Create file5_Total_differential_approximation.py

1 files changed, 48 insertions, 0 deletions

diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file5_Total_differential_approximation.py b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file5_Total_differential_approximation.py
new file mode 100644
index 0000000..83017ed
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file5_Total_differential_approximation.py
@@ -0,0 +1,48 @@
+from manimlib.imports import*
+
+
+class firstScene(ThreeDScene):
+    
+    def construct(self):
+    
+        axes = ThreeDAxes().rotate(1.571)
+        surface = ParametricSurface(
+            lambda u, v: np.array([
+                np.sin(u),
+                v,
+                -u**2-v
+            ]),u_min=-1,u_max=1, v_min=-1,v_max=1).set_color("#00008B").scale(2).shift(3.8*UP+2*LEFT)
+        
+        d = Dot([1.4,1.75,1],color = '#00FFFF').rotate(1.571,UP)
+        d2 = Dot([2,2,1],color = '#00FFFF').rotate(1.571,UP)
+
+        l = DashedLine(color = '#800000').rotate(1.571,UP).scale(1).shift(1.7*UP+1.6*RIGHT)
+        l2 = DashedLine(color = '#800000').rotate(1.571,UP).scale(0.8).shift(2.26*UP+1.2*RIGHT)
+
+        l_text = TextMobject("$(x_1,y_1)$",color = '#ADFF2F').scale(0.6).shift(2*RIGHT+1.6*DOWN)
+        l2_text = TextMobject("$(x_2,y_2)$",color = '#ADFF2F').scale(0.6).shift(2.7*RIGHT+1.2*DOWN)
+
+        plane = Rectangle(color = '#E6E6FA',fill_opacity = 1).scale(3).shift(1*RIGHT+3*UP).fade(0.9)
+
+        tangentplane = Rectangle(color = '#E6E6FA',fill_opacity = 1).scale(1.1).shift(2*LEFT+3.4*UP).fade(0.5).rotate(0.8,RIGHT)
+        tangentplane_text = TextMobject("Tangent Plane").scale(0.4).shift(3*RIGHT+1*UP)
+
+        label = TextMobject("$z = f(x,y)$").scale(0.6).shift(4*RIGHT+3*UP)
+
+        
+        self.add(axes)
+        self.set_camera_orientation(phi=75*DEGREES,theta=-10*DEGREES)
+        self.wait(1)
+        self.play(Write(plane))
+        self.wait(1)
+        self.play(Write(surface))
+        self.add_fixed_in_frame_mobjects(label)
+        self.wait(1.5)
+        self.play(ShowCreation(l),ShowCreation(l2),Write(d),Write(d2))           
+        self.wait(1)
+        self.add_fixed_in_frame_mobjects(l_text)
+        self.add_fixed_in_frame_mobjects(l2_text)
+        self.wait(1)
+        self.play(Write(tangentplane))
+        self.add_fixed_in_frame_mobjects(tangentplane_text)        
+        self.wait(2)