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Merge pull request #1 from GSri30/master
Updated Sri Harsha's readme.md
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‎FSF-2020/series-and-transformations/Power Series/PowerSeriesQuestions.pdf‎

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‎FSF-2020/series-and-transformations/Power Series/script1.py‎

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from manimlib.imports import *
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def formFormula(coeff_list,variable_list):
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coeff_list=[TextMobject("${ a }_{ 0 }$"),TextMobject("${ a }_{ 1 }$"),TextMobject("${ a }_{ 2 }$")]
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variable_list=[TextMobject("+"),TextMobject("${ x }$+"),TextMobject("${ x }^{ 2 }$")]
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coeff_list[0].shift(2.2*UP+1.6*LEFT)
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for i in range(0,3):
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coeff_list[i].set_color(GOLD_A)
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variable_list[i].next_to(coeff_list[i],buff=0.1)
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if i!=2:
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coeff_list[i+1].next_to(variable_list[i],buff=0.1)
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dots=TextMobject("...")
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dots.next_to(variable_list[2])
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expansion=VGroup(coeff_list[0],coeff_list[1],coeff_list[2],variable_list[0],variable_list[1],variable_list[2],dots)
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expansion.scale(0.7)
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return expansion
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class pieChart(Scene):
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def construct(self):
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circle1=Circle(radius=3,color=BLUE)
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powerText=TextMobject("Power Series")
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powerText.scale(0.8)
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self.play(FadeIn(powerText))
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self.play(ShowCreation(circle1))
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self.wait(1)
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powerGroup=VGroup(circle1,powerText)
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self.play(ApplyMethod(powerGroup.scale,0.5))
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self.play(ApplyMethod(powerGroup.move_to,2.2*UP))
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self.wait(0.5)
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expansion_power_coeff=[]
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variables_power=[]
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expansion_power=formFormula(expansion_power_coeff,variables_power)
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self.play(ReplacementTransform(powerText,expansion_power))
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self.wait(1)
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circle2=Circle(radius=1.5)
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circle2.shift(2.2*UP)
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expansion_geo_coeff=[0]*3
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variables_geo=[0]*3
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arrow1_2=Line(start=0.7*UP,end=2.5*LEFT)
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expansion_geo_coeff=[TextMobject("${ a }_{ 0 }$"),TextMobject("${ a }_{ 1 }$"),TextMobject("${ a }_{ 2 }$")]
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for i in range(0,3):
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expansion_geo_coeff[i].set_color(GOLD_A)
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variables_geo=[TextMobject("+"),TextMobject("${ x }$+"),TextMobject("${ x }^{ 2 }$")]
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expansion_geo_coeff[0].shift(2.2*UP+1.6*LEFT)
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for i in range(0,3):
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variables_geo[i].next_to(expansion_geo_coeff[i],buff=0.1)
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if i!=2:
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expansion_geo_coeff[i+1].next_to(variables_geo[i],buff=0.1)
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dots=TextMobject("...")
