Uploaded multivariable-functions Folder

11 files changed, 529 insertions, 0 deletions

diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/Multivariable_Functions_Quiz.pdf b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/Multivariable_Functions_Quiz.pdf
new file mode 100644
index 0000000..7895843
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/Multivariable_Functions_Quiz.pdf
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file1_multivariable_func_respresentation.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file1_multivariable_func_respresentation.py
new file mode 100644
index 0000000..4bfcf21
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file1_multivariable_func_respresentation.py
@@ -0,0 +1,80 @@
+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(2)

+

+        self.play(Write(topic))

+        self.wait(1)

+        self.play(FadeOut(topic))

+

+

+        circle = Circle()

+        circle.scale(3)

+

+        eqn1 = TextMobject(r"f(x,y) = $x^2y$")

+        eqn1.set_color(YELLOW)

+        

+

+

+        number1 = TextMobject("(2,1)")

+        number1.move_to(3*UP+ 3*LEFT)

+        number1.scale(1.2)

+        number1.set_color(GREEN)

+

+        output1 = TextMobject("4")

+        output1.scale(1.5)

+        output1.set_color(BLUE)

+

+        eqn1_1 = TextMobject(r"f(2,1) = $2^2(1)$")

+        eqn1_1.set_color(YELLOW)

+

+

+        self.play(ShowCreation(circle),Write(eqn1))

+        self.wait(1)

+        self.play(ApplyMethod(number1.move_to, 0.6*LEFT))

+        self.play(FadeOut(number1))

+        self.play(Transform(eqn1, eqn1_1))

+        self.wait(1)

+        self.play(ApplyMethod(output1.move_to, 3*DOWN+4*RIGHT))

+        self.wait(1)

+        self.play(FadeOut(output1))

+

+

+        eqn2 = TextMobject(r"f(x,y,z) = $x^2y+2yz$")

+        eqn2.set_color(YELLOW)

+

+        number2 = TextMobject("(2,1,3)")

+        number2.move_to(3*UP+ 3*LEFT)

+        number2.scale(1.2)

+        number2.set_color(GREEN)

+

+        output2 = TextMobject("8")

+        output2.scale(1.5)

+        output2.set_color(BLUE)

+

+        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(FadeOut(eqn1))

+        self.play(Write(eqn2))

+

+        self.wait(1)

+        self.play(ApplyMethod(number2.move_to, 1.2*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, 3*DOWN+4*RIGHT))

+        self.wait(1)

+        self.play(FadeOut(output2),FadeOut(eqn2),FadeOut(circle))

+        self.wait(2)
\ No newline at end of file
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file2_multivariable_func_examples.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file2_multivariable_func_examples.py
new file mode 100644
index 0000000..7322e47
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file2_multivariable_func_examples.py
@@ -0,0 +1,69 @@
+from manimlib.imports import *

+

+class Examples(GraphScene):

+    def construct(self):

+       

+        rectangle = Rectangle(height = 3, width = 4, color = GREEN)

+        square = Square(side_length = 5, color = PURPLE)

+        circle = Circle(radius = 2, color = PINK)

+        radius = Line(ORIGIN,2*RIGHT)

+        

+        radius.set_color(RED)

+

+        rectangle_area_func = TextMobject(r"$Area = f(Length, Breadth)$")

+        rectangle_area_func.scale(0.6)

+        square_area_func = TextMobject(r"$Area = f(Length)$")

+        circle_area_func = TextMobject(r"$Area = f(r)$")

+

+

+        rectangle_area = TextMobject(r"$Area = Length \times Breadth$")

+        rectangle_area.scale(0.6)

+        square_area = TextMobject(r"$Area = Length^2$")

+        circle_area = TextMobject(r"$Area = \pi r^2$")

+

+        braces_rect1 = Brace(rectangle, LEFT)

+        eq_text1 = braces_rect1.get_text("Length")

+        braces_rect2 = Brace(rectangle, UP)

+        eq_text2 = braces_rect2.get_text("Breadth")

+

+        braces_square = Brace(square, LEFT)

+        braces_square_text = braces_square.get_text("Length")

+

+        radius_text = TextMobject("r")

+        radius_text.next_to(radius,UP)

+

+        

+

+        self.play(ShowCreation(rectangle))

+        self.wait(1)

