{x}_{1}$").next_to(brace2, DOWN)
+ self.play(ShowCreation(graph_1), ShowCreation(dot2), ShowCreation(dot3))
+ self.play(MoveAlongPath(dot1, graph_2), ShowCreation(vec1), ShowCreation(vec2), run_time = 3)
+ self.wait(1)
+ self.play(ShowCreation(brace1), ShowCreation(brace2))
+ self.play(ShowCreation(br1text), ShowCreation(br2text))
+ self.wait(2)
+ self.play(GrowFromCenter(text3))
+ self.wait(2.5)
+ self.play(ReplacementTransform(text3, text4))
+ self.wait(2)
+ self.play(ReplacementTransform(text4, text5))
+ self.wait(2)
diff --git a/FSF-2020/calculus/intro-to-calculus/intro-to-derivative/derivative2.py b/FSF-2020/calculus/intro-to-calculus/intro-to-derivative/derivative2.py
new file mode 100644
index 0000000..d6aab15
--- /dev/null
+++ b/FSF-2020/calculus/intro-to-calculus/intro-to-derivative/derivative2.py
@@ -0,0 +1,78 @@
+from manimlib.imports import *
+class derivative2(GraphScene, MovingCameraScene):
+ def setup(self):
+ GraphScene.setup(self)
+ MovingCameraScene.setup(self)
+ CONFIG = {
+ "y_max" : 100,
+ "y_min" : 0,
+ "x_max" : 10,
+ "x_min" : 0,
+ "y_tick_frequency" : 100,
+ "x_tick_frequency" : 10,
+ "axes_color" : WHITE,
+ "num_graph_anchor_points": 3000, #this is the number of points that graph manim
+ "graph_origin" : ORIGIN,
+ "x_labeled_nums": None,#list(range(0,11)),
+ "y_labeled_nums": None,#list(range(0,101))[::10],
+ "x_axis_label":"$x$",
+ "y_axis_label":"$f(x)$",
+ "x_axis_width": 5,
+ "y_axis_height": 5,
+ "start_x" : 2,
+ "start_dx" : 6,
+ "df_color" : YELLOW,
+ "dx_color" : GREEN,
+ "secant_line_color" : MAROON_B,
+ "zoomed_camera_frame_starting_position": ORIGIN+2*DOWN+6*LEFT,
+ }
+ def construct(self):
+ self.setup()
+ self.camera_frame.save_state()
+ self.graph_origin = ORIGIN+2*DOWN+6*LEFT
+ self.setup_axes()
+ graph23 = self.get_graph(lambda x : x**2+7, color = GREEN_SCREEN, x_min = 0, x_max = 10)
+ graph24 = self.get_graph(lambda x : x**2+7, color = GREEN_SCREEN, x_min = 8, x_max = 2.01)
+ line_1 = DashedVMobject(Line(np.array([-5,-2,0]), np.array([-5,-1.42,0])))
+ textdef = TextMobject("")
+ text1 = TexMobject("{ x }_{ 0 }").move_to(np.array([-5,-2.2,0]))
+ text2 = TextMobject("The line becomes tangential to the curve").move_to(self.graph_origin+RIGHT+0.5*UP).scale(0.01)
+ text3 = TexMobject(r"\frac { df }{ dx } =\frac { f({ x }_{ 0 }+h)-f({ x }_{ 0 }) }{ h-0 }").move_to(2*RIGHT)
+ text4 = TexMobject(r"\frac { df }{ dx } =\lim _{ h\rightarrow 0 }{ \frac { f({ x }_{ 0 }+h)-f({ x }_{ 0 }) }{ h } }").move_to(2*RIGHT)
+ squareobj = Square(side_length = 15).move_to(self.graph_origin+RIGHT+0.53*UP)
+ ss_group = self.get_secant_slope_group(
+ self.start_x, graph23,
+ dx = self.start_dx,
+ dx_label = "h",
+ df_label = "df",
+ df_line_color = self.df_color,
+ dx_line_color = self.dx_color,
+ secant_line_color = self.secant_line_color,
+ dot_df_top = True,
+ dot_dx_start = True,
+ dot_df_top_label = "Q",
+ dot_dx_start_label = "P",
+ secant_line_length = 8
+ )
+ self.play(ShowCreation(graph23))
+ self.wait()
+ self.play(ShowCreation(ss_group.secant_line))
+ self.add(text1)
+ self.play(ShowCreation(line_1))
+ self.wait(3)
+ self.play(ShowCreation(ss_group.dx_line))
+ self.play(ShowCreation(ss_group.dx_label))
+ self.play(ShowCreation(ss_group.df_line))
+ self.play(Write(ss_group.df_label))
+ self.play(ShowCreation(ss_group.dot_df_top), ShowCreation(ss_group.dot_dx_start))
+ self.play(ShowCreation(ss_group.dot_df_top_label), ShowCreation(ss_group.dot_dx_start_label))
+ self.wait()
+ self.play(ShowCreation(text3))
+ self.wait(2)
+ self.play(ReplacementTransform(text3, text4))
+ self.animate_secant_slope_group_change(ss_group, target_dx = 0.01, run_time = 5)
+ self.wait(2)
+ self.play(self.camera_frame.set_width,0.2,self.camera_frame.move_to,squareobj,run_time = 2)
+ self.wait()
+ self.play(ShowCreation(text2))
+ self.wait(3)
diff --git a/FSF-2020/calculus/intro-to-calculus/intro-to-derivative/derivative3.py b/FSF-2020/calculus/intro-to-calculus/intro-to-derivative/derivative3.py
new file mode 100644
index 0000000..ebbacb1
--- /dev/null
+++ b/FSF-2020/calculus/intro-to-calculus/intro-to-derivative/derivative3.py
@@ -0,0 +1,57 @@
+from manimlib.imports import *
+class derivative3(GraphScene, Scene):
+ def setup(self):
+ Scene.setup(self)
+ #ZoomedScene.setup(self)
+ CONFIG = {
+ "y_max" : 8,
+ "y_min" : 0,
+ "x_max" : 11,
+ "x_min" : 0,
+ "y_tick_frequency" : 1,
+ "x_tick_frequency" : 1,
+ "axes_color" : WHITE,
+ "num_graph_anchor_points": 3000, #this is the number of points that graph manim
+ "graph_origin" : ORIGIN+3*DOWN+6.5*LEFT,
+ "x_labeled_nums": list(range(0,12))[::1],
+ "y_labeled_nums": list(range(0,9))[::1],
+ "x_axis_label":"$t$",
+ "y_axis_label":"$s$",
+ "x_axis_width": 5,
+ "y_axis_height": 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()
+ graph_1 = self.get_graph(lambda x : -(x-2)**2+4, color = GOLD_A, x_min = 0, x_max = 1.5)
+ graph_2 = self.get_graph(lambda x : 1*x+2.25, color = GOLD_A, x_min = 1.5, x_max = 5)
+ graph_3 = self.get_graph(lambda x : 7.25, color = GOLD_A, x_min = 5, x_max = 8)
+ graph_4 = self.get_graph(lambda x : -3.625*x + 36.25, color = GOLD_A, x_min = 8, x_max = 10)
+
+ self.y_max = 5
+ self.x_max = 10
+ self.x_min = 0
+ self.y_min = -5
+ self.x_labeled_nums = list(range(0,11))
+ self.y_labeled_nums = list(range(-5,6))[::1]
+ self.x_axis_label = r"$t$"
+ self.y_axis_label = r"$v$"
+ self.y_tick_frequency = 1
+ self.x_tick_frequency = 1
+ self.graph_origin = ORIGIN+1*RIGHT
+ self.setup_axes()
+ graph_5 = self.get_graph(lambda x : 2*(x-2)+4, color = GREEN_SCREEN, x_min = 0, x_max = 1.5)
+ graph_6 = self.get_graph(lambda x : 3, color = GREEN_SCREEN, x_min = 1.5, x_max = 5)
+ graph_7 = self.get_graph(lambda x : 0, color = GREEN_SCREEN, x_min = 5, x_max = 8)
+ graph_8 = self.get_graph(lambda x : -3.625, color = GREEN_SCREEN, x_min = 8, x_max = 10)
+ line1 = DashedVMobject(Line(self.graph_origin+2.5*RIGHT, self.graph_origin+2.5*RIGHT+1.5*UP))
+ line2 = DashedVMobject(Line(self.graph_origin+4*RIGHT, self.graph_origin+4*RIGHT+1.835*DOWN))
+ self.play(ShowCreation(graph_1), ShowCreation(graph_5), run_time = 3)
+ self.play(ShowCreation(graph_2), ShowCreation(graph_6), run_time = 3)
+ self.add(line1)
+ self.play(ShowCreation(graph_3), ShowCreation(graph_7), run_time = 3)
+ self.add(line2)
+ self.play(ShowCreation(graph_4), ShowCreation(graph_8), run_time = 3)
+ self.wait(3)
diff --git a/FSF-2020/calculus/intro-to-calculus/introderivative/derivative1.py b/FSF-2020/calculus/intro-to-calculus/introderivative/derivative1.py
deleted file mode 100644
index 79a6fc6..0000000
