Updated gifs and scripts

FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file1_multivar_func_examples.py

@@ -17,45 +17,35 @@ def construct(self):
         rectangle_area[2].set_color(YELLOW_C)
         rectangle_area[4].set_color(BLUE_C)
 
+
+        triangle = Polygon(np.array([-3,-1.5,0]), np.array([2,-1.5,0]), np.array([2,1.5,0]), np.array([-3,-1.5,0]), color = PURPLE)
 
-        square = Square(side_length = 5, color = PURPLE)
-        square_area_func = TexMobject("Area", "=", "f(", "Length", ")")
-        square_area_func[0].set_color(GREEN_C)
-        square_area_func[2].set_color(ORANGE)
-        square_area_func[3].set_color(BLUE_C)
-        square_area_func[4].set_color(ORANGE)
-
-        square_area = TexMobject("Area", "=", "Length^2")
-        square_area[0].set_color(GREEN_C)
-        square_area[2].set_color(BLUE_C)
-
+        triangle_area_func = TexMobject("Area", "=", "f(", "Base", ",", "Height", ")").scale(0.6).move_to(1*DOWN)
+        triangle_area_func[0].set_color(RED_C)
+        triangle_area_func[2].set_color(ORANGE)
+        triangle_area_func[3].set_color(YELLOW_C)
+        triangle_area_func[5].set_color(BLUE_C)
+        triangle_area_func[6].set_color(ORANGE)
 
-        circle = Circle(radius = 2, color = PINK)
-        circle_area_func = TexMobject("Area", "=", "f(", "r", ")")
-        circle_area_func[0].set_color(YELLOW_C)
-        circle_area_func[2].set_color(ORANGE)
-        circle_area_func[3].set_color(GREEN_C)
-        circle_area_func[4].set_color(ORANGE)
+        triangle_area = TexMobject("Area", "=", "\\frac{1}{2}", "\\times", "Base", "\\times", "Height").scale(0.6).move_to(1*DOWN)
+        triangle_area[0].set_color(RED_C)
+        triangle_area[2].set_color(GREEN_C)
+        triangle_area[4].set_color(YELLOW_C)
+        triangle_area[6].set_color(BLUE_C)
 
-        circle_area = TexMobject("Area", "=", "\\pi", "r^2")
-        circle_area[0].set_color(YELLOW_C)
-        circle_area[2].set_color(BLUE_C)
-        circle_area[3].set_color(GREEN_C)
-
-        radius = Line(ORIGIN,2*RIGHT, color = RED_C)
-
 
 
         braces_rect1 = Brace(rectangle, LEFT)
         eq_text1 = braces_rect1.get_text("Length").set_color(YELLOW_C)
         braces_rect2 = Brace(rectangle, UP)
         eq_text2 = braces_rect2.get_text("Breadth").set_color(BLUE_C)
-
-        braces_square = Brace(square, LEFT)
-        braces_square_text = braces_square.get_text("Length").set_color(BLUE_C)
-
-        radius_text = TexMobject("r", color = GREEN_C).next_to(radius,UP)
 
+
+        braces_triangle_height = Brace(triangle, RIGHT)
+        braces_triangle_height_text = braces_triangle_height.get_text("Height").set_color(BLUE_C)
+
+        braces_triangle_base = Brace(triangle, DOWN)
+        braces_triangle_base_text = braces_triangle_base.get_text("Base").set_color(YELLOW_C)
 
 
         self.play(ShowCreation(rectangle))
@@ -69,28 +59,19 @@ def construct(self):
         self.play(FadeOut(braces_rect1),FadeOut(eq_text1),FadeOut(braces_rect2),FadeOut(eq_text2),FadeOut(rectangle_area_func))
 