+        self.play(GrowFromCenter(braces_rect1),Write(eq_text1),GrowFromCenter(braces_rect2),Write(eq_text2))

+        self.wait(1)

+        self.play(Write(rectangle_area_func))

+        self.wait(1)

+        self.play(Transform(rectangle_area_func, rectangle_area))

+        self.wait(1)

+        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.wait(1)

+        self.play(Write(square_area_func))

+        self.wait(1)

+        self.play(Transform(square_area_func, square_area))

+        self.wait(1)

+        self.play(FadeOut(braces_square),FadeOut(braces_square_text),FadeOut(square_area_func))

+

+

+        self.play(Transform(rectangle, circle))

+        self.wait(1)

+        self.play(ShowCreation(radius),Write(radius_text))

+        self.wait(1)

+        self.play(FadeOut(radius_text),FadeOut(radius))

+        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))
\ No newline at end of file
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file3_plot_sphere.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file3_plot_sphere.py
new file mode 100644
index 0000000..baf08b1
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file3_plot_sphere.py
@@ -0,0 +1,42 @@
+from manimlib.imports import *

+

+class Sphere(ThreeDScene):

+    def construct(self):

+        axes = ThreeDAxes() # creates a 3D Axis

+

+        sphere = ParametricSurface(

+            lambda u, v: np.array([

+                np.sin(u)*np.cos(v),

+                np.sin(u)*np.sin(v),

+                np.cos(u)

+            ]),u_min=0,u_max=PI,v_min=0,v_max=2*PI,checkerboard_colors=[RED_D, RED_E],

+            resolution=(15, 32)).scale(2)

+

+

+

+        #self.set_camera_orientation(phi=0 * DEGREES,theta=270*DEGREES)

+

+        text3d = TextMobject(r"$f(x,y) \rightarrow Point(x,y,z)$")

+        text3d1 = TextMobject(r"$f(x,y) \rightarrow Point(x,y, 1 - x^2 - y^2)$")

+        self.add_fixed_in_frame_mobjects(text3d)

+        text3d.scale(0.7)

+        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.wait(1)

+        

+        self.play(Transform(text3d,text3d1))

+        self.add_fixed_in_frame_mobjects(text3d1)

+        self.play(FadeOut(text3d))

+

+        

+        self.set_camera_orientation(phi=75 * DEGREES)

+        self.begin_ambient_camera_rotation(rate=0.3)

+

+

+        self.add(axes)

+        self.play(Write(sphere))

+        self.wait(5)
\ No newline at end of file
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file4_vectorvf_sine.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file4_vectorvf_sine.py
new file mode 100644
index 0000000..06e225e
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file4_vectorvf_sine.py
@@ -0,0 +1,91 @@
+from manimlib.imports import *

+

+class SineVectors(GraphScene):

+    CONFIG = {

+    "x_min": 0,

+    "x_max": 10,

+    "y_min": -1,

+    "y_max": 1,

+    "graph_origin": ORIGIN+4*LEFT,

+    #"x_labeled_nums": list(range(-5, 6)),

+    #"y_labeled_nums": list(range(0, 5)),

+    }

+    def construct(self):

+

+       

+        

+

+

+        XTD = self.x_axis_width/(self.x_max - self.x_min)

+        YTD = self.y_axis_height/(self.y_max - self.y_min)

+

+        self.setup_axes(animate = True)

+

+

+        sine1 = self.get_graph(lambda x :  np.sin(x), x_min = 0, x_max = 1.575, color = GREEN)

+

+        point1 = Dot().shift(self.graph_origin+1*YTD*UP + 1.575*XTD*RIGHT)

+        point1_lab = TextMobject(r"$t = (\frac{\pi}{2})$") 

+        point1_lab.scale(0.7)

+        point1_lab.next_to(point1, UP)

+

+        vector1 = Arrow(self.graph_origin, self.graph_origin+1*YTD*UP + 1.575*XTD*RIGHT, buff=0.1, color = RED)

+        vector1_lab = TextMobject(r"$r(\frac{\pi}{2})$", color = RED) 

+        vector1_lab.move_to(self.graph_origin+1.5*XTD*RIGHT+ 0.5*YTD*UP)

+

+        self.play(GrowArrow(vector1),Write(vector1_lab))

+        self.play(ShowCreation(point1), Write(point1_lab))