--- a/FSF-2020/calculus/intro-to-calculus/introderivative/derivative1.py
+++ /dev/null
@@ -1,55 +0,0 @@
-from manimlib.imports import *
-class derivative1(GraphScene, Scene):
- def setup(self):
- GraphScene.setup(self)
- CONFIG = {
- "y_max" : 4,
- "y_min" : -2,
- "x_max" : 4,
- "x_min" : -2,
- "y_tick_frequency" : 1,
- "x_tick_frequency" : 1,
- "axes_color" : WHITE,
- "num_graph_anchor_points": 3000, #this is the number of points that graph manim
- "graph_origin" : ORIGIN+2*DOWN+4*LEFT,
- "x_labeled_nums": list(range(-2,5)),
- "y_labeled_nums": list(range(-2,5)),
- "x_axis_label":"$x$",
- "y_axis_label":r"$f(x)=y= 3-\frac { 3 }{ 2 } x$",
- "x_axis_width": 5,
- "y_axis_height": 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)
-
- text1 = TextMobject("")
- text2 = TexMobject("{y}_{2}-{y}_{1}")
- text2 = TexMobject("{x}_{2}-{x}_{1}")
- text3 = TexMobject(r"m\quad =\frac { { y }_{ 2 }-{ y }_{ 1 } }{ { x }_{ 2 }-{ x }_{ 1 } }").move_to(np.array([3,0,0]))
- text4 = TexMobject(r"m\quad =\frac { 3 }{ -2 }").move_to(np.array([3,0,0]))
- text5 = TexMobject(r"m\quad =\quad -1.5").move_to(np.array([3,0,0]))
- self.setup_axes()
- graph_1 = self.get_graph(lambda x : 3-1.5*x, color = GREEN_SCREEN, x_min = -1, x_max = 3)
- graph_2 = self.get_graph(lambda x : 3.1-1.5*x, color = ORANGE, x_min = 0, x_max = 2)
- dot1 = Dot()
- dot2 = SmallDot(self.graph_origin+1.7*RIGHT, color = PINK)
- dot3 = SmallDot(self.graph_origin+2.5*UP, color = RED_B)
- vec1 = Vector(2.5*DOWN, color = PINK).shift(self.graph_origin+2.5*UP)
- vec2 = Vector(1.7*RIGHT, color = RED_B).shift(self.graph_origin)
- brace1 = Brace(vec1, LEFT)
- brace2 = Brace(vec2, DOWN)
- br1text = brace1.get_text(r"${y}_{2}-{y}_{1}$").next_to(brace1, LEFT)
- br2text = brace2.get_text(r"${x}_{2}-{x}_{1}$").next_to(brace2, DOWN)
- self.play(ShowCreation(graph_1), ShowCreation(dot2), ShowCreation(dot3))
- self.play(MoveAlongPath(dot1, graph_2), ShowCreation(vec1), ShowCreation(vec2), run_time = 3)
- self.wait(1)
- self.play(ShowCreation(brace1), ShowCreation(brace2))
- self.play(ShowCreation(br1text), ShowCreation(br2text))
- self.wait(2)
- self.play(GrowFromCenter(text3))
- self.wait(2.5)
- self.play(ReplacementTransform(text3, text4))
- self.wait(2)
- self.play(ReplacementTransform(text4, text5))
- self.wait(2)
diff --git a/FSF-2020/calculus/intro-to-calculus/introderivative/derivative2.py b/FSF-2020/calculus/intro-to-calculus/introderivative/derivative2.py
deleted file mode 100644
index d6aab15..0000000
--- a/FSF-2020/calculus/intro-to-calculus/introderivative/derivative2.py
+++ /dev/null
@@ -1,78 +0,0 @@
-from manimlib.imports import *
-class derivative2(GraphScene, MovingCameraScene):
- def setup(self):
- GraphScene.setup(self)
- MovingCameraScene.setup(self)
- CONFIG = {
- "y_max" : 100,
- "y_min" : 0,
- "x_max" : 10,
- "x_min" : 0,
- "y_tick_frequency" : 100,
- "x_tick_frequency" : 10,
- "axes_color" : WHITE,
- "num_graph_anchor_points": 3000, #this is the number of points that graph manim
- "graph_origin" : ORIGIN,
- "x_labeled_nums": None,#list(range(0,11)),
- "y_labeled_nums": None,#list(range(0,101))[::10],
- "x_axis_label":"$x$",
- "y_axis_label":"$f(x)$",
- "x_axis_width": 5,
- "y_axis_height": 5,
- "start_x" : 2,
- "start_dx" : 6,
- "df_color" : YELLOW,
- "dx_color" : GREEN,
- "secant_line_color" : MAROON_B,
- "zoomed_camera_frame_starting_position": ORIGIN+2*DOWN+6*LEFT,
- }
- def construct(self):
- self.setup()
- self.camera_frame.save_state()
- self.graph_origin = ORIGIN+2*DOWN+6*LEFT
- self.setup_axes()
- graph23 = self.get_graph(lambda x : x**2+7, color = GREEN_SCREEN, x_min = 0, x_max = 10)
- graph24 = self.get_graph(lambda x : x**2+7, color = GREEN_SCREEN, x_min = 8, x_max = 2.01)
- line_1 = DashedVMobject(Line(np.array([-5,-2,0]), np.array([-5,-1.42,0])))
- textdef = TextMobject("")
- text1 = TexMobject("{ x }_{ 0 }").move_to(np.array([-5,-2.2,0]))
- text2 = TextMobject("The line becomes tangential to the curve").move_to(self.graph_origin+RIGHT+0.5*UP).scale(0.01)
- text3 = TexMobject(r"\frac { df }{ dx } =\frac { f({ x }_{ 0 }+h)-f({ x }_{ 0 }) }{ h-0 }").move_to(2*RIGHT)
- text4 = TexMobject(r"\frac { df }{ dx } =\lim _{ h\rightarrow 0 }{ \frac { f({ x }_{ 0 }+h)-f({ x }_{ 0 }) }{ h } }").move_to(2*RIGHT)
- squareobj = Square(side_length = 15).move_to(self.graph_origin+RIGHT+0.53*UP)
- ss_group = self.get_secant_slope_group(
- self.start_x, graph23,
- dx = self.start_dx,
- dx_label = "h",
- df_label = "df",
- df_line_color = self.df_color,
- dx_line_color = self.dx_color,
- secant_line_color = self.secant_line_color,
- dot_df_top = True,
- dot_dx_start = True,
- dot_df_top_label = "Q",
- dot_dx_start_label = "P",
- secant_line_length = 8
- )
- self.play(ShowCreation(graph23))
- self.wait()
- self.play(ShowCreation(ss_group.secant_line))
- self.add(text1)
- self.play(ShowCreation(line_1))
- self.wait(3)
- self.play(ShowCreation(ss_group.dx_line))
- self.play(ShowCreation(ss_group.dx_label))
- self.play(ShowCreation(ss_group.df_line))
- self.play(Write(ss_group.df_label))
- self.play(ShowCreation(ss_group.dot_df_top), ShowCreation(ss_group.dot_dx_start))
- self.play(ShowCreation(ss_group.dot_df_top_label), ShowCreation(ss_group.dot_dx_start_label))
- self.wait()
- self.play(ShowCreation(text3))
- self.wait(2)
- self.play(ReplacementTransform(text3, text4))
- self.animate_secant_slope_group_change(ss_group, target_dx = 0.01, run_time = 5)
- self.wait(2)
- self.play(self.camera_frame.set_width,0.2,self.camera_frame.move_to,squareobj,run_time = 2)
- self.wait()
- self.play(ShowCreation(text2))
- self.wait(3)
diff --git a/FSF-2020/calculus/intro-to-calculus/introderivative/derivative3.py b/FSF-2020/calculus/intro-to-calculus/introderivative/derivative3.py
deleted file mode 100644
index ebbacb1..0000000
--- a/FSF-2020/calculus/intro-to-calculus/introderivative/derivative3.py
+++ /dev/null
@@ -1,57 +0,0 @@
-from manimlib.imports import *
-class derivative3(GraphScene, Scene):
- def setup(self):
- Scene.setup(self)
- #ZoomedScene.setup(self)
- CONFIG = {
- "y_max" : 8,
- "y_min" : 0,
- "x_max" : 11,
- "x_min" : 0,
- "y_tick_frequency" : 1,
- "x_tick_frequency" : 1,
- "axes_color" : WHITE,
- "num_graph_anchor_points": 3000, #this is the number of points that graph manim
- "graph_origin" : ORIGIN+3*DOWN+6.5*LEFT,
- "x_labeled_nums": list(range(0,12))[::1],
- "y_labeled_nums": list(range(0,9))[::1],
- "x_axis_label":"$t$",
- "y_axis_label":"$s$",
- "x_axis_width": 5,
- "y_axis_height": 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()
- graph_1 = self.get_graph(lambda x : -(x-2)**2+4, color = GOLD_A, x_min = 0, x_max = 1.5)