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dots.next_to(variables_geo[2])
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expansion_geo=VGroup(expansion_geo_coeff[0],expansion_geo_coeff[1],expansion_geo_coeff[2],variables_geo[0],variables_geo[1],variables_geo[2],dots)
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expansion_geo.scale(0.7)
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self.play(ApplyMethod(circle2.shift,4*LEFT+2.5*DOWN),ApplyMethod(expansion_geo.shift,4*LEFT+2.5*DOWN))
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self.add(arrow1_2)
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self.wait(1)
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ones=[TextMobject("1"),TextMobject("1"),TextMobject("1")]
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for i in range(0,3):
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ones[i].set_color(GOLD_A)
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ones[0].shift(0.3*DOWN,5*LEFT)
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ones[1].next_to(ones[0],buff=0.5)
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ones[2].next_to(ones[1],buff=0.7)
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self.play(ReplacementTransform(expansion_geo_coeff[0],ones[0]),ReplacementTransform(expansion_geo_coeff[1],ones[1]),ReplacementTransform(expansion_geo_coeff[2],ones[2]))
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self.wait(1)
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expansion_geo=VGroup(ones[0],ones[1],ones[2],variables_geo[0],variables_geo[1],variables_geo[2],dots)
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expansion_geo_final=TextMobject("$1+x+{ x }^{ 2 }..$")
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expansion_geo_final.scale(0.8)
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expansion_geo_final.shift(0.3*DOWN+4*LEFT)
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self.play(ReplacementTransform(expansion_geo,expansion_geo_final))
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self.wait(1)
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circle3=Circle(radius=1.5,color=GREEN)
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circle3.shift(2.2*UP)
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expansion_taylor_coeff=[0]*3
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variables_taylor=[0]*3
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arrow1_3=Line(start=0.7*UP,end=DOWN*0.3)
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expansion_taylor_coeff=[TextMobject("${ a }_{ 0 }$"),TextMobject("${ a }_{ 1 }$"),TextMobject("${ a }_{ 2 }$")]
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for i in range(0,3):
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expansion_taylor_coeff[i].set_color(GOLD_A)
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variables_taylor=[TextMobject("+"),TextMobject("${ x }$+"),TextMobject("${ x }^{ 2 }$")]
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expansion_taylor_coeff[0].shift(2.2*UP+1.6*LEFT)
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for i in range(0,3):
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variables_taylor[i].next_to(expansion_taylor_coeff[i],buff=0.1)
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if i!=2:
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expansion_taylor_coeff[i+1].next_to(variables_taylor[i],buff=0.1)
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dots=TextMobject("...")
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dots.next_to(variables_taylor[2])
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expansion_taylor=VGroup(expansion_taylor_coeff[0],expansion_taylor_coeff[1],expansion_taylor_coeff[2],variables_taylor[0],variables_taylor[1],variables_taylor[2],dots)
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expansion_taylor.scale(0.7)
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self.play(ApplyMethod(circle3.shift,4*DOWN),ApplyMethod(expansion_taylor.shift,4*DOWN))
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self.add(arrow1_3)
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self.wait(1)
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differentials=[TextMobject("$f(0)$"),TextMobject("${ f'\left( 0 \\right) }$"),TextMobject("$\\frac { f''\left( 0 \\right) }{ 2! }$")]
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for i in range(0,3):
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differentials[i].set_color(GOLD_A)
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differentials[0].shift(1.8*DOWN+1.15*LEFT)
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differentials[1].shift(1.8*DOWN+0.45*LEFT)
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differentials[2].shift(1.8*DOWN+0.45*RIGHT)
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differentials[0].scale(0.35)
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differentials[1].scale(0.35)
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differentials[2].scale(0.35)
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self.play(ReplacementTransform(expansion_taylor_coeff[0],differentials[0]),ReplacementTransform(expansion_taylor_coeff[1],differentials[1]),ReplacementTransform(expansion_taylor_coeff[2],differentials[2]))
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self.wait(2)
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expansion_taylor_final=VGroup(differentials[0],differentials[1],differentials[2],variables_taylor[0],variables_taylor[1],variables_taylor[2],dots)
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self.play(FadeOut(expansion_geo_final),FadeOut(expansion_taylor_final))
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geoText=TextMobject("Geometric Series")
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geoText.scale(0.7)
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geoText.shift(4*LEFT+0.3*DOWN)
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taylorText=TextMobject("Taylor Series")
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taylorText.scale(0.7)
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taylorText.shift(1.8*DOWN)
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self.play(FadeIn(geoText),FadeIn(taylorText))
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self.wait(1)
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soOntext=TextMobject("So on..!")
