diff options
Added Multivariable Function folder
Diffstat (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_derivative_vectorvf.py')
| -rw-r--r-- | FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_derivative_vectorvf.py | 247 |
1 files changed, 247 insertions, 0 deletions
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_derivative_vectorvf.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/Multivariable Functions/multivariable_func_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/multivariable_func_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)
+
+
+
+
+
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