- graph_2 = self.get_graph(lambda x : 1*x+2.25, color = GOLD_A, x_min = 1.5, x_max = 5)
- graph_3 = self.get_graph(lambda x : 7.25, color = GOLD_A, x_min = 5, x_max = 8)
- graph_4 = self.get_graph(lambda x : -3.625*x + 36.25, color = GOLD_A, x_min = 8, x_max = 10)
-
- self.y_max = 5
- self.x_max = 10
- self.x_min = 0
- self.y_min = -5
- self.x_labeled_nums = list(range(0,11))
- self.y_labeled_nums = list(range(-5,6))[::1]
- self.x_axis_label = r"$t$"
- self.y_axis_label = r"$v$"
- self.y_tick_frequency = 1
- self.x_tick_frequency = 1
- self.graph_origin = ORIGIN+1*RIGHT
- self.setup_axes()
- graph_5 = self.get_graph(lambda x : 2*(x-2)+4, color = GREEN_SCREEN, x_min = 0, x_max = 1.5)
- graph_6 = self.get_graph(lambda x : 3, color = GREEN_SCREEN, x_min = 1.5, x_max = 5)
- graph_7 = self.get_graph(lambda x : 0, color = GREEN_SCREEN, x_min = 5, x_max = 8)
- graph_8 = self.get_graph(lambda x : -3.625, color = GREEN_SCREEN, x_min = 8, x_max = 10)
- line1 = DashedVMobject(Line(self.graph_origin+2.5*RIGHT, self.graph_origin+2.5*RIGHT+1.5*UP))
- line2 = DashedVMobject(Line(self.graph_origin+4*RIGHT, self.graph_origin+4*RIGHT+1.835*DOWN))
- self.play(ShowCreation(graph_1), ShowCreation(graph_5), run_time = 3)
- self.play(ShowCreation(graph_2), ShowCreation(graph_6), run_time = 3)
- self.add(line1)
- self.play(ShowCreation(graph_3), ShowCreation(graph_7), run_time = 3)
- self.add(line2)
- self.play(ShowCreation(graph_4), ShowCreation(graph_8), run_time = 3)
- self.wait(3)
diff --git a/FSF-2020/calculus/intro-to-calculus/limit/limitdef.py b/FSF-2020/calculus/intro-to-calculus/limit/limitdef.py
deleted file mode 100644
index 15f2845..0000000
--- a/FSF-2020/calculus/intro-to-calculus/limit/limitdef.py
+++ /dev/null
@@ -1,73 +0,0 @@
-from manimlib.imports import *
-class limitdef(GraphScene, Scene):
- CONFIG = {
- "y_max" : 5,
- "y_min" : 0,
- "x_max" : 5,
- "x_min" : -5,
- "y_tick_frequency" : 1,
- "x_tick_frequency" : 1,
- "axes_color" : WHITE,
- "num_graph_anchor_points": 3000, #this is the number of points that graph manim
- "graph_origin" : ORIGIN+2*DOWN,
- "x_labeled_nums": None,#list(range(-1,2)),
- "y_labeled_nums": None,#list(range(0,2)),
- "x_axis_label":"$x$",
- "y_axis_label":"$f(x)$",
- "x_axis_width": 10,
- "y_axis_height": 5,
- }
- def construct(self):
- Ldot = MediumDot(self.graph_origin+2.1*UP).set_color(GREEN_SCREEN)
- adot = MediumDot(self.graph_origin+3*RIGHT).set_color(PINK)
- epline1 = DashedVMobject(Line(self.graph_origin+1*LEFT+2.5*UP, self.graph_origin+4*RIGHT+2.5*UP))
- epline2 = DashedVMobject(Line(self.graph_origin+1*LEFT+1.7*UP, self.graph_origin+4*RIGHT+1.7*UP))
- epline3 = DashedVMobject(Line(self.graph_origin+3.5*RIGHT+0.5*DOWN, self.graph_origin+3.5*RIGHT+2.5*UP))
- epline4 = DashedVMobject(Line(self.graph_origin+2.5*RIGHT+0.5*DOWN, self.graph_origin+2.5*RIGHT+2.5*UP))
- Lline = Line(self.graph_origin+2.1*UP, self.graph_origin+3*RIGHT+2.1*UP).set_color(GREEN_SCREEN)
- aline = Line(self.graph_origin+3*RIGHT, self.graph_origin+3*RIGHT+2.1*UP).set_color(PINK)
- vertical_rectangle = Rectangle(width = 1, height = 0.8, color = PINK, fill_opacity = 0.5, fill_color = LIGHT_PINK).move_to(self.graph_origin+3*RIGHT+2.1*UP)
- horizontal_rectangle = Rectangle(width = 1, height = 0.8, color = GREEN_SCREEN, fill_opacity = 0.5, fill_color = GREEN).move_to(self.graph_origin+3*RIGHT+2.1*UP)
- vec1 = Line(self.graph_origin+2.5*UP, self.graph_origin+2.1*UP)
- vec2 = Line(self.graph_origin+2.1*UP, self.graph_origin+1.7*UP)
- vec3 = Line(self.graph_origin+2.5*RIGHT, self.graph_origin+3*RIGHT)
- vec4 = Line(self.graph_origin+3*RIGHT, self.graph_origin+3.5*RIGHT)
- brace1 = Brace(vec1, LEFT)
- brace2 = Brace(vec2, LEFT)
- brace3 = Brace(vec3, DOWN)
- brace4 = Brace(vec4, DOWN)
- br1text = brace1.get_text(r"$\epsilon$").next_to(brace1, LEFT)
- br2text = brace2.get_text(r"$\epsilon$").next_to(brace2, LEFT)
- br3text = brace3.get_text(r"$\delta$").next_to(brace3, DOWN)
- br4text = brace4.get_text(r"$\delta$").next_to(brace4, DOWN)
- epgrp = VGroup(epline1, epline2, Ldot, adot, Lline, aline, epline4, epline3)
- recgrp = VGroup(vertical_rectangle, horizontal_rectangle)
- epbrgrp = VGroup(brace1, brace2, br1text, br2text)
- delbrgrp = VGroup(brace3, brace4, br3text, br4text)
- self.setup_axes()
- graph_1 = self.get_graph(lambda x :0.1*(x+1)**2 +0.5, x_min = -5, x_max = 5)
- graph_2 = self.get_graph(lambda x : 0.1*(x+1)**2 +0.5, x_min = 2.5, x_max = 3.5, color = YELLOW_A)
- graph_2.shift(2.5*LEFT)
- self.play(ShowCreation(graph_1))
- self.wait(2)
- self.play(ShowCreation(epgrp), ShowCreation(horizontal_rectangle), ShowCreation(vertical_rectangle))
- self.wait(2)
- self.play(ShowCreation(epbrgrp))
- self.play(ShowCreation(delbrgrp))
- self.wait(2)
- self.play(FadeOut(recgrp))
- self.wait(2)
- for i in range(0,1):
- self.play(ApplyMethod(graph_2.shift, 2.5*RIGHT))
- self.wait(1)
- self.play(ApplyMethod(graph_2.shift, 1.7*DOWN))
- self.play(ApplyMethod(graph_2.shift, 1.7*UP))
- self.wait(1)
- self.play(ApplyMethod(graph_2.shift, 2.5*LEFT))
- self.play(ApplyMethod(graph_2.shift, 2.5*RIGHT))
- self.wait(1)
- self.play(ApplyMethod(graph_2.shift, 1.7*DOWN))
- self.play(ApplyMethod(graph_2.shift, 1.7*UP))
- self.wait(1)
- self.play(ApplyMethod(graph_2.shift, 2.5*LEFT))
- self.wait()
diff --git a/FSF-2020/calculus/intro-to-calculus/limit/limitfin1.py b/FSF-2020/calculus/intro-to-calculus/limit/limitfin1.py
new file mode 100644
index 0000000..ba57a15
--- /dev/null
+++ b/FSF-2020/calculus/intro-to-calculus/limit/limitfin1.py
@@ -0,0 +1,76 @@
+from manimlib.imports import *
+class limitfin1(GraphScene):
+ CONFIG = {
+ "x_min" : -8,
+ "x_max" : 8,
+ "x_labeled_nums" : list(range(-8, 10, 3)),
+ "x_axis_width" : FRAME_WIDTH - LARGE_BUFF,
+ "y_min" : -4,
+ "y_max" : 4,
+ "y_labeled_nums" : None,
+ "y_axis_height" : FRAME_HEIGHT+2*LARGE_BUFF,
+ "graph_origin" : DOWN,
+ "graph_color" : BLUE,
+ "x_axis_width":20,
+ "y_axis_height":10,
+ }
+ def construct(self):
+ self.setup_axes()
+ XTD = 10/(8 - (-8))
+ YTD = 10/(4 - (-4))
+ graph1 = self.get_graph(lambda x: x**3 +1.5, x_min = self.x_min, x_max = -0.1)
+ graph2 = self.get_graph(lambda x: x**3 +1.5, x_min = 0.1, x_max = self.x_max, color = self.graph_color)
+ dot2 = Circle(radius = 0.1).move_to(self.graph_origin+1.5*UP*YTD)
+ text0 = TextMobject("Let L be the value of f(x) at point denoted by circle").move_to(self.graph_origin+2*DOWN)
+ text1 = TexMobject(r"\text{As }", r"\delta",r"\text{ tends to zero }" ,r"\epsilon" r"\text{ tends to zero}").move_to(self.graph_origin+2*DOWN)
