From fe5e18510140b3e02f3f6f03ad449c218f1b8579 Mon Sep 17 00:00:00 2001 From: Purusharth S Date: Sat, 23 May 2020 18:57:11 +0530 Subject: add topic-name folder --- .../Taylor Series/script1.py | 198 --------------------- 1 file changed, 198 deletions(-) delete mode 100644 FSF-2020/series-and-transformations/Taylor Series/script1.py (limited to 'FSF-2020/series-and-transformations/Taylor Series/script1.py') diff --git a/FSF-2020/series-and-transformations/Taylor Series/script1.py b/FSF-2020/series-and-transformations/Taylor Series/script1.py deleted file mode 100644 index e83eff8..0000000 --- a/FSF-2020/series-and-transformations/Taylor Series/script1.py +++ /dev/null @@ -1,198 +0,0 @@ -from manimlib.imports import* -import math - -def formFormula(coeff_list,variable_list): - coeff_list=[TextMobject("${ a }_{ 0 }$"),TextMobject("${ a }_{ 1 }$"),TextMobject("${ a }_{ 2 }$")] - variable_list=[TextMobject("+"),TextMobject("${ x }$+"),TextMobject("${ x }^{ 2 }$")] - coeff_list[0].shift(2.2*UP+1.6*LEFT) - for i in range(0,3): - coeff_list[i].set_color(GOLD_A) - variable_list[i].next_to(coeff_list[i],buff=0.1) - if i!=2: - coeff_list[i+1].next_to(variable_list[i],buff=0.1) - dots=TextMobject("...") - dots.next_to(variable_list[2]) - expansion=VGroup(coeff_list[0],coeff_list[1],coeff_list[2],variable_list[0],variable_list[1],variable_list[2],dots) - #expansion.scale(0.7) - return expansion,coeff_list - -class intro(Scene): - def construct(self): - equation=TextMobject("$f(x)=$","${ e }^{ -x^{ 2 } }$") - equation.scale(2) - equation.set_color_by_tex_to_color_map({"${ e }^{ -x^{ 2 } }$":RED}) - text=TextMobject("let $a=0$") - text.scale(0.7) - text.shift(DOWN) - - self.play(Write(equation)) - self.wait(0.5) - self.play(FadeIn(text)) - self.wait(0.7) - self.play(FadeOut(equation),FadeOut(text)) - -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(-8, 8, 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) - - generalized_eq_coeff=[] - variables_eq=[] - eq,generalized_eq_coeff=formFormula(generalized_eq_coeff,variables_eq) - trText1=TextMobject("let $T_{ n }(x)$:=") - eq.next_to(trText1) - trTextGrup=VGroup(trText1,eq) - trTextGrup.scale(0.5) - trTextGrup.to_corner(UP+RIGHT) - self.play(Write(trTextGrup)) - self.setup_axes(animate=True) - - fx=TextMobject("${ e }^{ -x^{ 2 } }$") - fx.scale(0.5) - fx.shift(ORIGIN+x_each_unit*7.5*RIGHT+y_each_unit*0.5*UP) - mainfunction=self.get_graph(lambda x:math.exp(-1*pow(x,2)),color=RED,x_min=-8,x_max=8) - self.play(ShowCreation(mainfunction)) - self.play(FadeIn(fx)) - self.wait(1.4) - - coeff=[TextMobject("$1$"),TextMobject("$f'(x)$"),TextMobject("$\\frac { f''(x) }{ 2! } $")] - coeff[0].shift(3.39*UP+4.88*RIGHT) - coeff[0].scale(0.5) - coeff[1].shift(3.39*UP+5.3*RIGHT) - coeff[1].scale(0.275) - coeff[2].shift(3.39*UP+5.98*RIGHT) - coeff[2].scale(0.28) - - for obj in coeff: - obj.set_color(GOLD_A) - - firstApprox=[self.get_graph(lambda x:1,color=BLUE)] - secondApprox=[self.get_graph(lambda x:1,color=BLUE), - self.get_graph(lambda x:x+1,color=BLUE), - self.get_graph(lambda x:-x+1,color=BLUE)] - thirdApprox=[self.get_graph(lambda x:1-2*math.pow(x,2),color=BLUE), - self.get_graph(lambda