+        self.play(ShowCreation(sine1))

+        self.wait(1)

+

+

+        sine2 = self.get_graph(lambda x :  np.sin(x), x_min = 1.575, x_max = 3.15, color = GREEN)

+

+        point2 = Dot().shift(self.graph_origin+3.15*XTD*RIGHT)

+        point2_lab = TextMobject(r"$t = (\pi)$") 

+        point2_lab.scale(0.7)

+        point2_lab.next_to(point2, UP+RIGHT)

+

+        vector2 = Arrow(self.graph_origin, self.graph_origin+3.15*XTD*RIGHT, buff=0.1, color = BLUE)

+        vector2_lab = TextMobject(r"$r(\pi)$", color = BLUE) 

+        vector2_lab.move_to(self.graph_origin+1.5*XTD*RIGHT+ 0.15*YTD*UP)

+

+        self.play(GrowArrow(vector2),Write(vector2_lab))

+        self.play(ShowCreation(point2), Write(point2_lab))

+        self.play(ShowCreation(sine2))

+        self.wait(1)

+

+

+        sine3 = self.get_graph(lambda x :  np.sin(x), x_min = 3.15, x_max = 4.725, color = GREEN)

+

+        point3 = Dot().shift(self.graph_origin+1*YTD*DOWN + 4.725*XTD*RIGHT)

+        point3_lab = TextMobject(r"$t = (\frac{3\pi}{2})$") 

+        point3_lab.scale(0.7)

+        point3_lab.next_to(point3, DOWN)

+

+        vector3 = Arrow(self.graph_origin, self.graph_origin+1*YTD*DOWN + 4.725*XTD*RIGHT, buff=0.1, color = YELLOW_C)

+        vector3_lab = TextMobject(r"$r(\frac{3\pi}{2})$", color = YELLOW_C) 

+        vector3_lab.move_to(self.graph_origin+2*XTD*RIGHT+ 0.7*YTD*DOWN)

+

+        self.play(GrowArrow(vector3),Write(vector3_lab))

+        self.play(ShowCreation(point3), Write(point3_lab))

+        self.play(ShowCreation(sine3))

+        self.wait(1)

+

+

+        sine4 = self.get_graph(lambda x :  np.sin(x), x_min = 4.725, x_max = 6.3, color = GREEN)

+

+        point4 = Dot().shift(self.graph_origin+6.3*XTD*RIGHT)

+        point4_lab = TextMobject(r"$t = (2\pi)$") 

+        point4_lab.scale(0.7)

+        point4_lab.next_to(point4, UP+RIGHT)

+

+        vector4 = Arrow(self.graph_origin, self.graph_origin+6.3*XTD*RIGHT, buff=0.1, color = PURPLE)

+        vector4_lab = TextMobject(r"$r(2\pi)$", color = PURPLE) 

+        vector4_lab.move_to(self.graph_origin+4.5*XTD*RIGHT+ 0.15*YTD*DOWN)

+

+        self.play(GrowArrow(vector4),Write(vector4_lab))

+        self.play(ShowCreation(point4), Write(point4_lab))

+        self.play(ShowCreation(sine4))

+        self.wait(3)

+

diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file5_derivative_vectorvf.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file5_derivative_vectorvf.py
new file mode 100644
index 0000000..466e389
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file5_derivative_vectorvf.py
@@ -0,0 +1,247 @@
+from manimlib.imports import *

+

+class Derivative(GraphScene):

+    CONFIG = {

+    "x_min": 0,

+    "x_max": 3,

+    "y_min": 0,

+    "y_max": 5,

+    "graph_origin": ORIGIN+6*LEFT+3*DOWN,

+    "x_axis_width": 6,

+    "x_labeled_nums": list(range(0, 4)),

+    "y_labeled_nums": list(range(0, 6)),

+    }

+    def construct(self):

+

+        XTD = self.x_axis_width/(self.x_max - self.x_min)

+        YTD = self.y_axis_height/(self.y_max - self.y_min)

+

+        self.setup_axes(animate = True)

+

+        graph = self.get_graph(lambda x :  x*x, x_min = 0.5, x_max = 2, color = GREEN)

+

+        point1 = Dot().shift(self.graph_origin+0.25*YTD*UP + 0.5*XTD*RIGHT)