+ text2 = TexMobject(r"\text{For all values in }", r"(-\delta, +\delta)",r"\text{ you will always find a real and finite value of f(x) in }",r"(L-\epsilon, L+\epsilon)").move_to(self.graph_origin+2*DOWN).scale(0.6)
+ self.play(ShowCreation(graph1), ShowCreation(graph2), ShowCreation(text0), FadeIn(dot2))
+ line1 = DashedVMobject(Line(self.graph_origin+1*DOWN*YTD+1*LEFT*XTD, self.graph_origin+4*UP*YTD+1*LEFT*XTD), num_dashes = 50).set_color(PINK)
+ line2 = DashedVMobject(Line(self.graph_origin+1*DOWN*YTD+1*RIGHT*XTD, self.graph_origin+4*UP*YTD+1*RIGHT*XTD), num_dashes = 50).set_color(PINK)
+ line3 = DashedVMobject(Line(self.graph_origin+1.5*UP*YTD+5*LEFT*XTD, self.graph_origin+1.5*UP*YTD+4*RIGHT*XTD), num_dashes = 50).set_color(GOLD)
+ line4 = DashedVMobject(Line(self.graph_origin+0.5*UP*YTD+5*LEFT*XTD, self.graph_origin+0.5*UP*YTD+4*RIGHT*XTD), num_dashes = 50).set_color(GOLD)
+ line5 = DashedVMobject(Line(self.graph_origin+2.5*UP*YTD+5*LEFT*XTD, self.graph_origin+2.5*UP*YTD+4*RIGHT*XTD), num_dashes = 50).set_color(GOLD)
+ self.play(ShowCreation(line1), ShowCreation(line2))
+ vec1 = Line(self.graph_origin, self.graph_origin+1*RIGHT*XTD)
+ vec2 = Line(self.graph_origin, self.graph_origin+1*LEFT*XTD)
+ vec5 = Line(self.graph_origin+2.5*UP*YTD+4*RIGHT*XTD, self.graph_origin+1.5*UP*YTD+4*RIGHT*XTD)
+ vec6 = Line(self.graph_origin+0.5*UP*YTD+4*RIGHT*XTD, self.graph_origin+1.5*UP*YTD+4*RIGHT*XTD)
+ brace1 = Brace(vec1, DOWN)
+ brace2 = Brace(vec2, DOWN)
+ br1text = brace1.get_text(r"$\delta$").next_to(brace1, DOWN)
+ br2text = brace2.get_text(r"$\delta$").next_to(brace2, DOWN)
+ brace5 = Brace(vec5, RIGHT)
+ brace6 = Brace(vec6, RIGHT)
+ br5text = brace5.get_text(r"$\epsilon$").next_to(brace5, RIGHT)
+ br6text = brace6.get_text(r"$\epsilon$").next_to(brace6, RIGHT)
+ self.wait(3)
+ self.play(ShowCreation(brace1), ShowCreation(brace2), ShowCreation(br1text), ShowCreation(br2text))
+ self.wait(3)
+ self.play(ReplacementTransform(text0, text1))
+ self.play(ShowCreation(line3), ShowCreation(line4), ShowCreation(line5), ShowCreation(brace5), ShowCreation(brace6), ShowCreation(br5text), ShowCreation(br6text))
+ vec3 = Line(self.graph_origin, self.graph_origin+0.1*RIGHT*XTD)
+ vec4 = Line(self.graph_origin, self.graph_origin+0.11*LEFT*XTD)
+ brace3 = Brace(vec3, DOWN)
+ brace4 = Brace(vec4, DOWN)
+ vec7 = Line(self.graph_origin+1.6*UP*YTD+4*RIGHT*XTD, self.graph_origin+1.5*UP*YTD+4*RIGHT*XTD)
+ vec8 = Line(self.graph_origin+1.4*UP*YTD+4*RIGHT*XTD, self.graph_origin+1.5*UP*YTD+4*RIGHT*XTD)
+ brace7 = Brace(vec7, RIGHT)
+ brace8 = Brace(vec8, RIGHT)
+ self.play(Transform(brace1, brace3), Transform(brace2, brace4), ApplyMethod(line2.shift, 0.8*LEFT*XTD),
+ ApplyMethod(line1.shift, 0.8*RIGHT*XTD), ApplyMethod(br1text.scale, 0.3), ApplyMethod(br2text.scale, 0.3),
+ Transform(brace5, brace7), Transform(brace6, brace8), ApplyMethod(line4.shift, 1.8*UP*XTD),
+ ApplyMethod(line5.shift, 1.8*DOWN*XTD))
+ self.wait(3)
+ self.play(ReplacementTransform(text1, text2))
+ self.play(FadeOut(brace5), FadeOut(brace6), FadeOut(brace1), FadeOut(brace2))
+ self.play(ApplyMethod(line2.shift, 0.8*RIGHT*XTD), ApplyMethod(line1.shift, 0.8*LEFT*XTD), ApplyMethod(br1text.scale, 10/3), ApplyMethod(br2text.scale, 10/3),
+ ApplyMethod(line5.shift, 1.8*UP*XTD), ApplyMethod(line4.shift, 1.8*DOWN*XTD))
+ for i in range(0,3):
+ self.play(ApplyMethod(line2.shift, 0.8*LEFT*XTD), ApplyMethod(line1.shift, 0.8*RIGHT*XTD), ApplyMethod(br1text.scale, 0.3), ApplyMethod(br2text.scale, 0.3),
+ ApplyMethod(line5.shift, 1.8*DOWN*XTD), ApplyMethod(line4.shift, 1.8*UP*XTD), ApplyMethod(br5text.scale, 0.3), ApplyMethod(br6text.scale, 0.3), run_time = 0.5)
+ self.play(ApplyMethod(line2.shift, 0.8*RIGHT*XTD), ApplyMethod(line1.shift, 0.8*LEFT*XTD), ApplyMethod(br1text.scale, 10/3), ApplyMethod(br2text.scale, 10/3),
+ ApplyMethod(line5.shift, 1.8*UP*XTD), ApplyMethod(line4.shift, 1.8*DOWN*XTD), ApplyMethod(br5text.scale, 10/3), ApplyMethod(br6text.scale ,10/3), run_time = 0.5)
+ self.play(ApplyMethod(line2.shift, 0.8*LEFT*XTD), ApplyMethod(line1.shift, 0.8*RIGHT*XTD), ApplyMethod(br1text.scale, 0.3), ApplyMethod(br2text.scale, 0.3),
+ ApplyMethod(line5.shift, 1.8*DOWN*XTD), ApplyMethod(line4.shift, 1.8*UP*XTD),ApplyMethod(br5text.scale, 0.3), ApplyMethod(br6text.scale, 0.3), run_time = 0.5)
+
+ self.wait(5)
\ No newline at end of file
diff --git a/FSF-2020/calculus/intro-to-calculus/limit/limitfin2.py b/FSF-2020/calculus/intro-to-calculus/limit/limitfin2.py
new file mode 100644
index 0000000..36ca388
--- /dev/null
+++ b/FSF-2020/calculus/intro-to-calculus/limit/limitfin2.py
@@ -0,0 +1,70 @@
+from manimlib.imports import *
+class limitfin2(GraphScene):
+ CONFIG = {
+ "x_min" : -8,
+ "x_max" : 8,
+ "x_labeled_nums" : list(range(-8, 10, 3)),
+ "x_axis_width" : FRAME_WIDTH - LARGE_BUFF,
+ "y_min" : -4,
+ "y_max" : 4,
+ "y_labeled_nums" : None,#list(range(3,,)),
+ "y_axis_height" : FRAME_HEIGHT+2*LARGE_BUFF,
+ "graph_origin" : DOWN,
+ "graph_color" : BLUE,
+ "x_axis_width":20,
+ "y_axis_height":10,
+ }
+ def construct(self):
+ self.setup_axes()
+ XTD = 10/(8 - (-8))
+ YTD = 10/(4 - (-4))
+ graph1 = self.get_graph(lambda x: -(-(0.25*x**2)-1), x_min = self.x_min, x_max = -0.1)
+ graph2 = self.get_graph(lambda x: ((0.25*x**2)+2), x_min = 0.1, x_max = self.x_max, color = self.graph_color)
+ dot1 = Circle(radius = 0.1).move_to(self.graph_origin+1*UP*YTD)
+ dot2 = Circle(radius = 0.1).move_to(self.graph_origin+2*UP*YTD)
+ text1 = TexMobject(r"\text{It doesn't matter how small }", r"\delta",r"\text{ gets, }" r"\epsilon" r"\text{ does not tend to zero}").move_to(self.graph_origin+2*DOWN)
+ self.play(ShowCreation(graph1), ShowCreation(graph2), ShowCreation(text1), FadeIn(dot1), FadeIn(dot2))
+ line1 = DashedVMobject(Line(self.graph_origin+1*DOWN*YTD+1*LEFT*XTD, self.graph_origin+4*UP*YTD+1*LEFT*XTD), num_dashes = 50).set_color(PINK)
+ line2 = DashedVMobject(Line(self.graph_origin+1*DOWN*YTD+1*RIGHT*XTD, self.graph_origin+4*UP*YTD+1*RIGHT*XTD), num_dashes = 50).set_color(PINK)
+ line3 = DashedVMobject(Line(self.graph_origin+1.5*UP*YTD+5*LEFT*XTD, self.graph_origin+1.5*UP*YTD+4*RIGHT*XTD), num_dashes = 50).set_color(GOLD)
+ line4 = DashedVMobject(Line(self.graph_origin+0.5*UP*YTD+5*LEFT*XTD, self.graph_origin+0.5*UP*YTD+4*RIGHT*XTD), num_dashes = 50).set_color(GOLD)
+ line5 = DashedVMobject(Line(self.graph_origin+2.5*UP*YTD+5*LEFT*XTD, self.graph_origin+2.5*UP*YTD+4*RIGHT*XTD), num_dashes = 50).set_color(GOLD)
+ self.play(ShowCreation(line1), ShowCreation(line2))
+ vec1 = Line(self.graph_origin, self.graph_origin+1*RIGHT*XTD)
