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| -rw-r--r-- | FSF-2020/calculus/series-and-transformations/Power Series/video3_convergence_of_a_function.py | 156 |
1 files changed, 0 insertions, 156 deletions
diff --git a/FSF-2020/calculus/series-and-transformations/Power Series/video3_convergence_of_a_function.py b/FSF-2020/calculus/series-and-transformations/Power Series/video3_convergence_of_a_function.py deleted file mode 100644 index f710f42..0000000 --- a/FSF-2020/calculus/series-and-transformations/Power Series/video3_convergence_of_a_function.py +++ /dev/null @@ -1,156 +0,0 @@ -from manimlib.imports import* -import math - -class intro(Scene): - def construct(self): - introText1=TextMobject("Let's analyse") - introText2=TextMobject("for") - function_main=TextMobject("$\sum { { (-1) }^{ n }{ x }^{ 2n } }$") - function_main.set_color(GREEN) - introText1.scale(1.2) - introText1.shift(2*UP) - introText2.scale(0.7) - introText2.shift(UP) - function_main.scale(2) - function_main.shift(DOWN) - function_expan=TextMobject("$1-{ x }^{ 2 }+{ x }^{ 4 }-{ x }^{ 6 }+{ x }^{ 8 }+..$") - function_expan.set_color(RED) - function_expan.scale(1.2) - function_expan.shift(2*UP) - - self.play(Write(introText1)) - self.play(FadeIn(introText2)) - self.wait(0.5) - self.play(Write(function_main)) - self.wait(1) - - self.play(FadeOut(introText1),FadeOut(introText2)) - self.play(ApplyMethod(function_main.shift,3*UP)) - self.wait(0.5) - self.play(ReplacementTransform(function_main,function_expan)) - self.wait(1) - self.play(ApplyMethod(function_expan.scale,0.5)) - function_expan.to_edge(UP+RIGHT) - self.play(ReplacementTransform(function_expan,function_expan)) - self.wait(1) - - -class graphScene(GraphScene): - CONFIG = { - "x_min": -8, - "x_max": 8, - "y_min": -8, - "y_max": 8, - "graph_origin": ORIGIN, - "function_color": RED, - "axes_color": GREEN, - "x_axis_label": "$x$", - "y_axis_label": "$y$", - "exclude_zero_label": True, - "x_labeled_nums": range(-1, 2, 1), - "y_labeled_nums": range(0,2,1) - } - - def construct(self): - - x_each_unit = self.x_axis_width / (self.x_max - self.x_min) - y_each_unit = self.y_axis_height / (self.y_max - self.y_min) - - function_expan=TextMobject("$1-{ x }^{ 2 }+{ x }^{ 4 }-{ x }^{ 6 }+{ x }^{ 8 }+..$") - function_expan.set_color(RED) - function_expan.scale(0.6) - function_expan.to_edge(UP+RIGHT) - self.add(function_expan) - - self.setup_axes(animate=True) - - eqText=[TextMobject("$1$"),TextMobject("$1-{ x }^{ 2 }$"),TextMobject("$1-{ x }^{ 2 }+{ x }^{ 4 }$"),TextMobject("$1-{ x }^{ 2 }+{ x }^{ 4 }-{ x }^{ 6 }$")] - for i in range(0,len(eqText)): - eqText[i].scale(0.6) - eqText[i].set_color(BLUE) - eqText[i].shift(ORIGIN+UP*2*y_each_unit+RIGHT*3.3*x_each_unit) - eqTextTerm=TextMobject("And so on..!") - eqTextTerm.set_color(BLUE) - eqTextTerm.scale(0.6) - eqTextTerm.shift(ORIGIN+UP*2*y_each_unit+3*RIGHT*x_each_unit) - equation1 = self.get_graph(lambda x : 1,color = RED,x_min = -8,x_max=8) - equation2 = self.get_graph(lambda x : 1-math.pow(x,2),color = RED,x_min = -1.7,x_max=1.7) - equation3 = self.get_graph(lambda x : 1-math.pow(x,2)+math.pow(x,4),color = RED,x_min = -1.6,x_max=1.6) - equation4 = self.get_graph(lambda x : 1-math.pow(x,2)+math.pow(x,4)-math.pow(x,6),color = RED,x_min = -1.45,x_max=1.45) - equation5 = self.get_graph(lambda x : 1-math.pow(x,2)+math.pow(x,4)-math.pow(x,6)+math.pow(x,8),color = RED,x_min = -1.35,x_max=1.35) - equation6 = self.get_graph(lambda x : 1-math.pow(x,2)+math.pow(x,4)-math.pow(x,6)+math.pow(x,8)-math.pow(x,10),color = RED,x_min = -1.3,x_max=1.3) - equation7 = self.get_graph(lambda x : 