1 files changed, 85 insertions, 0 deletions
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/file1_directional_deriv.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/file1_directional_deriv.py
new file mode 100644
index 0000000..677d821
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/file1_directional_deriv.py
@@ -0,0 +1,85 @@
+from manimlib.imports import *
+
+class GeomRepresen(ThreeDScene):
+    def construct(self):
+        axes = ThreeDAxes() 
+
+        paraboloid = ParametricSurface(
+            lambda u, v: np.array([
+                3*np.sin(u)*np.cos(v),
+                3*np.sin(u)*np.sin(v),
+                -0.25*3*3*np.sin(u)*np.sin(u)+2
+            ]),u_min=0,u_max=PI/4,v_min=0,v_max=2*PI, color = BLUE_C, fill_color = BLUE_C, fill_opacity = 0.7,
+            resolution=(15, 32)).scale(1)
+
+        parabola_curve = ParametricFunction(
+                lambda u : np.array([
+                u,
+                -u,
+                -0.5*(u*u)+2
+            ]),color=PINK,t_min=-1.5,t_max=1.5,
+            )
+
+        circle = Circle(radius = 2.22 , color = BLACK, fill_color = BLUE_C, fill_opacity= 0.3, stroke_width=0.1)
+
+        plane = Polygon(np.array([2.5,-2.5,0]),np.array([-2.5,2.5,0]),np.array([-2.5,2.5,2.5]),np.array([2.5,-2.5,2.5]),np.array([2.5,-2.5,0]), color = BLACK, fill_color = PINK, fill_opacity= 0.2, stroke_width=0.1)
+
+        line = DashedLine(np.array([1,-1,0]), np.array([1,-1,1.5]), color = YELLOW_C) 
+
+        tangent_line = Line(np.array([1.5,-1.5,1]), np.array([0.5,-0.5,2]), color = RED_C)
+
+        vector = Arrow(np.array([1,-1,0]), np.array([0.5,-0.5,0]), buff=0.01, color = GREEN_C)
+
+        dot1 =Sphere(radius=0.08).move_to(np.array([1,-1,0])).set_fill(YELLOW_C)
+        dot2 =Sphere(radius=0.08).move_to(np.array([1,-1,1.5])).set_fill(YELLOW_C)
+
+        dot1_lab = TextMobject(r"$P_0$").scale(0.6).move_to(np.array([1,-1,1.8])).set_color(RED_C)
+        dot2_lab = TextMobject(r"$(x_0,y_0)$").scale(0.6).move_to(np.array([1.6,-1,0])).set_color(PURPLE)
+        vector_lab = TextMobject(r"$\hat{u}$").scale(0.8).move_to(np.array([1.2,-0.5,0])).set_color(GREEN_C)
+        domain_lab = TextMobject(r"$D$").scale(0.6).move_to(np.array([1,1,0])).set_color(GREEN_C)
+        func_lab = TextMobject(r"$z = f(x,y)$").scale(0.6).move_to(1*UP + 2.8*RIGHT).set_color(BLUE_C)
+        directional_deriv_lab = TextMobject(r"Slope = $D_{\hat{u}}f(x_0,y_0)$").scale(0.6).move_to(2.2*UP + 1.5*RIGHT).set_color(YELLOW_C)
+
+        self.add(axes)
+
+        axis = TextMobject(r"X",r"Y",r"Z")
+        axis[0].move_to(6*RIGHT)
+        axis[1].move_to(6*UP)
+        axis[2].move_to(np.array([0,0,3.7]))
+
+        self.add_fixed_orientation_mobjects(axis[2])
+        self.add_fixed_orientation_mobjects(axis[0])
+        self.add_fixed_orientation_mobjects(axis[1]) 
+
+        self.set_camera_orientation(phi=65 * DEGREES, theta = 20*DEGREES)
+
+        self.play(ShowCreation(paraboloid))
+        self.add_fixed_in_frame_mobjects(func_lab)
+        self.wait()
+
+        #self.play(ShowCreation(circle))
+        self.bring_to_front(circle)
+        self.wait()
+        self.add_fixed_orientation_mobjects(domain_lab)
+        self.wait()
+
+        self.play(ShowCreation(plane), ShowCreation(parabola_curve))
+        self.play(ShowCreation(dot1), GrowArrow(line), ShowCreation(dot2))
+        self.add_fixed_orientation_mobjects(dot1_lab)
+        self.wait()
+        self.add_fixed_orientation_mobjects(dot2_lab)
+        self.wait()
+
+        self.play(ShowCreation(tangent_line))
+        self.add_fixed_in_frame_mobjects(directional_deriv_lab)
+        self.wait()
+
+        self.play(GrowArrow(vector))
+        self.add_fixed_orientation_mobjects(vector_lab)
+        self.wait()
+
+        
+        self.begin_ambient_camera_rotation(rate=0.1)
+        self.wait(3)
+
+