+ vec2 = Line(self.graph_origin, self.graph_origin+1*LEFT*XTD)
+ vec5 = Line(self.graph_origin+2.5*UP*YTD+4*RIGHT*XTD, self.graph_origin+1.5*UP*YTD+4*RIGHT*XTD)
+ vec6 = Line(self.graph_origin+0.5*UP*YTD+4*RIGHT*XTD, self.graph_origin+1.5*UP*YTD+4*RIGHT*XTD)
+ brace1 = Brace(vec1, DOWN)
+ brace2 = Brace(vec2, DOWN)
+ br1text = brace1.get_text(r"$\delta$").next_to(brace1, DOWN)
+ br2text = brace2.get_text(r"$\delta$").next_to(brace2, DOWN)
+ brace5 = Brace(vec5, RIGHT)
+ brace6 = Brace(vec6, RIGHT)
+ br5text = brace5.get_text(r"$\epsilon$").next_to(brace5, RIGHT)
+ br6text = brace6.get_text(r"$\epsilon$").next_to(brace6, RIGHT)
+ self.wait(3)
+ self.play(ShowCreation(brace1), ShowCreation(brace2), ShowCreation(br1text), ShowCreation(br2text))
+ self.wait(3)
+ self.play(ShowCreation(line3), ShowCreation(line4), ShowCreation(line5), ShowCreation(brace5), ShowCreation(brace6), ShowCreation(br5text), ShowCreation(br6text))
+ vec3 = Line(self.graph_origin, self.graph_origin+0.1*RIGHT*XTD)
+ vec4 = Line(self.graph_origin, self.graph_origin+0.11*LEFT*XTD)
+ brace3 = Brace(vec3, DOWN)
+ brace4 = Brace(vec4, DOWN)
+ vec7 = Line(self.graph_origin+2.1*UP*YTD+4*RIGHT*XTD, self.graph_origin+1.5*UP*YTD+4*RIGHT*XTD)
+ vec8 = Line(self.graph_origin+0.9*UP*YTD+4*RIGHT*XTD, self.graph_origin+1.5*UP*YTD+4*RIGHT*XTD)
+ brace7 = Brace(vec7, RIGHT)
+ brace8 = Brace(vec8, RIGHT)
+ self.play(Transform(brace1, brace3), Transform(brace2, brace4), ApplyMethod(line2.shift, 0.8*LEFT*XTD),
+ ApplyMethod(line1.shift, 0.8*RIGHT*XTD), ApplyMethod(br1text.scale, 0.3), ApplyMethod(br2text.scale, 0.3),
+ Transform(brace5, brace7), Transform(brace6, brace8), ApplyMethod(line4.shift, 0.8*UP*XTD),
+ ApplyMethod(line5.shift, 0.8*DOWN*XTD))
+
+ self.play(FadeOut(brace3), FadeOut(brace4), FadeOut(brace1), FadeOut(brace2))
+ self.play(ApplyMethod(line2.shift, 0.8*RIGHT*XTD), ApplyMethod(line1.shift, 0.8*LEFT*XTD), ApplyMethod(br1text.scale, 10/3), ApplyMethod(br2text.scale, 10/3))
+ for i in range(0,3):
+ self.play(ApplyMethod(line2.shift, 0.8*LEFT*XTD), ApplyMethod(line1.shift, 0.8*RIGHT*XTD), ApplyMethod(br1text.scale, 0.3), ApplyMethod(br2text.scale, 0.3), run_time = 0.5)
+ self.play(ApplyMethod(line2.shift, 0.8*RIGHT*XTD), ApplyMethod(line1.shift, 0.8*LEFT*XTD), ApplyMethod(br1text.scale, 10/3), ApplyMethod(br2text.scale, 10/3), run_time = 0.5)
+
+ self.play(ApplyMethod(line2.shift, 0.8*LEFT*XTD), ApplyMethod(line1.shift, 0.8*RIGHT*XTD), ApplyMethod(br1text.scale, 0.3), ApplyMethod(br2text.scale, 0.3), run_time = 0.5)
+
+ self.wait(5)
\ No newline at end of file
diff --git a/FSF-2020/calculus/intro-to-calculus/riemann-integrals/README.md b/FSF-2020/calculus/intro-to-calculus/riemann-integrals/README.md
new file mode 100644
index 0000000..a9ad0bb
--- /dev/null
+++ b/FSF-2020/calculus/intro-to-calculus/riemann-integrals/README.md
@@ -0,0 +1,18 @@
+rierect1.gif
+
+
+
+rierect2.gif
+
+
+
+rierect3.gif
+
+
+
+RiemannRectanglesAnimation.
+
+
+
+mimi.gif
+
diff --git a/FSF-2020/calculus/intro-to-calculus/riemann-integrals/RiemannRectanglesAnimation.py b/FSF-2020/calculus/intro-to-calculus/riemann-integrals/RiemannRectanglesAnimation.py
new file mode 100644
index 0000000..1757231
--- /dev/null
+++ b/FSF-2020/calculus/intro-to-calculus/riemann-integrals/RiemannRectanglesAnimation.py
@@ -0,0 +1,66 @@
+from manimlib.imports import *
+class RiemannRectanglesAnimation(GraphScene):
+ CONFIG = {
+ "y_max": 5,
+ "x_max": 6,
+ "x_min": 0,
+ "y_min": 0,
+ "x_axis_width": 5,
+ "y_axis_height": 5,
+ "init_dx":0.5,
+ "graph_origin": ORIGIN+2*DOWN+6*LEFT,
+ }
+ def construct(self):
+ self.setup_axes()
+ def func(x):
+ return 0.1*(x)*(x-3)*(x-7)+3
+
+ graph1=self.get_graph(func,x_min=0,x_max=6)
+ kwargs = {
+ "x_min" : 1.5,
+ "x_max" : 5.5,
+ "fill_opacity" : 0.75,
+ "stroke_width" : 0.25,
+ "input_sample_type": "right",
+ }
+ flat_rectangles1 = self.get_riemann_rectangles(self.get_graph(lambda x : 0),dx=self.init_dx,start_color=invert_color(PURPLE),end_color=invert_color(ORANGE),**kwargs)
+ riemann_rectangles_list1 = self.get_riemann_rectangles_list(graph1,6,max_dx=self.init_dx,power_base=2,start_color=PURPLE,end_color=ORANGE,**kwargs)
+ self.add(graph1)
+ self.graph_origin = ORIGIN+2*DOWN+1*RIGHT
+ self.setup_axes()
+ graph2=self.get_graph(func,x_min=0,x_max=6)
+ kwargs = {
+ "x_min" : 1.5,
+ "x_max" : 5.5,
+ "fill_opacity" : 0.75,
+ "stroke_width" : 0.25,
+ "input_sample_type": "left",
+ }
+ flat_rectangles2 = self.get_riemann_rectangles(self.get_graph(lambda x : 0),dx=self.init_dx,start_color=invert_color(PURPLE),end_color=invert_color(ORANGE),**kwargs)
+ riemann_rectangles_list2 = self.get_riemann_rectangles_list(graph2,6,max_dx=self.init_dx,power_base=2,start_color=PURPLE,end_color=ORANGE,**kwargs)
+ self.add(graph2)
+ text1 = TextMobject("Left Riemann sum").move_to(np.array([-3,-2.5,0]))
+ text2 = TextMobject("Right Riemann sum").move_to(np.array([4,-2.5,0]))
+ grp1 = VGroup(text1, text2)
+ text3 = TexMobject(r"n \rightarrow \infty").move_to(np.array([0, -3, 0]))
+ text4 = TextMobject("Left and Right Riemann sums are equal").move_to(np.array([0, -3, 0]))
+ text5 = TextMobject("Hence function is Riemann integrable and value of integral equals area covered").move_to(np.array([0, -3, 0])).scale(0.6)
+ grp2 = VGroup(text1, text2, text3)
+ # Show Riemann rectangles
+ self.play(ReplacementTransform(flat_rectangles1,riemann_rectangles_list1[0]), ReplacementTransform(flat_rectangles2, riemann_rectangles_list2[0]))
+ self.wait()
+ self.play(ShowCreation(grp1))
+ for r in range(1,len(riemann_rectangles_list1)-3):
+ self.transform_between_riemann_rects(riemann_rectangles_list1[r-1],riemann_rectangles_list1[r],replace_mobject_with_target_in_scene = True,)
+ self.transform_between_riemann_rects(riemann_rectangles_list2[r-1],riemann_rectangles_list2[r],replace_mobject_with_target_in_scene = True,)
+ self.play(ShowCreation(text3))
+ for r in range(len(riemann_rectangles_list1)-3,len(riemann_rectangles_list1)):
+ self.transform_between_riemann_rects(riemann_rectangles_list1[r-1],riemann_rectangles_list1[r],replace_mobject_with_target_in_scene = True,)
+ self.transform_between_riemann_rects(riemann_rectangles_list2[r-1],riemann_rectangles_list2[r],replace_mobject_with_target_in_scene = True,)
+ self.wait(2)
+ grp3 = VGroup(graph1, riemann_rectangles_list1[5])
+ grp4 = VGroup(graph2, riemann_rectangles_list2[5])
+ self.play(ReplacementTransform(grp2, text4))
+ self.wait(2)
+ self.play(ReplacementTransform(text4, text5), ApplyMethod(grp4.shift, 7*LEFT), ApplyMethod(self.axes.shift, 7*LEFT), )