 
-        self.play(Transform(rectangle, square))
-        self.wait(1)
-        self.play(GrowFromCenter(braces_square),Write(braces_square_text))
+        self.play(Transform(rectangle, triangle))
         self.wait(1)
-        self.play(Write(square_area_func))
+        self.play(GrowFromCenter(braces_triangle_height),Write(braces_triangle_height_text))
         self.wait(1)
-        self.play(Transform(square_area_func, square_area))
+        self.play(GrowFromCenter(braces_triangle_base),Write(braces_triangle_base_text))
         self.wait(1)
-        self.play(FadeOut(braces_square),FadeOut(braces_square_text),FadeOut(square_area_func))
-
-
-        self.play(Transform(rectangle, circle))
+        self.play(Write(triangle_area_func))
         self.wait(1)
-        self.play(ShowCreation(radius),Write(radius_text))
+        self.play(Transform(triangle_area_func, triangle_area))
         self.wait(1)
-        self.play(FadeOut(radius_text),FadeOut(radius))
+        self.play(FadeOut(braces_triangle_height),FadeOut(braces_triangle_height_text),FadeOut(braces_triangle_base),FadeOut(braces_triangle_base_text),FadeOut(triangle_area_func))
         self.wait(1)
-        self.play(Write(circle_area_func))
-        self.wait(1)
-        self.play(Transform(circle_area_func, circle_area))
-        self.wait(1)
-        self.play(FadeOut(circle_area_func))
+
 
 
 

FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file2_multivariable_func_respresentation.py

@@ -12,9 +12,6 @@ def construct(self):
         self.play(FadeOut(topic))
 
 
-        #circle = Circle()
-        #circle.scale(3)
-
         scalar_function = TextMobject("Scalar Valued Function")
         scalar_function.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
         scalar_function.scale(1.5)
@@ -69,30 +66,83 @@ def construct(self):
         number2.set_color(ORANGE)
 
         output2 = TextMobject(r"$ \begin{bmatrix} 4 \\ 6  \end{bmatrix}$")
-        #output2.scale(1.5)
         output2.set_color(BLUE_C)
         output2.move_to(3*RIGHT)
 
-        #eqn2_1 = TextMobject(r"f(2,1,3) = $2^2(1) + 2(1)(3)$")
-        #eqn2_1.set_color(YELLOW)
-
-        #eqn2_2 = TextMobject(r"f(2,1,3) = $2 + 6$")
-        #eqn2_2.set_color(YELLOW)
-
+
 
         self.play(Write(eqn2))
 
         self.wait()
         self.play(ApplyMethod(number2.move_to, 3*LEFT))
         self.play(FadeOut(number2))
 