+        point1_lab = TextMobject(r"$t = a$") 

+        point1_lab.scale(0.7)

+        point1_lab.next_to(point1, RIGHT)

+

+        point2 = Dot().shift(self.graph_origin+2*XTD*RIGHT+4*YTD*UP)

+        point2_lab = TextMobject(r"$t = b$") 

+        point2_lab.scale(0.7)

+        point2_lab.next_to(point2, RIGHT)

+

+

+        vector1 = Arrow(self.graph_origin, self.graph_origin+1*YTD*UP + 1*XTD*RIGHT, buff=0.02, color = RED)

+        vector1_lab = TextMobject(r"$\vec r(t)$", color = RED) 

+        vector1_lab.move_to(self.graph_origin+1.2*XTD*RIGHT+ 0.75*YTD*UP)

+        vector1_lab.scale(0.8)

+

+        vector2 = Arrow(self.graph_origin, self.graph_origin+2.25*YTD*UP + 1.5*XTD*RIGHT, buff=0.02, color = YELLOW_C)

+        vector2_lab = TextMobject(r"$\vec r(t + h)$", color = YELLOW_C) 

+        vector2_lab.move_to(self.graph_origin+0.5*XTD*RIGHT+ 2*YTD*UP)

+        vector2_lab.scale(0.8)

+

+        vector3 = Arrow(self.graph_origin+1*YTD*UP + 1*XTD*RIGHT, self.graph_origin+2.25*YTD*UP + 1.5*XTD*RIGHT, buff=0.02, color = PINK)

+        vector3_lab = TextMobject(r"$\vec r(t + h) - \vec r(t)$", color = PINK) 

+        vector3_lab.move_to(self.graph_origin+2*XTD*RIGHT+ 1.5*YTD*UP)

+        vector3_lab.scale(0.8)

+        

+

+        self.play(ShowCreation(graph))

+        self.play(ShowCreation(point1), Write(point1_lab))

+        self.play(ShowCreation(point2), Write(point2_lab))

+

+        self.play(GrowArrow(vector1),Write(vector1_lab))

+        self.play(GrowArrow(vector2),Write(vector2_lab))

+        self.play(GrowArrow(vector3),Write(vector3_lab))

+        self.wait(1)

+

+        self.display_text()

+

+        self.play(ApplyMethod(vector3_lab.move_to,(self.graph_origin+2.3*XTD*RIGHT+ 2.2*YTD*UP)))

+

+        vector4 = Arrow(self.graph_origin+1*YTD*UP + 1*XTD*RIGHT, self.graph_origin+1*YTD*UP + 1.5*XTD*RIGHT, buff=0.02, color = PURPLE)

+        vector4_lab = TextMobject(r"$dx$", color = PURPLE) 

+        vector4_lab.move_to(self.graph_origin+1.7*XTD*RIGHT+ 0.8*YTD*UP)

+        vector4_lab.scale(0.7)

+

+        vector5 = Arrow(self.graph_origin+1*YTD*UP + 1.5*XTD*RIGHT, self.graph_origin+2.25*YTD*UP + 1.5*XTD*RIGHT, buff=0.02, color = ORANGE)

+        vector5_lab = TextMobject(r"$dy$", color = ORANGE) 

+        vector5_lab.move_to(self.graph_origin+1.7*XTD*RIGHT+ 1.4*YTD*UP)

+        vector5_lab.scale(0.7)

+

+        self.play(GrowArrow(vector4),Write(vector4_lab))

+        self.play(GrowArrow(vector5),Write(vector5_lab))

+        self.wait(2)

+

+        

+

+    def display_text(self):

+        text1 = TextMobject(r"$\vec r(t)$",r"+", r"$\vec r(t + h) - \vec r(t)$")

+        text1[0].set_color(RED)

+        text1[2].set_color(PINK)

+        text1.scale(0.7)

+

+        text2 = TextMobject(r"$\vec r(t + h)$", color = YELLOW_C)

+        text2.scale(0.7)

+

+        text3 = TextMobject(r"$ \vec r(t + h) - \vec r(t)$", color = PINK)

+        text3.scale(0.7)

+

+        text4 = TextMobject(r"[", r"$x(t+h)$", r"$\vec i$", r"+", r"$y(t+h)$", r"$\vec j$", r"$]  - [$", r"$x(t)$", r"$\vec i$", r"+", r"y(t)", r"$\vec j$", r"]")