+ self.wait(4)
\ No newline at end of file
diff --git a/FSF-2020/calculus/intro-to-calculus/riemann-integrals/mimi.py b/FSF-2020/calculus/intro-to-calculus/riemann-integrals/mimi.py
new file mode 100644
index 0000000..2471c87
--- /dev/null
+++ b/FSF-2020/calculus/intro-to-calculus/riemann-integrals/mimi.py
@@ -0,0 +1,53 @@
+class mimi(GraphScene):
+ CONFIG = {
+ "y_max": 5,
+ "x_max": 6,
+ "x_min": 0,
+ "y_min": 0,
+ "x_axis_width": 5,
+ "y_axis_height": 5,
+ "init_dx":0.5,
+ "graph_origin": ORIGIN+2*DOWN+6*LEFT,
+ }
+ def construct(self):
+ self.setup_axes()
+ def func(x):
+ return 0.1*(x)*(x-3)*(x-7)+3
+
+ graph=self.get_graph(func,x_min=0,x_max=6)
+ kwargs = {
+ "x_min" : 1.5,
+ "x_max" : 5.5,
+ "fill_opacity" : 0.5,
+ "stroke_width" : 0.25,
+ }
+ flat_rectangles = self.get_riemann_rectangles(self.get_graph(lambda x : 0),dx=self.init_dx,**kwargs)
+ riemann_rectangles_list = self.get_riemann_rectangles_list(graph,8,max_dx=self.init_dx,power_base=2,start_color=PURPLE,end_color=ORANGE,**kwargs, input_sample_type = "right")
+ riemann_rectangles_list1 = self.get_riemann_rectangles_list(graph,8,max_dx=self.init_dx,power_base=2,start_color=PURPLE,end_color=ORANGE,**kwargs, input_sample_type = "left")
+ self.add(graph)
+ self.play(ReplacementTransform(flat_rectangles,riemann_rectangles_list[0]), ReplacementTransform(flat_rectangles,riemann_rectangles_list1[0]))
+ #self.play(ReplacementTransform(flat_rectangles,riemann_rectangles_list1[0]))
+ self.wait(2)
+ kwargs = {
+ "x_min" : 3,
+ "x_max" : 3.5,
+ "fill_opacity" : 0.5,
+ "stroke_width" : 0.25,
+ }
+ riemann_rectangles_list2 = self.get_riemann_rectangles_list(graph,8,max_dx=self.init_dx,power_base=2,start_color=PURPLE,end_color=ORANGE,**kwargs, input_sample_type = "right")
+ riemann_rectangles_list3 = self.get_riemann_rectangles_list(graph,8,max_dx=self.init_dx,power_base=2,start_color=PURPLE,end_color=ORANGE,**kwargs, input_sample_type = "left")
+ #self.play(FadeOut(riemann_rectangles_list[0]), FadeOut(riemann_rectangles_list1[0]))
+ self.play(ReplacementTransform(flat_rectangles,riemann_rectangles_list2[0]), ReplacementTransform(flat_rectangles,riemann_rectangles_list3[0]), FadeOut(riemann_rectangles_list[0]), FadeOut(riemann_rectangles_list1[0]))
+ minlim = self.get_vertical_line_to_graph(3,graph,DashedLine)
+ maxlim = self.get_vertical_line_to_graph(3.5,graph,DashedLine)
+ line2 = Line(self.graph_origin+2.5*RIGHT, self.graph_origin+2.9*RIGHT)
+ brace1 = Brace(minlim, LEFT)
+ brace2 = Brace(line2, DOWN)
+ brace3 = Brace(maxlim, RIGHT)
+ br1text = brace1.get_text(r"${M}_{i}$").next_to(brace1, LEFT)
+ br2text = brace2.get_text(r"$\Delta x$").next_to(brace2, DOWN)
+ br3text = brace3.get_text(r"${m}_{i}$").next_to(brace3, RIGHT)
+ text1 = TexMobject(r"\Delta x=(b-a)/n").shift(2*RIGHT)
+ grp3 = VGroup(br1text, br2text, br3text, brace1, brace2, brace3, text1)
+ self.play(ShowCreation(grp3))
+ self.wait(5)
diff --git a/FSF-2020/calculus/intro-to-calculus/riemann-integrals/rierect1.py b/FSF-2020/calculus/intro-to-calculus/riemann-integrals/rierect1.py
new file mode 100644
index 0000000..748d766
--- /dev/null
+++ b/FSF-2020/calculus/intro-to-calculus/riemann-integrals/rierect1.py
@@ -0,0 +1,31 @@
+from manimlib.imports import *
+class rierect1(GraphScene):
+ CONFIG = {
+ "y_max" : 6,
+ "y_min" : 0,
+ "x_max" : 4,
+ "x_min" : 0,
+ "y_tick_frequency" : 1,
+ "x_tick_frequency" : 1,
+ "axes_color" : WHITE,
+ "num_graph_anchor_points": 3000, #this is the number of points that graph manim
+ "graph_origin" : ORIGIN+2*DOWN+4*LEFT,
+ "x_labeled_nums": None,#list(range(-1,2)),
+ "y_labeled_nums": None,#list(range(0,2)),
+ "x_axis_label":"$x$",
+ "y_axis_label":"$f(x)$",
+ "x_axis_width": 10,
+ "y_axis_height": 5,
+ }
+ def construct(self):
+ self.setup_axes()
+ graph1 = self.get_graph(lambda x : (0.1*(1.5*x+1)**2 +0.5), x_min = 0, x_max = 4)
+ minlim = self.get_vertical_line_to_graph(1,graph1,DashedLine, color = PINK)
+ maxlim = self.get_vertical_line_to_graph(3,graph1,DashedLine,color = PINK)
+ x1 = TexMobject(r"{x}_{1}").next_to(minlim, DOWN)
+ x2 = TexMobject(r"{x}_{2}").next_to(maxlim, DOWN)
+ rie1 = self.get_riemann_rectangles(graph1, x_min = 1, x_max = 3, dx = 0.4, input_sample_type = "left", fill_opacity = 1, start_color = YELLOW, end_color = YELLOW)
+ #rie2 = self.get_riemann_rectangles(graph1, x_min = 1, x_max = 3, dx = 0.01, input_sample_type = "right", fill_opacity = 0.5, start_color = PINK, end_color = LIGHT_PINK)
+ group = VGroup(graph1, minlim, maxlim, x1, x2, rie1)
+ self.play(ShowCreation(group))
+ self.wait(1.5)
diff --git a/FSF-2020/calculus/intro-to-calculus/riemann-integrals/rierect2.py b/FSF-2020/calculus/intro-to-calculus/riemann-integrals/rierect2.py
new file mode 100644
index 0000000..e300250
--- /dev/null
+++ b/FSF-2020/calculus/intro-to-calculus/riemann-integrals/rierect2.py
@@ -0,0 +1,31 @@
+from manimlib.imports import *
+class rierect2(GraphScene):
+ CONFIG = {
+ "y_max" : 6,
+ "y_min" : 0,
+ "x_max" : 4,
+ "x_min" : 0,
+ "y_tick_frequency" : 1,
+ "x_tick_frequency" : 1,
+ "axes_color" : WHITE,
+ "num_graph_anchor_points": 3000, #this is the number of points that graph manim
+ "graph_origin" : ORIGIN+2*DOWN+4*LEFT,
+ "x_labeled_nums": None,#list(range(-1,2)),
+ "y_labeled_nums": None,#list(range(0,2)),
+ "x_axis_label":"$x$",
+ "y_axis_label":"$f(x)$",
+ "x_axis_width": 10,
+ "y_axis_height": 5,
+ }
+ def construct(self):
+ self.setup_axes()
+ graph1 = self.get_graph(lambda x : (0.1*(1.5*x+1)**2 +0.5), x_min = 0, x_max = 4)
+ minlim = self.get_vertical_line_to_graph(1,graph1,DashedLine, color = PINK)
+ maxlim = self.get_vertical_line_to_graph(3,graph1,DashedLine,color = PINK)
+ x1 = TexMobject(r"{x}_{1}").next_to(minlim, DOWN)
+ x2 = TexMobject(r"{x}_{2}").next_to(maxlim, DOWN)
+ rie1 = self.get_riemann_rectangles(graph1, x_min = 1, x_max = 3, dx = 0.1, input_sample_type = "left", fill_opacity = 1, start_color = YELLOW, end_color = YELLOW)
+ #rie2 = self.get_riemann_rectangles(graph1, x_min = 1, x_max = 3, dx = 0.01, input_sample_type = "right", fill_opacity = 0.5, start_color = PINK, end_color = LIGHT_PINK)
+ group = VGroup(graph1, minlim, maxlim, x1, x2, rie1)
+ self.play(ShowCreation(group))
+ self.wait(1.5)
diff --git a/FSF-2020/calculus/intro-to-calculus/riemann-integrals/rierect3.py b/FSF-2020/calculus/intro-to-calculus/riemann-integrals/rierect3.py
new file mode 100644
index 0000000..3542358
--- /dev/null
+++ b/FSF-2020/calculus/intro-to-calculus/riemann-integrals/rierect3.py
@@ -0,0 +1,31 @@
+from manimlib.imports import *
+class rierect3(GraphScene):