1-math.pow(x,2)+math.pow(x,4)-math.pow(x,6)+math.pow(x,8)-math.pow(x,10)+math.pow(x,12),color = RED,x_min = -1.25,x_max=1.25) - equation8 = self.get_graph(lambda x : 1-math.pow(x,2)+math.pow(x,4)-math.pow(x,6)+math.pow(x,8)-math.pow(x,10)+math.pow(x,12)-math.pow(x,14),color = RED,x_min = -1.2,x_max=1.2) - equation9 = self.get_graph(lambda x : 1-math.pow(x,2)+math.pow(x,4)-math.pow(x,6)+math.pow(x,8)-math.pow(x,10)+math.pow(x,12)-math.pow(x,14)+math.pow(x,16),color = RED,x_min = -1.15,x_max=1.15) - equation10 = self.get_graph(lambda x : 1-math.pow(x,2)+math.pow(x,4)-math.pow(x,6)+math.pow(x,8)-math.pow(x,10)+math.pow(x,12)-math.pow(x,14)+math.pow(x,16)-math.pow(x,18),color = RED,x_min = -1.15,x_max=1.15) - - textBtwAnim1=TextMobject("Here the graph just","oscilates") - textBtwAnim1.set_color_by_tex_to_color_map({"oscilates":BLUE}) - textBtwAnim2=TextMobject("after","the","point","(as we add higher order terms)") - textBtwAnim2.set_color_by_tex_to_color_map({"after":BLUE,"point":YELLOW}) - textBtwAnim3=TextMobject("$x=1$") - textBtwAnim1.scale(0.4) - textBtwAnim2.scale(0.4) - textBtwAnim3.scale(1.2) - textBtwAnim1.shift(2.1*DOWN+4.3*RIGHT) - textBtwAnim2.shift(2.4*DOWN+4.1*RIGHT) - textBtwAnim3.shift(2.9*DOWN+4.3*RIGHT) - - self.play(ShowCreation(equation1),run_time=0.8) - self.add(eqText[0]) - self.wait(1) - self.play(ReplacementTransform(equation1,equation2),ReplacementTransform(eqText[0],eqText[1])) - self.wait(0.5) - self.play(ReplacementTransform(equation2,equation3),ReplacementTransform(eqText[1],eqText[2])) - self.wait(0.4) - self.play(ReplacementTransform(equation3,equation4),ReplacementTransform(eqText[2],eqText[3])) - self.wait(0.3) - self.play(FadeOut(eqText[3])) - self.play(FadeIn(eqTextTerm)) - self.play(Write(textBtwAnim1),Write(textBtwAnim2)) - self.play(FadeIn(textBtwAnim3)) - self.play(ReplacementTransform(equation4,equation5)) - self.wait(0.2) - self.play(ReplacementTransform(equation5,equation6)) - self.wait(0.2) - self.play(ReplacementTransform(equation6,equation7)) - self.wait(0.2) - self.play(ReplacementTransform(equation7,equation8)) - self.wait(0.2) - self.play(ReplacementTransform(equation8,equation9)) - self.wait(0.2) - self.play(ReplacementTransform(equation9,equation10)) - self.wait(1) - - self.play(FadeOut(textBtwAnim1),FadeOut(textBtwAnim2),FadeOut(textBtwAnim3),FadeOut(equation10),FadeOut(eqTextTerm)) - self.wait(1) - - convergeLine=Line(start=ORIGIN+x_each_unit*LEFT,end=ORIGIN+x_each_unit*RIGHT,color=WHITE) - divergeLineLeft=Line(start=ORIGIN+x_each_unit*LEFT,end=ORIGIN+x_each_unit*LEFT*8,color=RED) - divergeLineRight=Line(start=ORIGIN+x_each_unit*RIGHT,end=ORIGIN+x_each_unit*8*RIGHT,color=RED) - circle1=Circle(radius=0.01,color=PURPLE_E) - circle2=Circle(radius=0.01,color=PURPLE_E) - circle1.shift(ORIGIN+LEFT*x_each_unit) - circle2.shift(ORIGIN+RIGHT*x_each_unit) - convergeText=TextMobject("Converges") - divergeText1=TextMobject("Diverges") - divergeText2=TextMobject("Diverges") - convergeText.set_color(GREEN) - divergeText1.set_color(RED) - divergeText2.set_color(RED) - convergeText.scale(0.5) - divergeText1.scale(0.5) - divergeText2.scale(0.5) - convergeText.shift(1.6*UP) - divergeText1.shift(0.3*UP+1.5*LEFT) - divergeText2.shift(0.3*UP+1.5*RIGHT) - self.play(Write(divergeLineLeft),Write(divergeLineRight)) - self.play(FadeIn(convergeLine)) - self.wait(0.5) - self.play(FadeOut(self.axes)) - self.play(Write(circle1),Write(circle2)) - self.wait(0.5) - self.play(ApplyMethod(convergeLine.shift,1.3*UP),ApplyMethod(function_expan.shift,5*LEFT+DOWN)) - self.play(FadeIn(convergeText),FadeIn(divergeText1),FadeIn(divergeText2)) - self.wait(2) - |