1 files changed, 50 insertions, 0 deletions
diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Tangent-Plane-Approximations/file1_Tangent_Plane.py b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Tangent-Plane-Approximations/file1_Tangent_Plane.py
new file mode 100644
index 0000000..4c17f90
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Tangent-Plane-Approximations/file1_Tangent_Plane.py
@@ -0,0 +1,50 @@
+from manimlib.imports import*
+
+#---- tangent plane is parallel to the surface of the funtion at a point
+class firstScene(ThreeDScene):
+    def construct(self):
+
+        s1_text=TextMobject("Suppose, the point $(x,y)$ lies on the surface of the function.").scale(0.5).shift(2*UP)
+        s2_text=TextMobject("When zooming on that point, the surface would appear more and more like a plane.").scale(0.5).shift(1*UP)
+        s3_text=TextMobject("This plane is called the tangent plane.").scale(0.5)
+
+        #---- graph of function f(x,y) = -x^2-y^2 
+
+        f = 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]).shift([0,0,0]).scale(1)
+
+        
+        d = Dot([0,0,0],color = '#800000')  #---- critical point
+
+        r = Rectangle(color = PURPLE,fill_opacity=0.2).shift([0.1,0,0]).scale(0.3)  #---- tangent plane 
+
+        s = 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]).shift([0,0,0]).scale(3.5)
+
+        d2 = Dot([0,0,2.5],color = '#800000') #---- changing position of critical point 
+
+        r2 = Rectangle(color = PURPLE,fill_opacity=0.5).shift([0.1,0,2.5]).scale(0.3) #---- changing position of tangent plane 
+        
+        self.set_camera_orientation(phi = 50 * DEGREES, theta = 45 * DEGREES)
+        self.add_fixed_in_frame_mobjects(s1_text)
+        self.add_fixed_in_frame_mobjects(s2_text)
+        self.add_fixed_in_frame_mobjects(s3_text)
+        self.wait(2)
+        self.play(FadeOut(s1_text))
+        self.play(FadeOut(s2_text))
+        self.play(FadeOut(s3_text))
+        self.wait(1)
+        self.play(Write(f))
+        self.play(Write(d))
+        self.play(Write(r))
+        self.wait(2)
+        self.play(ReplacementTransform(f,s),ReplacementTransform(d,d2),ReplacementTransform(r,r2))
+        self.wait(2)