Update and rename file4_Types_of_critical_points.py to file4_Relative_Maxima_and_Relative_Minima.py

2 files changed, 51 insertions, 134 deletions

diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Critical-Points/file4_Relative_Maxima_and_Relative_Minima.py b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Critical-Points/file4_Relative_Maxima_and_Relative_Minima.py
new file mode 100644
index 0000000..7999527
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Critical-Points/file4_Relative_Maxima_and_Relative_Minima.py
@@ -0,0 +1,51 @@
+from manimlib.imports import*
+import math as m
+
+#---- locating extrema of a funtion using critical points
+class Extrema(ThreeDScene):
+    def construct(self):
+
+        h_text = TextMobject("Relative Maxima and Relative Minima",color = GREEN)
+    
+        axes = ThreeDAxes()
+        label_x = TextMobject("$x$").shift([5.5,-0.3,0]) #---- x axis
+        label_y = TextMobject("$y$").shift([-0.3,5.5,0]).rotate(-4.5) #---- y axis
+        
+        #---- f(x,y) = 5(x+y)e^(-x^2-y^2)
+        surface = ParametricSurface(
+            lambda u, v: np.array([
+                u,
+                v,
+                5*(u+v)*m.exp(-u**2-v**2)
+            ]),u_min = -PI, u_max = PI, v_min = -PI, v_max = PI).set_color(TEAL).shift([0,0,0]).fade(0.4)
+        
+        d1 = Dot(color = YELLOW).shift([0.5,0.5,3.02]) #---- critical point for maxima 
+        l1 = Line([0.5,0.5,0.1],[0.5,0.5,3],color = YELLOW)
+
+        d2 = Dot(color = YELLOW).shift([-1.15,0,-2.98]) #---- critical point for minima
+        l2 = Line([-1.15,0,0],[-1.15,0,-2.98],color = YELLOW)
+
+        max_text = TextMobject("Relative Maxima").shift(3.1*UP+1.5*RIGHT).scale(0.5)
+        min_text = TextMobject("Relative Minima").shift(3.1*DOWN+1.5*LEFT).scale(0.5)
+
+        self.add_fixed_in_frame_mobjects(h_text)
+        self.wait(1)
+        self.wait(1)
+        self.play(FadeOut(h_text))
+        self.wait(1)    
+        self.set_camera_orientation(phi = 100*DEGREES, theta = -40*DEGREES) 
+        self.add(axes)     
+        self.add(label_x)
+        self.add(label_y)       
+        self.play(Write(surface))
+        self.wait(1)
+        self.play(Write(l1),Write(d1))
+        self.add_fixed_in_frame_mobjects(max_text)
+        self.wait(1)
+        self.play(Write(l2),Write(d2))        
+        self.add_fixed_in_frame_mobjects(min_text)
+        self.wait(1)
+        self.wait(1)
+        self.play(FadeOut(l1),FadeOut(d1),FadeOut(l2),FadeOut(d2),FadeOut(max_text),FadeOut(min_text))
+        self.begin_ambient_camera_rotation(rate = 0.3)        
+        self.wait(3)     
diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Critical-Points/file4_Types_of_critical_points.py b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Critical-Points/file4_Types_of_critical_points.py
deleted file mode 100644
index 656fb68..0000000
--- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Critical-Points/file4_Types_of_critical_points.py
+++ /dev/null
@@ -1,134 +0,0 @@
-from manimlib.imports import*
- 
-
-#---- Relative Maxima 
-class firstScene(ThreeDScene):
-    def construct(self):
-
-        r_text = TextMobject("Relative Maximum at ORIGIN",color ='#87CEFA')
-
-        axes = ThreeDAxes()
-        label_x = TextMobject("$x$").shift([5.5,-0.5,0]) #---- x axis
-        label_y = TextMobject("$y$").shift([-0.5,5.5,0]).rotate(-4.5) #---- y axis
-
-        #----graph of the function f(x,y) = -x**2-y**2
-        surface = ParametricSurface(
-            lambda u, v: np.array([
-                u,
-                v,
-                -u**2-v**2
-            ]),v_min = -1, v_max = 1, u_min = -1, u_max = 1, checkerboard_colors = [YELLOW_B,YELLOW_C,YELLOW_D, YELLOW_E]).scale(1.5).shift([0,0,-0.51]).fade(0.3)
-
-        f_text = TextMobject("$f(x,y) = -x^2-y^2$").to_corner(UL)
-
-        d = Dot(color = "#800000").shift([0,0,0]) #---- critical point
-
-        self.set_camera_orientation(phi = 75 * DEGREES, theta = 45 * DEGREES)
