1 files changed, 131 insertions, 0 deletions
diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Conservative fields/Conservative_file3_path-independent.py b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Conservative fields/Conservative_file3_path-independent.py
new file mode 100644
index 0000000..c662c31
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Conservative fields/Conservative_file3_path-independent.py
@@ -0,0 +1,131 @@
+from manimlib.imports import *
+import numpy as np
+
+def func(coordinate):
+	x,y = coordinate[:2]
+	return np.array([
+		-2*x,
+		-2*y,
+		0
+	])
+
+
+
+
+class many_paths(GraphScene):
+	CONFIG = {
+			"x_min" : 0,
+			"x_max" : 8.5,
+			"x_axis_height": 8.5,
+			"y_min" : 0,
+			"y_max" : 8.5,
+			"y_axis_height": 8.5,
+			"graph_origin" : ORIGIN, 
+			"function_color" : RED,
+ 
+		} 
+	def construct(self):
+		self.setup_axes(animate=False)
+		self.remove(self.x_axis, self.y_axis)
+		background = VectorField(func,
+			x_min = 0, x_max = 8.5, y_min = 0, y_max = 8.5, colors = ["#DBD8AE"]
+			)
+		
+		pointer = Dot(np.array([0, 1.5, 0])).scale(0.7).set_color_by_gradient(["#84732B", YELLOW_E])
+		start = np.array([0, 1.5, 0])
+		end = np.array([7.53, 5.043, 0])
+		path_one= self.get_graph(self.one, x_min = 0, x_max = 7.53)
+		path_two= self.get_graph(self.two, x_min = 0, x_max = 7.53)
+		path_three = self.get_graph(self.three, x_min = 0, x_max = 7.53)
+
+		group = VGroup(path_one, path_two, background, path_three).move_to(np.array([-3,0, 0])).scale(0.75)
+
+
+		
+		path_one.set_color("#F6523C")
+		path_two.set_color("#80475E")
+		path_three.set_color("#0F7173")
+
+		# all the text
+		#function = TexMobject(r"f(x,y) = -(x^2 + y^2)").scale(0.6).set_color("#DBD8AE").shift(3.6*UP + 3*LEFT)
+		field = TexMobject(r"\vec F = -2x\hat i - 2y\hat j").set_color("#DBD8AE").shift(3.6*DOWN + 3*LEFT)
+		c1 = TexMobject(r"C_{1}: y = 6sin(\frac{x}{3} + 1.5)").scale(0.7).set_color("#0F7173").shift(3*UP + 4*RIGHT)
+		#c3 = TexMobject(r"C_{3}: y = 6sin(\frac{x}{3} + 1.5)").scale(0.7).set_color("#0F7173").next_to(li_path2, DOWN, buff = LARGE_BUFF)
+		li_path1 = TexMobject(r"\int_{C_{1}} \vec F \cdot \vec dr = ").set_color("#0F7173").next_to(c1, DOWN, buff = 0.2)
+		c2 = TexMobject(r"C_{2}: y = 0.47x + 1.5").scale(0.7).set_color("#80475E").next_to(li_path1, DOWN, buff = 0.4)
+		li_path2 = TexMobject(r"\int_{C_{2}} \vec F \cdot \vec dr = ").set_color("#80475E").next_to(c2, DOWN, buff = 0.2)
+		c3 = TexMobject(r"C_{3}: y = \frac{x^{16}}{2}+ 1.5").scale(0.7).set_color("#F6523C").next_to(li_path2, DOWN, buff = 0.4)
+		li_path3 = TexMobject(r"\int_{C_{3}} \vec F \cdot \vec dr = ").set_color("#F6523C").next_to(c3, DOWN, buff = 0.2)
+
+		cs = VGroup(c1, c2, c3)
+
+
+		c_1 = lambda x: c1_value.get_value()
+		c_2 = lambda x: c2_value.get_value()
+		c_3 = lambda x: c3_value.get_value()
+
+		c1_value = ValueTracker(0)
+		c2_value = ValueTracker(0)
+		c3_value = ValueTracker(0)
+
+		c1_tex = DecimalNumber(c1_value.get_value()).add_updater(lambda v: v.set_value(c1_value.get_value())).next_to(li_path1, RIGHT, buff = SMALL_BUFF).set_color("#0F7173")
+		c2_tex = DecimalNumber(c2_value.get_value()).add_updater(lambda v: v.set_value(c2_value.get_value())).next_to(li_path2, RIGHT, buff = SMALL_BUFF).set_color("#80475E")
+		c3_tex = DecimalNumber(c3_value.get_value()).add_updater(lambda v: v.set_value(c3_value.get_value())).next_to(li_path3, RIGHT, buff = SMALL_BUFF).set_color("#F6523C")
+
+
+		paths = VGroup(li_path1, li_path2, li_path3, c1_tex, c2_tex, c3_tex)
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+		
+
+
+		self.play(ShowCreation(field), ShowCreation(background))
+		self.wait()
+		self.play(ShowCreation(path_one), ShowCreation(path_two), ShowCreation(path_three), ShowCreation(cs))
+		self.wait(2)
+		self.add(c1_tex)
+		self.play(ShowCreation(li_path1))
+		self.play(MoveAlongPath(pointer, path_three), c1_value.set_value,-78.9,
+			rate_func=linear,
+			run_time=3
+			)
+		self.wait(2)
+		self.play(ShowCreation(li_path2))
+		self.add(c2_tex)
+		self.play(MoveAlongPath(pointer, path_two), c2_value.set_value,-78.9,
+			rate_func=linear,
+			run_time=3
+			)
+		self.play(ShowCreation(li_path3))
+		self.add(c3_tex)
+		self.play(MoveAlongPath(pointer, path_one), c3_value.set_value,-78.9,
+			rate_func=linear,
+			run_time=3
+			)
+		self.wait()
+		self.play(Indicate(paths))
+		self.wait()
+		#self.play(MoveAlongPath(pointer, path_three))
+		#self.wait(2)
+
+	def one(self,x):
+		return x**2/16 + 1.5
+
+	def three(self,x):
+		return 6*np.sin(x/3) + 1.5
+
+	def two(self,x):
+		return 0.4705*x + 1.5
+