+        text4.set_color_by_tex(r"\vec i", BLUE)

+        text4.set_color_by_tex(r"\vec j", GREEN)

+        text4[1].set_color(YELLOW_C)

+        text4[4].set_color(YELLOW_C)

+        text4[-6].set_color(RED)

+        text4[-3].set_color(RED)

+        text4.scale(0.7)

+

+        text5 = TextMobject(r"$[x(t+h) - x(t)]$", r"$\vec i$", r"+", r"$[y(t+h) + y(t)]$", r"$\vec j$")

+        text5.set_color_by_tex(r"\vec i", BLUE)

+        text5.set_color_by_tex(r"\vec j", GREEN)

+        text5[0].set_color(PURPLE)

+        text5[3].set_color(ORANGE)

+        text5.scale(0.7)

+

+        text6 = TextMobject(r"$\frac{[\vec r(t + h) - \vec r(t)]}{h}$", r"=", r"$\frac{[x(t+h) - x(t)]}{h}$", r"$\vec i$", r"+", r"$\frac{[y(t+h) + y(t)]}{h}$", r"$\vec j$")

+        text6.set_color_by_tex(r"\vec i", BLUE)

+        text6.set_color_by_tex(r"\vec j", GREEN)

+        text6[0].set_color(PINK)

+        text6[2].set_color(PURPLE)

+        text6[-2].set_color(ORANGE)

+        text6.scale(0.8)

+

+        text7 = TextMobject(r"$\lim_{h \rightarrow 0}$", r"$\frac{[\vec r(t + h) - \vec r(t)]}{h}$", r"=", r"$\lim_{h \rightarrow 0}$", r"$\frac{[x(t+h) - x(t)]}{h}$", r"$\vec i$", r"+", r"$\lim_{h \rightarrow 0}$", r"$\frac{[y(t+h) + y(t)]}{h}$", r"$\vec j$")

+        text7.set_color_by_tex(r"\vec i", BLUE)

+        text7.set_color_by_tex(r"\vec j", GREEN)

+        text7[1].set_color(PINK)

+        text7[4].set_color(PURPLE)

+        text7[-2].set_color(ORANGE)

+        text7.scale(0.6)

+

+        text8 = TextMobject(r"$\vec r'(t)$", r"=",r"$\vec x'(t)$", r"$\vec i$", r"+", r"$\vec y'(t)$", r"$\vec j$")

+        text8.set_color_by_tex(r"\vec i", BLUE)

+        text8.set_color_by_tex(r"\vec j", GREEN)

+        text8[0].set_color(PINK)

+        text8[2].set_color(PURPLE)

+        text8[5].set_color(ORANGE)

+        text8.scale(0.7)

+

+        text9 = TextMobject(r"$\frac{d \vec r}{dt}$", r"=", r"$\frac{d \vec x}{dt}$", r"$\vec i$", r"+", r"$\frac{d \vec y}{dt}$", r"$\vec j$")

+        text9.set_color_by_tex(r"\vec i", BLUE)

+        text9.set_color_by_tex(r"\vec j", GREEN)

+        text9[0].set_color(PINK)

+        text9[2].set_color(PURPLE)

+        text9[5].set_color(ORANGE)

+        text9.scale(0.7)

+

+

+        text10 = TextMobject(r"$d \vec r$", r"=", r"$\frac{d \vec x}{dt}dt$", r"$\vec i$", r"+", r"$\frac{d \vec y}{dt}dt$", r"$\vec j$")

+        text10.set_color_by_tex(r"\vec i", BLUE)

+        text10.set_color_by_tex(r"\vec j", GREEN)

+        text10[0].set_color(PINK)

+        text10[2].set_color(PURPLE)

+        text10[5].set_color(ORANGE)

+        text10.scale(0.7)

+

+        text11 = TextMobject(r"$d \vec r$", r"=", r"$x'(t)dt$", r"$\vec i$", r"+", r"$y'(t)dt$", r"$\vec j$")

+        text11.set_color_by_tex(r"\vec i", BLUE)

+        text11.set_color_by_tex(r"\vec j", GREEN)

+        text11[0].set_color(PINK)

+        text11[2].set_color(PURPLE)