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soOntext.shift(4*RIGHT)
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soOntext.scale(0.8)
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self.play(FadeIn(soOntext))
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self.wait(2)

‎FSF-2020/series-and-transformations/Power Series/script2.py‎

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from manimlib.imports import *
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import numpy as np
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class convergence(Scene):
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def construct(self):
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originalFormula=TextMobject("$\sum _{ n=0 }^{ \infty }{ { a }_{ n }{ x }^{ n } }$")
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originalFormula.set_color(RED)
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self.play(Write(originalFormula))
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self.wait(1)
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self.play(ApplyMethod(originalFormula.shift,2.7*UP))
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self.wait(1)
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terms=["$a_{ 0 }$","$a_{ 1 }x$","$a_{ 2 }x^{ 2 }$","$a_{ 3 }x^{ 3 }$","$a_{ 4 }x^{ 4 }$","$a_{ 5 }x^{ 5 }$","$a_{ 6 }x^{ 6 }$","$a_{ 7 }x^{ 7 }$","$a_{ 8 }x^{ 8 }$","$a_{ 9 }x^{ 9 }$","$a_{ 10 }x^{ 10 }$","$a_{ 11 }x^{ 11 }$"]
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termsTogetherString="+".join(terms)
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termsTogether=TextMobject(termsTogetherString+"...")
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termsTogether.scale(0.8)
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termsTogether.shift(2.7*UP)
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self.play(ReplacementTransform(originalFormula,termsTogether))
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self.wait(1)
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termMobjectRect=[0]*12
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termMobject=TextMobject(terms[0])
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termMobject.shift(2.7*UP+6.2*LEFT)
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for i in range(1,13):
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termMobjectOld=termMobject
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termMobjectOld.scale(0.8)
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if(i<12):
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termMobject=TextMobject(terms[i])
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termMobject.next_to(termMobjectOld)
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if(i==1):
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rectDefine=TextMobject("Here","each rectangle","represents the","value of the term")
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rectDefine.set_color_by_tex_to_color_map({"each rectangle":BLUE,"value of the term":YELLOW})
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rectDefine.scale(0.7)
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rectDefine.shift(3.2*DOWN)
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self.play(Write(rectDefine))
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self.wait(1)
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if(i==2):
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ratio=TextMobject("If $\\frac { a_{ n+1 } }{ { a }_{ n } } < 1$")
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ratio.set_color(RED)
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ratio.scale(0.7)
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ratio.move_to(3.2*DOWN)
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inequality=TextMobject("$a_{ n+1 } < a_{ n }$")
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inequality.set_color(RED)
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inequality.scale(0.7)
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inequality.move_to(3.2*DOWN)
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self.play(FadeOut(rectDefine))
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self.play(Write(ratio))
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self.wait(1)
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self.play(ReplacementTransform(ratio,inequality))
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self.wait(1)
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#self.play(ApplyMethod(termMobjectOld.move_to,(2-0.3*i)*DOWN+RIGHT*0.2*i))
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termMobjectRect[i-1]=Rectangle(height=0.1,width=(5-0.4*i))
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termMobjectRect[i-1].move_to((2-0.2*i)*DOWN+RIGHT*0.2*i)
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#rectangles[p] = termMobjectRect
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#p+=1
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self.play(ReplacementTransform(termMobjectOld,termMobjectRect[i-1]))
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uparrow=TextMobject("$\\uparrow$")
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uparrow.set_color(GREEN)
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uparrow.scale(6)
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uparrow.shift(4*RIGHT+0.5*DOWN)
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self.play(ShowCreation(uparrow))
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self.wait(1)
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converges=TextMobject("Converges!")
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converges.set_color(RED)
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converges.scale(0.6)
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converges.next_to(uparrow)
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self.play(FadeIn(converges))
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self.wait(2)
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self.play(FadeOut(converges),FadeOut(uparrow),FadeOut(inequality))
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self.wait(0.5)
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rect=VGroup(termMobjectRect[0],termMobjectRect[1],termMobjectRect[2],termMobjectRect[3],termMobjectRect[4],termMobjectRect[5],termMobjectRect[6],termMobjectRect[7],termMobjectRect[8],termMobjectRect[9],termMobjectRect[10],termMobjectRect[11])
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self.play(ApplyMethod(rect.scale,0.2))
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for i in range(0,12):
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self.play(ApplyMethod(termMobjectRect[i].shift,i*0.04*DOWN+(11-(3-0.11*i)*i)*LEFT*0.3))
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func=TextMobject("$\\approx$","$f(x)$")
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func.set_color_by_tex_to_color_map({"$f(x)$":RED})
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func.scale(0.8)
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func.shift(DOWN+4.5*RIGHT+0.1*UP)
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self.play(FadeIn(func))
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rightarrow=TextMobject("$\\rightarrow$")
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rightarrow.set_color(GREEN)
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rightarrow.scale(4)
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rightarrow.shift(2*DOWN)
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converges=TextMobject("Hence even the","sum converges!")