-        self.add_fixed_in_frame_mobjects(r_text)
-        self.wait(1)
-        self.play(FadeOut(r_text))
-        self.begin_ambient_camera_rotation(rate = 0.1) 
-        self.add(axes)
-        self.add(label_x)
-        self.add(label_y)
-        self.play(Write(surface),Write(d))
-        self.add_fixed_in_frame_mobjects(f_text)
-        self.wait(2)
-        self.play(FadeOut(axes),FadeOut(surface),FadeOut(f_text),FadeOut(d),FadeOut(label_x),FadeOut(label_y))
-
-
-#---- Relative Minima 
-class secondScene(ThreeDScene):
-    def construct(self):
-
-        r2_text = TextMobject("Relative Minimum at ORIGIN",color ='#87CEFA')
-
-        axes = ThreeDAxes()
-        label_x = TextMobject("$x$").shift([5.5,-0.5,0]) #---- x axis
-        label_y = TextMobject("$y$").shift([-0.5,5.5,0]).rotate(-4.5) #---- y axis
-
-        #----graph of the function g(x,y) = x**2+y**2
-        surface = ParametricSurface(
-            lambda u, v: np.array([
-                u,
-                v,
-                u**2+v**2
-            ]),v_min = -1, v_max = 1, u_min = -1, u_max = 1, checkerboard_colors =[TEAL_B,TEAL_C,TEAL_D,TEAL_E]).scale(1.5).shift([0,0,0.55]).fade(0.1)
-
-        d = Dot(color = "#800000").shift([0,0,0]) #---- critical point
-        
-        g_text = TextMobject("$f(x,y) = x^2+y^2$").to_corner(UL)   
-
-        self.set_camera_orientation(phi = 75 * DEGREES, theta = 45 * DEGREES)
-        self.add_fixed_in_frame_mobjects(r2_text)
-        self.wait(1)
-        self.play(FadeOut(r2_text))
-        self.begin_ambient_camera_rotation(rate = 0.1) 
-        self.add(axes)
-        self.add(label_x)
-        self.add(label_y)
-        self.play(Write(surface),Write(d))
-        self.add_fixed_in_frame_mobjects(g_text)
-        self.wait(2)
-        self.play(FadeOut(axes),FadeOut(surface),FadeOut(g_text),FadeOut(d),FadeOut(label_x),FadeOut(label_y))
-
-
-
-#---- Saddle Point
-class thirdScene(ThreeDScene):
-    def construct(self):
-
-        r3_text = TextMobject("Saddle Point", color = '#87CEFA')
-    
-        axes = ThreeDAxes()
-        label_x = TextMobject("$x$").shift([5.5,-0.5,0]) #---- x axis
-        label_y = TextMobject("$y$").shift([-0.5,5.5,0]).rotate(-4.5) #---- y axis     
-
-        #---- graph of function h(x,y) = -x^2 + y^2   
-        surface = ParametricSurface(
-            lambda u, v: np.array([
-                u,
-                v,
-                -u**2+v**2
-            ]),v_min = -1, v_max = 1, u_min = -1, u_max = 1,checkerboard_colors = [PURPLE_B,PURPLE_C,PURPLE_D,PURPLE_E]).scale(1.5).shift([0,0,0])
-        
-        #---- curve(trace) along x axis
-        curve_x = ParametricSurface(
-            lambda u, v: np.array([
-                u*0.4,
-                v,
-                v**2
-            ]),v_min = -1, v_max = 1, u_min = -0.2, u_max = 0.2).shift([0,0,0.34]).scale(1.5).set_color("#800000")
-
-        #---- curve(trace) along y axis
-        curve_y = ParametricSurface(
-            lambda u, v: np.array([
-                u,
-                v*0.4,
-                -u**2
-            ]),v_min = -0.2, v_max = 0.2, u_min = -1, u_max = 1).scale(1.6).shift([0,0,-0.1]).set_color("#800000")
-        
-        d = Dot(color = GREEN).shift([0,0,0.1]) #---- critical point
-
-        h_text = TextMobject("$f(x,y) = -x^2+y^2$").to_corner(UL)
-
-        self.add_fixed_in_frame_mobjects(r3_text)
-        self.wait(1)
-        self.set_camera_orientation(phi = 50 * DEGREES,theta = 45 * DEGREES)
-        self.play(FadeOut(r3_text))
-        self.add(axes)    
-        self.add(label_x)
-        self.add(label_y)    
-        self.begin_ambient_camera_rotation(rate = 0.3) 
-        self.add_fixed_in_frame_mobjects(h_text)
-        self.play(Write(surface))
-        self.wait(1)               
-        self.add(curve_y)
-        self.add(d)
-        self.wait(1)
-        self.play(FadeOut(curve_y))
-        self.wait(1)
-        self.add(curve_x)
-        self.wait(1)
-        self.add(d)  
-        self.wait(1)