-        #self.play(Transform(eqn2, eqn2_1))
-        #self.wait(1)
-        #self.play(Transform(eqn2, eqn2_2))
-        #self.wait(1)
-
         self.play(ApplyMethod(output2.move_to, 2.5*DOWN+4*RIGHT))
         self.wait()
         self.play(Write(vector_function))
         self.play(FadeOut(output2),FadeOut(eqn2), FadeOut(vector_function), FadeOut(rectangle))
-        self.wait()
+        self.wait()
+
+
+
+class VectorValuedFunc(Scene):
+    def construct(self):
+        numberplane = NumberPlane()
+
+        rectangle = Rectangle(height = 1, width = 2, color = PURPLE).move_to(2.5*UP+5*RIGHT)
+
+        eqn = TextMobject(r"f(x,y) = $ \begin{bmatrix} xy \\ \frac{y}{x}  \end{bmatrix}$").scale(0.6).move_to(2.5*UP+5*RIGHT).set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
+
+        dot1 = Dot().set_color(PINK).move_to(np.array([2,2,0]))
+
+        number1 = TextMobject("(2,2)").scale(0.6).next_to(dot1, RIGHT).set_color(PINK)
+
+        output1 = TextMobject(r"$ \begin{bmatrix} 4 \\ 1 \end{bmatrix}$").scale(0.6).set_color(YELLOW_C).move_to(2.5*UP+6.5*RIGHT)
+
+        vector1 = Arrow(np.array([2,2,0]), np.array([4,1,0]), color = RED_C, buff = 0.01, tip_length = 0.25)
+
+        dot2 = Dot().set_color(PINK).move_to(np.array([-1,2,0]))
+
+        number2 = TextMobject("(-1,2)").scale(0.6).next_to(dot2, RIGHT).set_color(PINK)
+
+        output2 = TextMobject(r"$ \begin{bmatrix} -2 \\ -2 \end{bmatrix}$").scale(0.6).set_color(YELLOW_C).move_to(2.5*UP+6.5*RIGHT)
+
+        vector2 = Arrow(np.array([-1,2,0]), np.array([-2,-2,0]), color = RED_C, buff = 0.01, tip_length = 0.25)
+
+
+        vector_valued_function = TextMobject("Vector Valued Function").move_to(2.5*UP+3*LEFT).set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
+
+
+        self.play(ShowCreation(numberplane))
+        self.wait()
+        self.play(ShowCreation(rectangle), ShowCreation(eqn))
+        self.wait()
+        self.play(ShowCreation(dot1), ShowCreation(number1))
+        self.wait(0.5)
+        self.play(ApplyMethod(number1.move_to, 2.5*UP+ 3.5*RIGHT))
+        self.wait(0.5)
+        self.play(FadeOut(number1))
+        self.wait(0.5)
+        self.play(ShowCreation(output1))
+        self.wait(0.5)
+        self.play(ShowCreation(vector1))
+        self.wait(0.5)
+        self.play(ApplyMethod(output1.move_to, 1*UP+ 4.5*RIGHT))
+        self.wait()
+
+
+        self.play(ShowCreation(dot2), ShowCreation(number2))
+        self.wait(0.5)
+        self.play(ApplyMethod(number2.move_to, 2.5*UP+ 3.5*RIGHT))
+        self.wait(0.5)
+        self.play(FadeOut(number2))
+        self.wait(0.5)
+        self.play(ShowCreation(output2))
+        self.wait(0.5)
+        self.play(ShowCreation(vector2))
+        self.wait(0.5)
+        self.play(ApplyMethod(output2.move_to, 2*DOWN+ 2.5*LEFT))
+        self.wait()
+        self.play(Write(vector_valued_function))
+        self.wait(2)
+

FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file3_sphere.py

@@ -4,28 +4,24 @@ class Sphere(ThreeDScene):
     def construct(self):
         axes = ThreeDAxes() # creates a 3D Axis
 
-        text3d = TextMobject(r"$f(x,y) \rightarrow Point(x,y,z)$")
-        text3d1 = TextMobject(r"$f(x,y) \rightarrow Point(x,y, \sqrt{r^2 - x^2 - y^2})$")
-        self.add_fixed_in_frame_mobjects(text3d)
-        text3d.scale(0.7)
+        text3d1 = TextMobject(r"$z = f(x,y) =  \sqrt{r^2 - x^2 - y^2}$")
+
         text3d1.scale(0.7)
-        text3d.to_corner(UL)
+
         text3d1.to_corner(UL)
-        text3d.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
+
         text3d1.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE) 
-        self.play(Write(text3d))
+        self.play(Write(text3d1))
         self.wait(1)
 
-        self.play(Transform(text3d,text3d1))
         self.add_fixed_in_frame_mobjects(text3d1)
-        self.play(FadeOut(text3d))
 
         sphere = ParametricSurface(
             lambda u, v: np.array([
                 2*np.sin(u)*np.cos(v),
                 2*np.sin(u)*np.sin(v),
                 2*np.cos(u)
-            ]),u_min=0,u_max=PI,v_min=0,v_max=2*PI,checkerboard_colors=[RED_D, RED_E],
+            ]),u_min=0,u_max=PI/2,v_min=0,v_max=2*PI,checkerboard_colors=[RED_D, RED_E],
             resolution=(15, 32)).scale(1)
 