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converges.set_color_by_tex_to_color_map({"sum converges!":RED})
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converges.move_to(3*DOWN)
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converges.scale(0.7)
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self.play(Write(rightarrow),FadeIn(converges))
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self.wait(2)

‎FSF-2020/series-and-transformations/Power Series/script3.py‎

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from manimlib.imports import*
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import math
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class intro(Scene):
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def construct(self):
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introText1=TextMobject("Let's analyse")
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introText2=TextMobject("for")
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function_main=TextMobject("$\sum { { (-1) }^{ n }{ x }^{ 2n } }$")
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function_main.set_color(GREEN)
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introText1.scale(1.2)
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introText1.shift(2*UP)
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introText2.scale(0.7)
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introText2.shift(UP)
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function_main.scale(2)
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function_main.shift(DOWN)
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function_expan=TextMobject("$1-{ x }^{ 2 }+{ x }^{ 4 }-{ x }^{ 6 }+{ x }^{ 8 }+..$")
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function_expan.set_color(RED)
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function_expan.scale(1.2)
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function_expan.shift(2*UP)
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self.play(Write(introText1))
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self.play(FadeIn(introText2))
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self.wait(0.5)
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self.play(Write(function_main))
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self.wait(1)
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self.play(FadeOut(introText1),FadeOut(introText2))
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self.play(ApplyMethod(function_main.shift,3*UP))
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self.wait(0.5)
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self.play(ReplacementTransform(function_main,function_expan))
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self.wait(1)
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self.play(ApplyMethod(function_expan.scale,0.5))
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function_expan.to_edge(UP+RIGHT)
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self.play(ReplacementTransform(function_expan,function_expan))
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self.wait(1)
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class graphScene(GraphScene):
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CONFIG = {
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"x_min": -8,
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"x_max": 8,
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"y_min": -8,
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"y_max": 8,
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"graph_origin": ORIGIN,
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"function_color": RED,
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"axes_color": GREEN,
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"x_axis_label": "$x$",
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"y_axis_label": "$y$",
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"exclude_zero_label": True,
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"x_labeled_nums": range(-1, 2, 1),
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"y_labeled_nums": range(0,2,1)
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}
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def construct(self):
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x_each_unit = self.x_axis_width / (self.x_max - self.x_min)
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y_each_unit = self.y_axis_height / (self.y_max - self.y_min)
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function_expan=TextMobject("$1-{ x }^{ 2 }+{ x }^{ 4 }-{ x }^{ 6 }+{ x }^{ 8 }+..$")
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function_expan.set_color(RED)
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function_expan.scale(0.6)
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function_expan.to_edge(UP+RIGHT)
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self.add(function_expan)
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self.setup_axes(animate=True)
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eqText=[TextMobject("$1$"),TextMobject("$1-{ x }^{ 2 }$"),TextMobject("$1-{ x }^{ 2 }+{ x }^{ 4 }$"),TextMobject("$1-{ x }^{ 2 }+{ x }^{ 4 }-{ x }^{ 6 }$")]
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for i in range(0,len(eqText)):
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eqText[i].scale(0.6)
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eqText[i].set_color(BLUE)
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eqText[i].shift(ORIGIN+UP*2*y_each_unit+RIGHT*3.3*x_each_unit)
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eqTextTerm=TextMobject("And so on..!")