+        text11[5].set_color(ORANGE)

+        text11.scale(0.7)

+

+        text12 = TextMobject(r"$d \vec r$", r"=", r"$dx$", r"$\vec i$", r"+", r"$dy$", r"$\vec j$")

+        text12.set_color_by_tex(r"\vec i", BLUE)

+        text12.set_color_by_tex(r"\vec j", GREEN)

+        text12[0].set_color(PINK)

+        text12[2].set_color(PURPLE)

+        text12[5].set_color(ORANGE)

+        text12.scale(0.7)

+

+

+        text1.move_to(1*UP+2.7*RIGHT)

+        text2.move_to(1*UP+2.7*RIGHT)

+        text3.move_to(1*UP+2.7*RIGHT)

+        text4.move_to(1*UP+2.7*RIGHT)

+        text5.move_to(1*UP+2.7*RIGHT)

+        text6.move_to(1*UP+2.7*RIGHT)

+        text7.move_to(1*UP+2.5*RIGHT)

+        text8.move_to(1*UP+2.7*RIGHT)

+        text9.move_to(1*UP+2.7*RIGHT)

+        text10.move_to(1*UP+2.7*RIGHT)

+        text11.move_to(1*UP+2.7*RIGHT)

+        text12.move_to(1*UP+2.7*RIGHT)

+

+        brace1 = Brace(text7[0:2], DOWN, buff = SMALL_BUFF)

+        brace2 = Brace(text7[3:6], UP, buff = SMALL_BUFF)

+        brace3 = Brace(text7[7:], DOWN, buff = SMALL_BUFF)

+        t1 = brace1.get_text(r"$\vec r'(t)$")

+        t1.set_color(PINK)

+

+        t2 = brace2.get_text(r"$\vec x'(t)$")

+        t2.set_color(PURPLE)

+

+        t3 = brace3.get_text(r"$\vec y'(t)$")

+        t3.set_color(ORANGE)

+

+

+        self.play(Write(text1))

+        self.play(Transform(text1, text2))

+        self.wait(1)

+

+        self.play(Transform(text1, text3))

+        self.wait(1)

+

+        self.play(Transform(text1, text4))

+        self.wait(1)

+

+        self.play(Transform(text1, text5))

+        self.wait(1)

+

+        self.play(Transform(text1, text6))

+        self.wait(1)

+

+        self.play(Transform(text1, text7))

+        self.wait(1)

+

+        self.play(

+            GrowFromCenter(brace1),

+            FadeIn(t1),

+            )

+        self.wait()

+        self.play(

+            ReplacementTransform(brace1.copy(),brace2),

+            ReplacementTransform(t1.copy(),t2)

+            )

+        self.wait()

+        self.play(

+            ReplacementTransform(brace2.copy(),brace3),

+            ReplacementTransform(t2.copy(),t3)

+            )

+        self.wait()

+

+        self.play(FadeOut(brace1), FadeOut(t1), FadeOut(brace2), FadeOut(t2), FadeOut(brace3), FadeOut(t3),)

+        self.wait()

+

+        self.play(Transform(text1, text8))

+        self.wait(1)

+

+        self.play(Transform(text1, text9))

+        self.wait(1)

+

+        self.play(Transform(text1, text10))

+        self.wait(1)

+

+        self.play(Transform(text1, text11))

+        self.wait(1)

+

+        self.play(Transform(text1, text12))

+        self.wait(1)

+

+

+

+

+

diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file1_multivariable_func_respresentation.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file1_multivariable_func_respresentation.gif
new file mode 100644
index 0000000..a173bda
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file1_multivariable_func_respresentation.gif
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file2_multivariable_func_examples.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file2_multivariable_func_examples.gif
new file mode 100644
index 0000000..11f66f1
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file2_multivariable_func_examples.gif
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file3_plot_sphere.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file3_plot_sphere.gif
new file mode 100644
index 0000000..ad7582c
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file3_plot_sphere.gif
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file4_vectorvf_sine.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file4_vectorvf_sine.gif
new file mode 100644
index 0000000..4f6b931
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file4_vectorvf_sine.gif
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file5_derivative_vectorvf.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file5_derivative_vectorvf.gif
new file mode 100644
index 0000000..a94de90
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file5_derivative_vectorvf.gif