 
@@ -53,89 +49,77 @@ def construct(self):
 
         dot_x_y1 = Dot().scale(0.75).set_fill(RED_C).move_to(np.array([-1,1,0]))
         dot_x_y_z1 = Dot().scale(0.75).set_fill(RED_C).move_to(np.array([-1,1,1.414]))
-        dot_x_y_z_1 = Dot().scale(0.75).set_fill(RED_C).move_to(np.array([-1,1,-1.414]))
-        line1 = DashedLine(np.array([-1,1,-1.414]), np.array([-1,1,1.414]), color = YELLOW_C)
+
+        line1 = DashedLine(np.array([-1,1,0]), np.array([-1,1,1.414]), color = YELLOW_C)
 
         point_x_y1 = TexMobject("(-1,1,0)").set_color(BLUE_C).move_to(np.array([-1.5,1.5,0])).scale(0.5)
         point_x_y_z1 = TexMobject("(-1,1,\\sqrt{r^2 - x^2 - y^2})").set_color(BLUE_C).move_to(np.array([-1.5,1.5,1.414])).scale(0.5)
         point_x_y_z1_2 = TexMobject("(-1,1,\\sqrt{4 - x^2 - y^2})").set_color(BLUE_C).move_to(np.array([-1.5,1.5,1.414])).scale(0.5)
         point_x_y_z1_3 = TexMobject("(-1,1,\\sqrt{4 - 1 - 1})").set_color(BLUE_C).move_to(np.array([-1.5,1.5,1.414])).scale(0.5)
         point_x_y_z1_4 = TexMobject("(-1,1,\\sqrt{2})").set_color(BLUE_C).move_to(np.array([-1.5,1.5,1.414])).scale(0.5)
         point_x_y_z1_5 = TexMobject("(-1,1,1.414)").set_color(BLUE_C).move_to(np.array([-1.5,1.5,1.414])).scale(0.5)
-
-        point_x_y_z_1 = TexMobject("(-1,1,\\sqrt{r^2 - x^2 - y^2})").set_color(BLUE_C).move_to(np.array([-1.5,1.5,-1.414])).scale(0.5)
-        point_x_y_z_1_2 = TexMobject("(-1,1,\\sqrt{4 - x^2 - y^2})").set_color(BLUE_C).move_to(np.array([-1.5,1.5,-1.414])).scale(0.5)
-        point_x_y_z_1_3 = TexMobject("(-1,1,\\sqrt{4 - 1 - 1})").set_color(BLUE_C).move_to(np.array([-1.5,1.5,-1.414])).scale(0.5)
-        point_x_y_z_1_4 = TexMobject("(-1,1,\\sqrt{2})").set_color(BLUE_C).move_to(np.array([-1.5,1.5,-1.414])).scale(0.5)
-        point_x_y_z_1_5 = TexMobject("(-1,1,-1.414)").set_color(BLUE_C).move_to(np.array([-1.5,1.5,-1.414])).scale(0.5)
-
+
 
         self.play(ShowCreation(dot_x_y1))
         self.add_fixed_orientation_mobjects(point_x_y1)
-        self.play(ShowCreation(dot_x_y_z1), ShowCreation(dot_x_y_z_1), ShowCreation(line1))
-        self.add_fixed_orientation_mobjects(point_x_y_z1, point_x_y_z_1)
+        self.play(ShowCreation(dot_x_y_z1), ShowCreation(line1))
+        self.add_fixed_orientation_mobjects(point_x_y_z1)
         self.wait(0.5)
-        self.play(ReplacementTransform(point_x_y_z1,point_x_y_z1_2), ReplacementTransform(point_x_y_z_1,point_x_y_z_1_2))
-        self.add_fixed_orientation_mobjects(point_x_y_z1_2, point_x_y_z_1_2)
+        self.play(ReplacementTransform(point_x_y_z1,point_x_y_z1_2))
+        self.add_fixed_orientation_mobjects(point_x_y_z1_2)
 
