Merge pull request #42 from vnb09/fsf_tasks

Added new files to Critical-Points

1 files changed, 56 insertions, 0 deletions

diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/file3_Degenerate_Hessian_Matrix.py b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/file3_Degenerate_Hessian_Matrix.py
new file mode 100644
index 0000000..732ef4f
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/file3_Degenerate_Hessian_Matrix.py
@@ -0,0 +1,56 @@
+from manimlib.imports import*
+import math as m
+ 
+class DegenerateHessian(ThreeDScene):
+    def construct(self):
+
+        heading = TextMobject("Degenerate Hessian Matrix",color = BLUE)
+
+        h_text = TextMobject("For $det \\hspace{1mm} H = 0$, the surface of the function at the critical point would be flat.").scale(0.7)
+
+        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
+
+        #---- function f(x,y)
+        f_surface = ParametricSurface(
+            lambda u, v: np.array([
+                u,
+                v,
+                -4*u**3-v**3
+            ]),u_min = -0.8, u_max = 0.8, v_min = -0.8, v_max = 0.8).set_color(TEAL).shift([0,1,0]).scale(1.3)
+        
+        #---- function f(x,y)
+        zoom_surface = ParametricSurface(
+            lambda u, v: np.array([
+                u,
+                v,
+                -4*u**3-v**3
+            ]),u_min = -0.8, u_max = 0.8, v_min = -0.8, v_max = 0.8).set_color(TEAL).shift([0,1,0]).scale(2.5)
+        
+        f_text= TextMobject("surface of the function").to_corner(UL).scale(0.5)
+        
+        d = Dot(color = "#800000").shift([0,1,0]) #---- critical point 
+        d2 = Dot(color = "#800000").shift([0,0.7,0]) #---- critical point 
+        plane = Rectangle(color = YELLOW,fill_opacity= 0.3).shift([0,0.6,0]).rotate(m.radians(90)).scale(0.4)
+        
+        self.set_camera_orientation(phi = 70*DEGREES, theta = 45*DEGREES) 
+        self.add_fixed_in_frame_mobjects(heading)
+        self.wait(1)
+        self.play(FadeOut(heading))
+        self.add_fixed_in_frame_mobjects(h_text)
+        self.wait(2)
+        self.play(FadeOut(h_text))
+        self.wait(1)
+        self.add(axes)     
+        self.add(label_x)
+        self.add(label_y)
+        self.play(Write(f_surface)) 
+        self.add_fixed_in_frame_mobjects(f_text)
+        self.wait(1)
+        self.play(Write(d))
+        self.wait(1) 
+        self.play(ReplacementTransform(f_surface,zoom_surface),ReplacementTransform(d,d2))
+        self.wait(2)
+        self.play(Write(plane))
+        self.wait(1)