+ CONFIG = {
+ "y_max" : 6,
+ "y_min" : 0,
+ "x_max" : 4,
+ "x_min" : 0,
+ "y_tick_frequency" : 1,
+ "x_tick_frequency" : 1,
+ "axes_color" : WHITE,
+ "num_graph_anchor_points": 3000, #this is the number of points that graph manim
+ "graph_origin" : ORIGIN+2*DOWN+4*LEFT,
+ "x_labeled_nums": None,#list(range(-1,2)),
+ "y_labeled_nums": None,#list(range(0,2)),
+ "x_axis_label":"$x$",
+ "y_axis_label":"$f(x)$",
+ "x_axis_width": 10,
+ "y_axis_height": 5,
+ }
+ def construct(self):
+ self.setup_axes()
+ graph1 = self.get_graph(lambda x : (0.1*(1.5*x+1)**2 +0.5), x_min = 0, x_max = 4)
+ minlim = self.get_vertical_line_to_graph(1,graph1,DashedLine, color = PINK)
+ maxlim = self.get_vertical_line_to_graph(3,graph1,DashedLine,color = PINK)
+ x1 = TexMobject(r"{x}_{1}").next_to(minlim, DOWN)
+ x2 = TexMobject(r"{x}_{2}").next_to(maxlim, DOWN)
+ rie1 = self.get_riemann_rectangles(graph1, x_min = 1, x_max = 3, dx = 0.01, input_sample_type = "left", fill_opacity = 1, start_color = YELLOW, end_color = YELLOW)
+ #rie2 = self.get_riemann_rectangles(graph1, x_min = 1, x_max = 3, dx = 0.01, input_sample_type = "right", fill_opacity = 0.5, start_color = PINK, end_color = LIGHT_PINK)
+ group = VGroup(graph1, minlim, maxlim, x1, x2, rie1)
+ self.play(ShowCreation(group))
+ self.wait(1.5)
diff --git a/FSF-2020/calculus/intro-to-calculus/riemannintegrals/README.md b/FSF-2020/calculus/intro-to-calculus/riemannintegrals/README.md
deleted file mode 100644
index a9ad0bb..0000000
--- a/FSF-2020/calculus/intro-to-calculus/riemannintegrals/README.md
+++ /dev/null
@@ -1,18 +0,0 @@
-rierect1.gif
-
-
-
-rierect2.gif
-
-
-
-rierect3.gif
-
-
-
-RiemannRectanglesAnimation.
-
-
-
-mimi.gif
-
diff --git a/FSF-2020/calculus/intro-to-calculus/riemannintegrals/RiemannRectanglesAnimation.py b/FSF-2020/calculus/intro-to-calculus/riemannintegrals/RiemannRectanglesAnimation.py
deleted file mode 100644
index 1757231..0000000
--- a/FSF-2020/calculus/intro-to-calculus/riemannintegrals/RiemannRectanglesAnimation.py
+++ /dev/null
@@ -1,66 +0,0 @@
-from manimlib.imports import *
-class RiemannRectanglesAnimation(GraphScene):
- CONFIG = {
- "y_max": 5,
- "x_max": 6,
- "x_min": 0,
- "y_min": 0,
- "x_axis_width": 5,
- "y_axis_height": 5,
- "init_dx":0.5,
- "graph_origin": ORIGIN+2*DOWN+6*LEFT,
- }
- def construct(self):
- self.setup_axes()
- def func(x):
- return 0.1*(x)*(x-3)*(x-7)+3
-
- graph1=self.get_graph(func,x_min=0,x_max=6)
- kwargs = {
- "x_min" : 1.5,
- "x_max" : 5.5,
- "fill_opacity" : 0.75,
- "stroke_width" : 0.25,
- "input_sample_type": "right",
- }
- flat_rectangles1 = self.get_riemann_rectangles(self.get_graph(lambda x : 0),dx=self.init_dx,start_color=invert_color(PURPLE),end_color=invert_color(ORANGE),**kwargs)
- riemann_rectangles_list1 = self.get_riemann_rectangles_list(graph1,6,max_dx=self.init_dx,power_base=2,start_color=PURPLE,end_color=ORANGE,**kwargs)
- self.add(graph1)
- self.graph_origin = ORIGIN+2*DOWN+1*RIGHT
- self.setup_axes()
- graph2=self.get_graph(func,x_min=0,x_max=6)
- kwargs = {
- "x_min" : 1.5,
- "x_max" : 5.5,
- "fill_opacity" : 0.75,
- "stroke_width" : 0.25,
- "input_sample_type": "left",
- }
- flat_rectangles2 = self.get_riemann_rectangles(self.get_graph(lambda x : 0),dx=self.init_dx,start_color=invert_color(PURPLE),end_color=invert_color(ORANGE),**kwargs)
- riemann_rectangles_list2 = self.get_riemann_rectangles_list(graph2,6,max_dx=self.init_dx,power_base=2,start_color=PURPLE,end_color=ORANGE,**kwargs)
- self.add(graph2)
- text1 = TextMobject("Left Riemann sum").move_to(np.array([-3,-2.5,0]))
- text2 = TextMobject("Right Riemann sum").move_to(np.array([4,-2.5,0]))
- grp1 = VGroup(text1, text2)
- text3 = TexMobject(r"n \rightarrow \infty").move_to(np.array([0, -3, 0]))
- text4 = TextMobject("Left and Right Riemann sums are equal").move_to(np.array([0, -3, 0]))
- text5 = TextMobject("Hence function is Riemann integrable and value of integral equals area covered").move_to(np.array([0, -3, 0])).scale(0.6)
- grp2 = VGroup(text1, text2, text3)
- # Show Riemann rectangles
- self.play(ReplacementTransform(flat_rectangles1,riemann_rectangles_list1[0]), ReplacementTransform(flat_rectangles2, riemann_rectangles_list2[0]))
- self.wait()
- self.play(ShowCreation(grp1))
- for r in range(1,len(riemann_rectangles_list1)-3):
- self.transform_between_riemann_rects(riemann_rectangles_list1[r-1],riemann_rectangles_list1[r],replace_mobject_with_target_in_scene = True,)
- self.transform_between_riemann_rects(riemann_rectangles_list2[r-1],riemann_rectangles_list2[r],replace_mobject_with_target_in_scene = True,)
- self.play(ShowCreation(text3))
- for r in range(len(riemann_rectangles_list1)-3,len(riemann_rectangles_list1)):
- self.transform_between_riemann_rects(riemann_rectangles_list1[r-1],riemann_rectangles_list1[r],replace_mobject_with_target_in_scene = True,)
- self.transform_between_riemann_rects(riemann_rectangles_list2[r-1],riemann_rectangles_list2[r],replace_mobject_with_target_in_scene = True,)
- self.wait(2)
- grp3 = VGroup(graph1, riemann_rectangles_list1[5])
- grp4 = VGroup(graph2, riemann_rectangles_list2[5])
- self.play(ReplacementTransform(grp2, text4))
- self.wait(2)
- self.play(ReplacementTransform(text4, text5), ApplyMethod(grp4.shift, 7*LEFT), ApplyMethod(self.axes.shift, 7*LEFT), )
- self.wait(4)
\ No newline at end of file
diff --git a/FSF-2020/calculus/intro-to-calculus/riemannintegrals/mimi.py b/FSF-2020/calculus/intro-to-calculus/riemannintegrals/mimi.py
deleted file mode 100644
index 2471c87..0000000
--- a/FSF-2020/calculus/intro-to-calculus/riemannintegrals/mimi.py
+++ /dev/null
@@ -1,53 +0,0 @@
-class mimi(GraphScene):
- CONFIG = {
- "y_max": 5,
- "x_max": 6,
- "x_min": 0,
- "y_min": 0,
- "x_axis_width": 5,
- "y_axis_height": 5,
- "init_dx":0.5,
- "graph_origin": ORIGIN+2*DOWN+6*LEFT,
- }
- def construct(self):
- self.setup_axes()
- def func(x):
- return 0.1*(x)*(x-3)*(x-7)+3
-
- graph=self.get_graph(func,x_min=0,x_max=6)
- kwargs = {
- "x_min" : 1.5,
- "x_max" : 5.5,
- "fill_opacity" : 0.5,
- "stroke_width" : 0.25,
- }
- flat_rectangles = self.get_riemann_rectangles(self.get_graph(lambda x : 0),dx=self.init_dx,**kwargs)
- riemann_rectangles_list = self.get_riemann_rectangles_list(graph,8,max_dx=self.init_dx,power_base=2,start_color=PURPLE,end_color=ORANGE,**kwargs, input_sample_type = "right")
- riemann_rectangles_list1 = self.get_riemann_rectangles_list(graph,8,max_dx=self.init_dx,power_base=2,start_color=PURPLE,end_color=ORANGE,**kwargs, input_sample_type = "left")
- self.add(graph)