         self.wait(0.5)
-        self.play(ReplacementTransform(point_x_y_z1_2,point_x_y_z1_3), ReplacementTransform(point_x_y_z_1_2,point_x_y_z_1_3))
-        self.add_fixed_orientation_mobjects(point_x_y_z1_3, point_x_y_z_1_3)
+        self.play(ReplacementTransform(point_x_y_z1_2,point_x_y_z1_3))
+        self.add_fixed_orientation_mobjects(point_x_y_z1_3)
         self.wait(0.5)
-        self.play(ReplacementTransform(point_x_y_z1_3,point_x_y_z1_4), ReplacementTransform(point_x_y_z_1_3,point_x_y_z_1_4))
-        self.add_fixed_orientation_mobjects(point_x_y_z1_4, point_x_y_z_1_4)
+        self.play(ReplacementTransform(point_x_y_z1_3,point_x_y_z1_4))
+        self.add_fixed_orientation_mobjects(point_x_y_z1_4)
         self.wait(0.5)
-        self.play(ReplacementTransform(point_x_y_z1_4,point_x_y_z1_5), ReplacementTransform(point_x_y_z_1_4,point_x_y_z_1_5))
-        self.add_fixed_orientation_mobjects(point_x_y_z1_5, point_x_y_z_1_5)
+        self.play(ReplacementTransform(point_x_y_z1_4,point_x_y_z1_5))
+        self.add_fixed_orientation_mobjects(point_x_y_z1_5)
 
 
 
         dot_x_y2 = Dot().scale(0.75).set_fill(RED_C).move_to(np.array([0.5,-0.5,0]))
         dot_x_y_z2 = Dot().scale(0.75).set_fill(RED_C).move_to(np.array([0.5,-0.5,1.87]))
-        dot_x_y_z_2 = Dot().scale(0.75).set_fill(RED_C).move_to(np.array([0.5,-0.5,-1.87]))
-        line2 = DashedLine(np.array([0.5,-0.5,-1.87]), np.array([0.5,-0.5,1.87]), color = YELLOW_C)
+
+        line2 = DashedLine(np.array([0.5,-0.5,0]), np.array([0.5,-0.5,1.87]), color = YELLOW_C)
 
         point_x_y2 = TexMobject("(0.5,-0.5,0)").set_color(BLUE_C).move_to(np.array([1.5,-1.5,0])).scale(0.5)
         point_x_y_z2 = TexMobject("(0.5,-0.5,\\sqrt{r^2 - x^2 - y^2})").set_color(BLUE_C).move_to(np.array([1.5,-1.5,1.87])).scale(0.5)
         point_x_y_z2_2 = TexMobject("(0.5,-0.5,\\sqrt{4 - x^2 - y^2})").set_color(BLUE_C).move_to(np.array([1.5,-1.5,1.87])).scale(0.5)
         point_x_y_z2_3 = TexMobject("(0.5,-0.5,\\sqrt{4 - 0.25 - 0.25})").set_color(BLUE_C).move_to(np.array([1.5,-1.5,1.87])).scale(0.5)
         point_x_y_z2_4 = TexMobject("(0.5,-0.5,\\sqrt{3.5})").set_color(BLUE_C).move_to(np.array([1.5,-1.5,1.87])).scale(0.5)
         point_x_y_z2_5 = TexMobject("(0.5,-0.5,1.87)").set_color(BLUE_C).move_to(np.array([1.5,-1.5,1.87])).scale(0.5)
-
-        point_x_y_z_2 = TexMobject("(0.5,-0.5,\\sqrt{r^2 - x^2 - y^2})").set_color(BLUE_C).move_to(np.array([1.5,-1.5,-1.87])).scale(0.5)
-        point_x_y_z_2_2 = TexMobject("(0.5,-0.5,\\sqrt{4 - x^2 - y^2})").set_color(BLUE_C).move_to(np.array([1.5,-1.5,-1.87])).scale(0.5)
-        point_x_y_z_2_3 = TexMobject("(0.5,-0.5,\\sqrt{4 - 0.25 - 0.25})").set_color(BLUE_C).move_to(np.array([1.5,-1.5,-1.87])).scale(0.5)
-        point_x_y_z_2_4 = TexMobject("(0.5,-0.5,\\sqrt{3.5})").set_color(BLUE_C).move_to(np.array([1.5,-1.5,-1.87])).scale(0.5)
-        point_x_y_z_2_5 = TexMobject("(0.5,-0.5,-1.87)").set_color(BLUE_C).move_to(np.array([1.5,-1.5,-1.87])).scale(0.5)
-
+
 
