From 71517eb42c1899541ba8f3d6c15dae10a2b4e671 Mon Sep 17 00:00:00 2001
From: Vaishnavi
Date: Tue, 28 Jul 2020 00:55:42 +0530
Subject: Update README.md
---
.../approximations-and-optimizations/Lagrange-Multipliers/README.md | 4 +---
1 file changed, 1 insertion(+), 3 deletions(-)
diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/README.md b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/README.md
index 903eaed..c9b7a17 100644
--- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/README.md
+++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/README.md
@@ -7,9 +7,7 @@
-file2_Constraint_circle_with_contour_plot_of_the_surface_x^2+y^2+x^3-y^3
-
-
+
--
cgit
From d70c002230a8c48b158045b96578912cbf2e61a4 Mon Sep 17 00:00:00 2001
From: Vaishnavi
Date: Tue, 28 Jul 2020 00:56:02 +0530
Subject: Delete
file2_Constraint_circle_with_contour_plot_of_the_surface_x^2+y^2+x^3-y^3.gif
---
...th_contour_plot_of_the_surface_x^2+y^2+x^3-y^3.gif | Bin 1810502 -> 0 bytes
1 file changed, 0 insertions(+), 0 deletions(-)
delete mode 100644 FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Constraint_circle_with_contour_plot_of_the_surface_x^2+y^2+x^3-y^3.gif
diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Constraint_circle_with_contour_plot_of_the_surface_x^2+y^2+x^3-y^3.gif b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Constraint_circle_with_contour_plot_of_the_surface_x^2+y^2+x^3-y^3.gif
deleted file mode 100644
index d8e03fd..0000000
Binary files a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Constraint_circle_with_contour_plot_of_the_surface_x^2+y^2+x^3-y^3.gif and /dev/null differ
--
cgit
From 7f730f692dd8cf53b2f4d7e2e0f760ae8078de89 Mon Sep 17 00:00:00 2001
From: Vaishnavi
Date: Tue, 28 Jul 2020 00:56:50 +0530
Subject: Update
file2_Constraint_circle_with_contour_plot_of_the_surface_x^2+y^2+x^3-y^3.py
---
..._contour_plot_of_the_surface_x^2+y^2+x^3-y^3.py | 121 +++++++++++++++------
1 file changed, 87 insertions(+), 34 deletions(-)
diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Constraint_circle_with_contour_plot_of_the_surface_x^2+y^2+x^3-y^3.py b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Constraint_circle_with_contour_plot_of_the_surface_x^2+y^2+x^3-y^3.py
index bbbf238..2ef7897 100644
--- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Constraint_circle_with_contour_plot_of_the_surface_x^2+y^2+x^3-y^3.py
+++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Constraint_circle_with_contour_plot_of_the_surface_x^2+y^2+x^3-y^3.py
@@ -1,47 +1,105 @@
from manimlib.imports import*
import math as m
-#---- contour plot of the surface with constraint circle
-class ContourScene(ThreeDScene):
+class Contourplots(ThreeDScene):
def construct(self):
- axes = ThreeDAxes().scale(0.7).rotate(m.radians(180)).fade(0.6)
+ axes = ThreeDAxes().scale(0.7).rotate(math.radians(180)).fade(0.6)
label_x = TextMobject("$x$").shift(4*LEFT).fade(0.4) #---- x axis
- label_y = TextMobject("$y$").shift(3.2*DOWN+0.2*RIGHT).rotate(m.radians(180)).fade(0.4) #---- y axis
+ label_y = TextMobject("$y$").shift(3.5*DOWN+0.2*RIGHT).rotate(math.radians(180)).fade(0.4) #---- y axis
- #---- surface of the function f(x,y) = x^2+y^2+x^3-y^3
+ #---- surface of the function
surface = ParametricSurface(
lambda u, v: np.array([
u,
v,
u**2+v**2+u**3-v**3
- ]),u_min=-0.5,u_max=0.5, v_min=-0.5,v_max=0.5).scale(5).shift([0,-0.5,2.5]).set_color(TEAL).fade(0.5)
-
+ ]),u_min=-0.5,u_max=0.5, v_min=-0.5,v_max=0.5).scale(6).shift([0,0,2.5]).set_color(TEAL).fade(0.5)
- #---- contour plots of the surface of the function
+ #---- contour plots
+ curve1 = ParametricSurface(
+ lambda u, v: np.array([
+ u*0.4,
+ m.exp(m.sin(v**2)),
+ -v*2.2
+ ]),v_min =-1.3 , v_max =1.3, u_min = -0.1, u_max = 0.1).scale(0.8).shift([0,-2.65,0]).set_color("#800000").rotate(1.2,DOWN)