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eqTextTerm.set_color(BLUE)
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eqTextTerm.scale(0.6)
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eqTextTerm.shift(ORIGIN+UP*2*y_each_unit+3*RIGHT*x_each_unit)
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equation1 = self.get_graph(lambda x : 1,color = RED,x_min = -8,x_max=8)
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equation2 = self.get_graph(lambda x : 1-math.pow(x,2),color = RED,x_min = -1.7,x_max=1.7)
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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)
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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)
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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)
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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)
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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)
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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)
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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)
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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)
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textBtwAnim1=TextMobject("Here the graph just","oscilates")
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textBtwAnim1.set_color_by_tex_to_color_map({"oscilates":BLUE})
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textBtwAnim2=TextMobject("after","the","point","(as we add higher order terms)")
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textBtwAnim2.set_color_by_tex_to_color_map({"after":BLUE,"point":YELLOW})
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textBtwAnim3=TextMobject("$x=1$")
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textBtwAnim1.scale(0.4)
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textBtwAnim2.scale(0.4)
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textBtwAnim3.scale(1.2)
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textBtwAnim1.shift(2.1*DOWN+4.3*RIGHT)
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textBtwAnim2.shift(2.4*DOWN+4.1*RIGHT)
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textBtwAnim3.shift(2.9*DOWN+4.3*RIGHT)
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self.play(ShowCreation(equation1),run_time=0.8)
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self.add(eqText[0])
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self.wait(1)
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self.play(ReplacementTransform(equation1,equation2),ReplacementTransform(eqText[0],eqText[1]))
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self.wait(0.5)
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self.play(ReplacementTransform(equation2,equation3),ReplacementTransform(eqText[1],eqText[2]))
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self.wait(0.4)
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self.play(ReplacementTransform(equation3,equation4),ReplacementTransform(eqText[2],eqText[3]))
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self.wait(0.3)
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self.play(FadeOut(eqText[3]))
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self.play(FadeIn(eqTextTerm))
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self.play(Write(textBtwAnim1),Write(textBtwAnim2))
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self.play(FadeIn(textBtwAnim3))
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self.play(ReplacementTransform(equation4,equation5))
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self.wait(0.2)
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self.play(ReplacementTransform(equation5,equation6))
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self.wait(0.2)
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self.play(ReplacementTransform(equation6,equation7))
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self.wait(0.2)
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self.play(ReplacementTransform(equation7,equation8))
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self.wait(0.2)
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self.play(ReplacementTransform(equation8,equation9))
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self.wait(0.2)
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self.play(ReplacementTransform(equation9,equation10))
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self.wait(1)
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self.play(FadeOut(textBtwAnim1),FadeOut(textBtwAnim2),FadeOut(textBtwAnim3),FadeOut(equation10),FadeOut(eqTextTerm))
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self.wait(1)
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convergeLine=Line(start=ORIGIN+x_each_unit*LEFT,end=ORIGIN+x_each_unit*RIGHT,color=WHITE)
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divergeLineLeft=Line(start=ORIGIN+x_each_unit*LEFT,end=ORIGIN+x_each_unit*LEFT*8,color=RED)
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divergeLineRight=Line(start=ORIGIN+x_each_unit*RIGHT,end=ORIGIN+x_each_unit*8*RIGHT,color=RED)
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circle1=Circle(radius=0.01,color=PURPLE_E)
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circle2=Circle(radius=0.01,color=PURPLE_E)
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circle1.shift(ORIGIN+LEFT*x_each_unit)
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circle2.shift(ORIGIN+RIGHT*x_each_unit)
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convergeText=TextMobject("Converges")
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divergeText1=TextMobject("Diverges")
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divergeText2=TextMobject("Diverges")
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convergeText.set_color(GREEN)
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divergeText1.set_color(RED)
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divergeText2.set_color(RED)
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convergeText.scale(0.5)
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divergeText1.scale(0.5)
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divergeText2.scale(0.5)
144+
convergeText.shift(1.6*UP)
145+
divergeText1.shift(0.3*UP+1.5*LEFT)
146+
divergeText2.shift(0.3*UP+1.5*RIGHT)
147+
self.play(Write(divergeLineLeft),Write(divergeLineRight))
148+
self.play(FadeIn(convergeLine))
149+
self.wait(0.5)
150+
self.play(FadeOut(self.axes))
151+
self.play(Write(circle1),Write(circle2))
152+
self.wait(0.5)
153+
self.play(ApplyMethod(convergeLine.shift,1.3*UP),ApplyMethod(function_expan.shift,5*LEFT+DOWN))
154+
self.play(FadeIn(convergeText),FadeIn(divergeText1),FadeIn(divergeText2))
155+
self.wait(2)
156+

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