         self.play(ShowCreation(dot_x_y2))
         self.add_fixed_orientation_mobjects(point_x_y2)
-        self.play(ShowCreation(dot_x_y_z2), ShowCreation(dot_x_y_z_2), ShowCreation(line2))
-        self.add_fixed_orientation_mobjects(point_x_y_z2, point_x_y_z_2)
+        self.play(ShowCreation(dot_x_y_z2), ShowCreation(line2))
+        self.add_fixed_orientation_mobjects(point_x_y_z2)
         self.wait(0.5)
-        self.play(ReplacementTransform(point_x_y_z2,point_x_y_z2_2), ReplacementTransform(point_x_y_z_2,point_x_y_z_2_2))
-        self.add_fixed_orientation_mobjects(point_x_y_z2_2, point_x_y_z_2_2)
+        self.play(ReplacementTransform(point_x_y_z2,point_x_y_z2_2))
+        self.add_fixed_orientation_mobjects(point_x_y_z2_2)
 
         self.wait(0.5)
-        self.play(ReplacementTransform(point_x_y_z2_2,point_x_y_z2_3), ReplacementTransform(point_x_y_z_2_2,point_x_y_z_2_3))
-        self.add_fixed_orientation_mobjects(point_x_y_z2_3, point_x_y_z_2_3)
+        self.play(ReplacementTransform(point_x_y_z2_2,point_x_y_z2_3))
+        self.add_fixed_orientation_mobjects(point_x_y_z2_3)
         self.wait(0.5)
-        self.play(ReplacementTransform(point_x_y_z2_3,point_x_y_z2_4), ReplacementTransform(point_x_y_z_2_3,point_x_y_z_2_4))
-        self.add_fixed_orientation_mobjects(point_x_y_z2_4, point_x_y_z_2_4)
+        self.play(ReplacementTransform(point_x_y_z2_3,point_x_y_z2_4))
+        self.add_fixed_orientation_mobjects(point_x_y_z2_4)
         self.wait(0.5)
-        self.play(ReplacementTransform(point_x_y_z2_4,point_x_y_z2_5), ReplacementTransform(point_x_y_z_2_4,point_x_y_z_2_5))
-        self.add_fixed_orientation_mobjects(point_x_y_z2_5, point_x_y_z_2_5)
+        self.play(ReplacementTransform(point_x_y_z2_4,point_x_y_z2_5))
+        self.add_fixed_orientation_mobjects(point_x_y_z2_5)
 
-        self.play(FadeOut(point_x_y1), FadeOut(point_x_y_z1_5), FadeOut(point_x_y_z_1_5), FadeOut(dot_x_y1), FadeOut(dot_x_y_z1), FadeOut(dot_x_y_z_1), FadeOut(line1))
-        self.play(FadeOut(point_x_y2), FadeOut(point_x_y_z2_5), FadeOut(point_x_y_z_2_5), FadeOut(dot_x_y2), FadeOut(dot_x_y_z2), FadeOut(dot_x_y_z_2), FadeOut(line2))
+        self.play(FadeOut(point_x_y1), FadeOut(point_x_y_z1_5))
+        self.play(FadeOut(point_x_y2), FadeOut(point_x_y_z2_5))
 
 
 
 
         sphere_final = []
 
-        for u in range(0, 180, 15): 
+        for u in range(0, 90, 15): 
             sphere_points1 = [np.array([2*np.sin(u*DEGREES)*np.cos(v*DEGREES), 2*np.sin(u*DEGREES)*np.sin(v*DEGREES), 2*np.cos(u*DEGREES)]) for v in range(0, 370, 10)]
             sphere_dots1 = [Dot().scale(0.75).set_fill(RED_C).move_to(pts) for pts in sphere_points1]
 
@@ -158,20 +142,4 @@ def construct(self):
         self.begin_ambient_camera_rotation(rate=0.5)
         self.wait(3)
         self.play(ReplacementTransform(sphere_final_with_dots, sphere))
-        self.wait(5)
-
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+        self.wait(5)