- c0 = Circle(color = '#800000').scale(0.5).shift([0,-0.5,0])
- c1 = Circle(color = '#800000').scale(1).shift([0,-0.5,0])
- c2 = Circle(color = '#800000').scale(1.5).shift([0,-0.5,0])
- c3 = Circle(color = '#800000').scale(2).shift([0,-0.5,0])
- c4 = Circle(color = '#800000').scale(2.5).shift([0,-0.5,0])
+ curve2 = ParametricSurface(
+ lambda u, v: np.array([
+ u*0.4,
+ m.exp(m.sin(v**2)),
+ -v*2.2
+ ]),v_min =-1.3 , v_max =1.3, u_min = -0.1, u_max = 0.1).scale(0.9).shift([0,-3,0]).set_color("#800000").rotate(1.2,DOWN)
- #---- constraint circle
- circle = Circle(color='#FF00FF',fill_opacity=0.3).shift([-0.5,-1.2,1.5]).rotate(1.9,UP).scale(0.8)
- circle2 = Circle(color='#FF00FF',fill_opacity=0.3).shift([0.74,0.95,1.5]).rotate(1.9,UP).scale(0.8)
+ curve3 = ParametricSurface(
+ lambda u, v: np.array([
+ u*0.4,
+ m.exp(m.sin(v**2)),
+ -v*2.2
+ ]),v_min =-1.3 , v_max =1.3 , u_min = -0.1, u_max = 0.1).scale(1).shift([0,-3.5,0]).set_color("#800000").rotate(1.2,DOWN)
+
+ curve4 = ParametricSurface(
+ lambda u, v: np.array([
+ u*0.4,
+ m.exp(m.sin(v**2)),
+ -v*2.2
+ ]),v_min =-1.3 , v_max =1.3 , u_min = -0.1, u_max = 0.1).scale(1.1).shift([0,-4,0]).set_color("#800000").rotate(1.2,DOWN)
+
+ curve5 = ParametricSurface(
+ lambda u, v: np.array([
+ u*0.4,
+ -m.exp(m.sin(v**2)),
+ v*2.2
+ ]),v_min =-1.3 , v_max =1.3, u_min = -0.1, u_max = 0.1).scale(0.9).shift([0,3,0]).set_color("#800000").rotate(1.2,DOWN)
+
+ curve6 = ParametricSurface(
+ lambda u, v: np.array([
+ u*0.4,
+ -m.exp(m.sin(v**2)),
+ v*2.2
+ ]),v_min =-1.3 , v_max =1.3, u_min = -0.1, u_max = 0.1).scale(1).shift([0,3.5,0]).set_color("#800000").rotate(1.2,DOWN)
+
+ curve7 = ParametricSurface(
+ lambda u, v: np.array([
+ u*0.4,
+ -m.exp(m.sin(v**2)),
+ v*2.2
+ ]),v_min =-1.3 , v_max =1.3, u_min = -0.1, u_max = 0.1).scale(1.1).shift([0,4,0]).set_color("#800000").rotate(1.2,DOWN)
+
+ curve8 = ParametricSurface(
+ lambda u, v: np.array([
+ u*0.4,
+ -m.exp(m.sin(v**2)),
+ v*2.2
+ ]),v_min =-1.3 , v_max =1.3, u_min = -0.1, u_max = 0.1).scale(0.8).shift([0,2.65,0]).set_color("#800000").rotate(1.2,DOWN)
- maxima = Dot(color = '#4169E1').shift([0.7,0.15,1.5]) #---- point of maxima
- minima = Dot(color = '#4169E1').shift([0.8,1.7,1.5]) #---- point of minima
+ #---------------
+
+ #---- label contours
+ label_c1 = TextMobject("4",color = '#FFA074').shift([0.2,3,0.5]).scale(0.5).rotate(m.radians(180))
+ label_c2 = TextMobject("3",color = '#FFA074').shift([0.2,2.4,0.5]).scale(0.5).rotate(m.radians(180))
+ label_c3 = TextMobject("2",color = '#FFA074').shift([0.2,1.9,0.5]).scale(0.5).rotate(m.radians(180))
+ label_c4 = TextMobject("1",color = '#FFA074').shift([0.2,1.4,0.5]).scale(0.5).rotate(m.radians(180))
+ label_c5 = TextMobject("1",color = '#FFA074').shift([0.2,-1.5,0.5]).scale(0.5).rotate(m.radians(180))
+ label_c6 = TextMobject("2",color = '#FFA074').shift([0.2,-2,0.5]).scale(0.5).rotate(m.radians(180))
+ label_c7 = TextMobject("3",color = '#FFA074').shift([0.2,-2.5,0.5]).scale(0.5).rotate(m.radians(180))
+ label_c8 = TextMobject("4",color = '#FFA074').shift([0.2,-3,0.5]).scale(0.5).rotate(m.radians(180))
+
+ contourplot = VGroup(curve1,curve2,curve3,curve4,curve5,curve6,curve7,curve8,label_c1,label_c2,label_c3,label_c4,label_c5,label_c6,label_c7,label_c8)
+
- min_text = TextMobject("minimum over $g(x,y)=k$",color = '#FFA074').scale(0.6).shift([-2,0.16,1.5])
- max_text = TextMobject("maximum over $g(x,y)=k$",color = '#FFA074').shift([-2.3,-2.6,1.5]).scale(0.6).shift(0.5*UP)
+ circle = Circle(color='#FF00FF',fill_opacity=0.3).shift([-0.5,-1.2,1.5]).rotate(1.9,UP).scale(0.8)
+ circle2 = ParametricSurface(
+ lambda u, v: np.array([
+ 1*np.sin(u)*np.cos(v),
+ 1*np.sin(u)*np.sin(v),
+ -1*np.sin(u)*np.sin(u)+2