- self.play(ReplacementTransform(flat_rectangles,riemann_rectangles_list[0]), ReplacementTransform(flat_rectangles,riemann_rectangles_list1[0]))
- #self.play(ReplacementTransform(flat_rectangles,riemann_rectangles_list1[0]))
- self.wait(2)
- kwargs = {
- "x_min" : 3,
- "x_max" : 3.5,
- "fill_opacity" : 0.5,
- "stroke_width" : 0.25,
- }
- riemann_rectangles_list2 = self.get_riemann_rectangles_list(graph,8,max_dx=self.init_dx,power_base=2,start_color=PURPLE,end_color=ORANGE,**kwargs, input_sample_type = "right")
- riemann_rectangles_list3 = self.get_riemann_rectangles_list(graph,8,max_dx=self.init_dx,power_base=2,start_color=PURPLE,end_color=ORANGE,**kwargs, input_sample_type = "left")
- #self.play(FadeOut(riemann_rectangles_list[0]), FadeOut(riemann_rectangles_list1[0]))
- self.play(ReplacementTransform(flat_rectangles,riemann_rectangles_list2[0]), ReplacementTransform(flat_rectangles,riemann_rectangles_list3[0]), FadeOut(riemann_rectangles_list[0]), FadeOut(riemann_rectangles_list1[0]))
- minlim = self.get_vertical_line_to_graph(3,graph,DashedLine)
- maxlim = self.get_vertical_line_to_graph(3.5,graph,DashedLine)
- line2 = Line(self.graph_origin+2.5*RIGHT, self.graph_origin+2.9*RIGHT)
- brace1 = Brace(minlim, LEFT)
- brace2 = Brace(line2, DOWN)
- brace3 = Brace(maxlim, RIGHT)
- br1text = brace1.get_text(r"${M}_{i}$").next_to(brace1, LEFT)
- br2text = brace2.get_text(r"$\Delta x$").next_to(brace2, DOWN)
- br3text = brace3.get_text(r"${m}_{i}$").next_to(brace3, RIGHT)
- text1 = TexMobject(r"\Delta x=(b-a)/n").shift(2*RIGHT)
- grp3 = VGroup(br1text, br2text, br3text, brace1, brace2, brace3, text1)
- self.play(ShowCreation(grp3))
- self.wait(5)
diff --git a/FSF-2020/calculus/intro-to-calculus/riemannintegrals/rierect1.py b/FSF-2020/calculus/intro-to-calculus/riemannintegrals/rierect1.py
deleted file mode 100644
index 748d766..0000000
--- a/FSF-2020/calculus/intro-to-calculus/riemannintegrals/rierect1.py
+++ /dev/null
@@ -1,31 +0,0 @@
-from manimlib.imports import *
-class rierect1(GraphScene):
- CONFIG = {
- "y_max" : 6,
- "y_min" : 0,
- "x_max" : 4,
- "x_min" : 0,
- "y_tick_frequency" : 1,
- "x_tick_frequency" : 1,
- "axes_color" : WHITE,
- "num_graph_anchor_points": 3000, #this is the number of points that graph manim
- "graph_origin" : ORIGIN+2*DOWN+4*LEFT,
- "x_labeled_nums": None,#list(range(-1,2)),
- "y_labeled_nums": None,#list(range(0,2)),
- "x_axis_label":"$x$",
- "y_axis_label":"$f(x)$",
- "x_axis_width": 10,
- "y_axis_height": 5,
- }
- def construct(self):
- self.setup_axes()
- graph1 = self.get_graph(lambda x : (0.1*(1.5*x+1)**2 +0.5), x_min = 0, x_max = 4)
- minlim = self.get_vertical_line_to_graph(1,graph1,DashedLine, color = PINK)
- maxlim = self.get_vertical_line_to_graph(3,graph1,DashedLine,color = PINK)
- x1 = TexMobject(r"{x}_{1}").next_to(minlim, DOWN)
- x2 = TexMobject(r"{x}_{2}").next_to(maxlim, DOWN)
- rie1 = self.get_riemann_rectangles(graph1, x_min = 1, x_max = 3, dx = 0.4, input_sample_type = "left", fill_opacity = 1, start_color = YELLOW, end_color = YELLOW)
- #rie2 = self.get_riemann_rectangles(graph1, x_min = 1, x_max = 3, dx = 0.01, input_sample_type = "right", fill_opacity = 0.5, start_color = PINK, end_color = LIGHT_PINK)
- group = VGroup(graph1, minlim, maxlim, x1, x2, rie1)
- self.play(ShowCreation(group))
- self.wait(1.5)
diff --git a/FSF-2020/calculus/intro-to-calculus/riemannintegrals/rierect2.py b/FSF-2020/calculus/intro-to-calculus/riemannintegrals/rierect2.py
deleted file mode 100644
index e300250..0000000
--- a/FSF-2020/calculus/intro-to-calculus/riemannintegrals/rierect2.py
+++ /dev/null
@@ -1,31 +0,0 @@
-from manimlib.imports import *
-class rierect2(GraphScene):
- CONFIG = {
- "y_max" : 6,
- "y_min" : 0,
- "x_max" : 4,
- "x_min" : 0,
- "y_tick_frequency" : 1,
- "x_tick_frequency" : 1,
- "axes_color" : WHITE,
- "num_graph_anchor_points": 3000, #this is the number of points that graph manim
- "graph_origin" : ORIGIN+2*DOWN+4*LEFT,
- "x_labeled_nums": None,#list(range(-1,2)),
- "y_labeled_nums": None,#list(range(0,2)),
- "x_axis_label":"$x$",
- "y_axis_label":"$f(x)$",
- "x_axis_width": 10,
- "y_axis_height": 5,
- }
- def construct(self):
- self.setup_axes()
- graph1 = self.get_graph(lambda x : (0.1*(1.5*x+1)**2 +0.5), x_min = 0, x_max = 4)
- minlim = self.get_vertical_line_to_graph(1,graph1,DashedLine, color = PINK)
- maxlim = self.get_vertical_line_to_graph(3,graph1,DashedLine,color = PINK)
- x1 = TexMobject(r"{x}_{1}").next_to(minlim, DOWN)
- x2 = TexMobject(r"{x}_{2}").next_to(maxlim, DOWN)
- rie1 = self.get_riemann_rectangles(graph1, x_min = 1, x_max = 3, dx = 0.1, input_sample_type = "left", fill_opacity = 1, start_color = YELLOW, end_color = YELLOW)
- #rie2 = self.get_riemann_rectangles(graph1, x_min = 1, x_max = 3, dx = 0.01, input_sample_type = "right", fill_opacity = 0.5, start_color = PINK, end_color = LIGHT_PINK)
- group = VGroup(graph1, minlim, maxlim, x1, x2, rie1)
- self.play(ShowCreation(group))
- self.wait(1.5)
diff --git a/FSF-2020/calculus/intro-to-calculus/riemannintegrals/rierect3.py b/FSF-2020/calculus/intro-to-calculus/riemannintegrals/rierect3.py
deleted file mode 100644
index 3542358..0000000
--- a/FSF-2020/calculus/intro-to-calculus/riemannintegrals/rierect3.py
+++ /dev/null
@@ -1,31 +0,0 @@
-from manimlib.imports import *
-class rierect3(GraphScene):
- CONFIG = {
- "y_max" : 6,
- "y_min" : 0,
- "x_max" : 4,
- "x_min" : 0,
- "y_tick_frequency" : 1,
- "x_tick_frequency" : 1,
- "axes_color" : WHITE,
- "num_graph_anchor_points": 3000, #this is the number of points that graph manim
- "graph_origin" : ORIGIN+2*DOWN+4*LEFT,
- "x_labeled_nums": None,#list(range(-1,2)),
- "y_labeled_nums": None,#list(range(0,2)),
- "x_axis_label":"$x$",
- "y_axis_label":"$f(x)$",
- "x_axis_width": 10,
- "y_axis_height": 5,
- }
- def construct(self):
- self.setup_axes()
- graph1 = self.get_graph(lambda x : (0.1*(1.5*x+1)**2 +0.5), x_min = 0, x_max = 4)
- minlim = self.get_vertical_line_to_graph(1,graph1,DashedLine, color = PINK)
- maxlim = self.get_vertical_line_to_graph(3,graph1,DashedLine,color = PINK)
- x1 = TexMobject(r"{x}_{1}").next_to(minlim, DOWN)
- x2 = TexMobject(r"{x}_{2}").next_to(maxlim, DOWN)
- rie1 = self.get_riemann_rectangles(graph1, x_min = 1, x_max = 3, dx = 0.01, input_sample_type = "left", fill_opacity = 1, start_color = YELLOW, end_color = YELLOW)
- #rie2 = self.get_riemann_rectangles(graph1, x_min = 1, x_max = 3, dx = 0.01, input_sample_type = "right", fill_opacity = 0.5, start_color = PINK, end_color = LIGHT_PINK)
- group = VGroup(graph1, minlim, maxlim, x1, x2, rie1)
- self.play(ShowCreation(group))
- self.wait(1.5)
--
cgit