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from manimlib.imports import *
class MultivariableFunc(Scene):
def construct(self):
topic = TextMobject("Multivariable Functions")
topic.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
topic.scale(1.5)
self.play(Write(topic))
self.wait()
self.play(FadeOut(topic))
scalar_function = TextMobject("Scalar Valued Function")
scalar_function.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
scalar_function.scale(1.5)
scalar_function.move_to(2.5*UP)
rectangle = Rectangle(height = 2, width = 4)
rectangle.set_color(PURPLE)
eqn1 = TextMobject(r"f(x,y) = $x^2y$")
eqn1.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE)
number1 = TextMobject("(2,1)")
number1.move_to(2.5*UP+ 4*LEFT)
number1.scale(1.2)
number1.set_color(ORANGE)
output1 = TextMobject("4")
output1.scale(1.5)
output1.set_color(BLUE_C)
output1.move_to(3*RIGHT)
eqn1_1 = TextMobject(r"f(2,1) = $2^2(1)$")
eqn1_1.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE)
self.play(Write(eqn1),ShowCreation(rectangle))
self.wait()
self.play(ApplyMethod(number1.move_to, 3*LEFT))
self.play(FadeOut(number1))
self.play(Transform(eqn1, eqn1_1))
self.wait()
self.play(ApplyMethod(output1.move_to, 2.5*DOWN+4*RIGHT))
self.wait()
self.play(Write(scalar_function))
self.play(FadeOut(output1), FadeOut(scalar_function), FadeOut(eqn1))
vector_function = TextMobject("Vector Valued Function")
vector_function.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
vector_function.scale(1.5)
vector_function.move_to(2.5*UP)
eqn2 = TextMobject(r"f(x,y,z) = $ \begin{bmatrix} x^2y \\ 2yz \end{bmatrix}$")
eqn2.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
number2 = TextMobject("(2,1,3)")
number2.move_to(2.5*UP+ 4*LEFT)
number2.scale(1.2)
number2.set_color(ORANGE)
output2 = TextMobject(r"$ \begin{bmatrix} 4 \\ 6 \end{bmatrix}$")
output2.set_color(BLUE_C)
output2.move_to(3*RIGHT)
self.play(Write(eqn2))
self.wait()
self.play(ApplyMethod(number2.move_to, 3*LEFT))
self.play(FadeOut(number2))
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()
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)
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