+ ]),u_min=0,u_max=PI/2,v_min=0,v_max=2*PI).set_color('#FF00FF').scale(0.6).shift([1.2,2,-3]).scale(1.24)
+ maxima = Dot(color = '#4169E1').shift([0.7,1.2,1.5])
+ minima = Dot(color = '#4169E1').shift([1.4,2.2,1.5])
- #---- labelling contour curves
- label_c0 = TextMobject("1",color = '#FFA074').shift([0.2,0.1,0.5]).scale(0.5)
- label_c1 = TextMobject("2",color = '#FFA074').shift([0.2,-0.6,0.5]).scale(0.5)
- label_c2 = TextMobject("3",color = '#FFA074').shift([0.2,-1.1,0.5]).scale(0.5)
- label_c3 = TextMobject("4",color = '#FFA074').shift([0.2,-1.6,0.5]).scale(0.5)
- label_c4 = TextMobject("5",color = '#FFA074').shift([0.2,-2.1,0.5]).scale(0.5)
+ min_text = TextMobject("minimum over $g(x,y)=k$",color = '#FFA074').scale(0.6).shift([-2.2,-1,1.5])
+ max_text = TextMobject("maximum over $g(x,y)=k$",color = '#FFA074').shift([-2.3,-2.6,1.5]).scale(0.6)
self.set_camera_orientation(phi=75 * DEGREES, theta = 45*DEGREES)
@@ -56,15 +114,10 @@ class ContourScene(ThreeDScene):
self.wait(1)
self.move_camera(phi=0 * DEGREES, theta = 90*DEGREES)
self.wait(1)
- self.play(Write(c0),Write(c1),Write(c2),Write(c3),Write(c4))
- self.play(FadeOut(surface))
- self.add_fixed_in_frame_mobjects(label_c0)
- self.add_fixed_in_frame_mobjects(label_c1)
- self.add_fixed_in_frame_mobjects(label_c2)
- self.add_fixed_in_frame_mobjects(label_c3)
- self.add_fixed_in_frame_mobjects(label_c4)
+ self.add(contourplot)
+ self.play(FadeOut(surface))
self.wait(1)
- self.play(Write(circle2))
+ self.add(circle2)
self.wait(1)
self.play(Write(minima),Write(maxima))
self.add_fixed_in_frame_mobjects(max_text)
--
cgit
From 7e23b6b62363c67ad499e006187c0607bf98b198 Mon Sep 17 00:00:00 2001
From: Vaishnavi
Date: Tue, 28 Jul 2020 01:00:29 +0530
Subject: Add files via upload
---
...th_contour_plot_of_the_surface_x^2+y^2+x^3-y^3.gif | Bin 0 -> 1927505 bytes
1 file changed, 0 insertions(+), 0 deletions(-)
create mode 100644 FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Constraint_circle_with_contour_plot_of_the_surface_x^2+y^2+x^3-y^3.gif
diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Constraint_circle_with_contour_plot_of_the_surface_x^2+y^2+x^3-y^3.gif b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Constraint_circle_with_contour_plot_of_the_surface_x^2+y^2+x^3-y^3.gif
new file mode 100644
index 0000000..d4c4bd6
Binary files /dev/null and b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Constraint_circle_with_contour_plot_of_the_surface_x^2+y^2+x^3-y^3.gif differ
--
cgit
From 0cc8a544920e5c711599b8661e03889b7a4da765 Mon Sep 17 00:00:00 2001
From: Vaishnavi
Date: Tue, 28 Jul 2020 01:03:06 +0530
Subject: Update README.md
---
.../approximations-and-optimizations/Lagrange-Multipliers/README.md | 3 ++-
1 file changed, 2 insertions(+), 1 deletion(-)
diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/README.md b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/README.md
index c9b7a17..f985f6c 100644
--- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/README.md
+++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/README.md
@@ -7,7 +7,8 @@
-
+file2_Constraint_circle_with_contour_plot_of_the_surface_x^2+y^2+x^3-y^3
+ 
--
cgit
From e4b4e1b7ea1ce287da638cf1e4d4f329a86fd67d Mon Sep 17 00:00:00 2001
From: Vaishnavi
Date: Tue, 28 Jul 2020 01:03:23 +0530
Subject: Update README.md
---
.../approximations-and-optimizations/Lagrange-Multipliers/README.md | 1 +
1 file changed, 1 insertion(+)
diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/README.md b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/README.md
index f985f6c..b6bf4e0 100644
--- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/README.md
+++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/README.md
@@ -8,6 +8,7 @@
file2_Constraint_circle_with_contour_plot_of_the_surface_x^2+y^2+x^3-y^3
+
--
cgit