1 files changed, 66 insertions, 0 deletions
diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Gradient/Gradient_file4_why-partials.py b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Gradient/Gradient_file4_why-partials.py
new file mode 100644
index 0000000..a46ea32
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Gradient/Gradient_file4_why-partials.py
@@ -0,0 +1,66 @@
+from manimlib.imports import *
+import numpy as np
+
+
+def function(coordinate):
+	x,y = coordinate[:2]
+	return np.array([
+		x,
+		y,
+		0,
+	])
+def x_dir(coordinate):
+	x,y = coordinate[:2]
+	return np.array([
+		x,
+		0,
+		0
+	])
+
+def y_dir(coordinate):
+	x,y = coordinate[:2]
+	return np.array([
+		0,
+		y,
+		0,
+	])
+
+
+class PartialDerivatives(MovingCameraScene):
+	def setup(self):
+		MovingCameraScene.setup(self)
+	
+	def construct(self):
+		dot = Dot().move_to(np.array([2.5,2,0]))
+
+		self.camera_frame.save_state()
+		self.play(
+			self.camera_frame.set_width,dot.get_width()*35,
+			self.camera_frame.move_to,dot)
+
+		dx = TexMobject(r"\frac{\partial f}{\partial x}").move_to(np.array([4,2.5, 0])).set_color(["#00635D", BLUE_E]).scale(0.5)
+		x_aros = VectorField(x_dir, x_min = 0.5, x_max = 3, y_min = 0.5, y_max =3).set_color(["#00635D", BLUE_E])
+
+		dy = TexMobject(r"\frac{\partial f}{\partial y}").move_to(np.array([4,1.5, 0])).set_color_by_gradient(["#BAAB68", WHITE]).scale(0.5)
+		y_aros = VectorField(y_dir, y_min = 0.5, y_max =3, x_min = 0.5, x_max = 3 ).set_color_by_gradient(["#BAAB68", WHITE])
+
+		partials = VGroup(x_aros, y_aros, dx, dy)
+
+		dxdy = VectorField(function, y_min = 0.5, y_max =3, x_min = 0.5, x_max = 3 ).set_color_by_gradient(["#BAAB68", "#00635D"])
+		field = VectorField(function, y_min = -3, y_max =3, x_min = -3, x_max = 3 ).set_color_by_gradient(["#BAAB68", "#00635D"])
+		vector = TexMobject(r"\nabla f =").set_color_by_gradient(["#BAAB68", "#00635D"]).move_to(np.array([4,2, 0])).scale(0.5)
+		threed = TexMobject(r"\textit{With respect to the function, the gradient is computed by...}").scale(0.3).move_to(dot.get_center())
+
+
+
+		self.play(Write(x_aros), Write(dx))
+		self.wait()
+		self.play(Write(y_aros), Write(dy))
+		self.wait()
+		self.play(Write(dxdy), Write(vector), ApplyMethod(dx.next_to,vector, RIGHT+0.3*UP), ApplyMethod(dy.next_to, vector, RIGHT+0.3*DOWN))
+		self.wait()
+		self.play(FadeOut(x_aros), FadeOut(dx), FadeOut(vector), FadeOut(dxdy), FadeOut(y_aros), FadeOut(dy), ShowCreation(threed))
+		self.wait(2)
+		self.play(Uncreate(threed))
+
+