x:1-0.1*math.pow(x,2),color=BLUE), - self.get_graph(lambda x:1,color=BLUE), - self.get_graph(lambda x:1+0.1*math.pow(x,2),color=BLUE), - self.get_graph(lambda x:1+math.pow(x,2),color=BLUE)] - - firstGraph=self.get_graph(lambda x:1,color=BLUE) - secondGraph=self.get_graph(lambda x:1-math.pow(x,2),color=BLUE) - - bottomText1=TextMobject("The polynomial should","satisfy","the function at $x=0$") - bottomText2=TextMobject("This gives","$a_{ 0 }=1$") - bottomText3=TextMobject("Now it could be of","any slope!") - #show graphs of second approx - bottomText4=TextMobject("Hence the","slopes","should","even match") - #final graph - bottomText5=TextMobject("This gives","$a_{ 1 }=0$") - bottomText6=TextMobject("Since the rate of change of this slope","could vary") - #show third approx graphs - bottomText7=TextMobject("Hence the","rate of change of these slopes","should also be","same!") - #final graph - bottomText8=TextMobject("This gives","$a_{ 2 }=-1$") - - bottomText1.set_color_by_tex_to_color_map({"satisfy":YELLOW}) - bottomText2.set_color_by_tex_to_color_map({"$a_{ 0 }=1$":BLUE}) - bottomText3.set_color_by_tex_to_color_map({"any slope!":YELLOW}) - bottomText4.set_color_by_tex_to_color_map({"slopes":BLUE,"even match":YELLOW}) - bottomText5.set_color_by_tex_to_color_map({"$a_{ 1 }=0$":BLUE}) - bottomText6.set_color_by_tex_to_color_map({"could vary":YELLOW}) - bottomText7.set_color_by_tex_to_color_map({"rate of change of these slopes":BLUE,"same!":YELLOW}) - bottomText8.set_color_by_tex_to_color_map({"$a_{ 2 }=-1$":BLUE}) - - bottomText1.scale(0.4) - bottomText2.scale(0.5) - bottomText3.scale(0.4) - bottomText4.scale(0.4) - bottomText5.scale(0.5) - bottomText6.scale(0.4) - bottomText7.scale(0.4) - bottomText8.scale(0.5) - - bottomText1.shift(4.5*RIGHT+2.5*DOWN) - bottomText2.shift(4.5*RIGHT+2.5*DOWN) - bottomText3.shift(4.5*RIGHT+2.5*DOWN) - bottomText4.shift(4.5*RIGHT+2.5*DOWN) - bottomText5.shift(4.5*RIGHT+2.5*DOWN) - bottomText6.shift(4.5*RIGHT+2.5*DOWN) - bottomText7.shift(4.5*RIGHT+2.5*DOWN) - bottomText8.shift(4.5*RIGHT+2.5*DOWN) - - self.play(Write(bottomText1)) - self.wait(1) - self.play(ShowCreation(firstApprox[0]),ReplacementTransform(bottomText1,bottomText2)) - #change coeff in tn(x) - self.play(ReplacementTransform(generalized_eq_coeff[0],coeff[0])) - self.wait(1.5) - self.play(ReplacementTransform(bottomText2,bottomText3)) - self.wait(0.5) - self.play(ReplacementTransform(firstApprox[0],secondApprox[1])) - self.wait(0.5) - self.play(ReplacementTransform(secondApprox[1],secondApprox[0])) - self.wait(0.5) - self.play(ReplacementTransform(secondApprox[0],secondApprox[2])) - self.wait(1) - self.play(ReplacementTransform(bottomText3,bottomText4),FadeOut(secondApprox[2])) - self.wait(1) - self.play(Write(firstGraph),ReplacementTransform(bottomText4,bottomText5)) - #change a1 coeff - self.play(ReplacementTransform(generalized_eq_coeff[1],coeff[1])) - self.wait(1.5) - self.play(ReplacementTransform(bottomText5,bottomText6)) - self.play(ReplacementTransform(firstGraph,thirdApprox[0])) - self.wait(0.6) - self.play(ReplacementTransform(thirdApprox[0],thirdApprox[1])) - self.wait(0.6) - self.play(ReplacementTransform(thirdApprox[1],thirdApprox[2])) - self.wait(0.6) - self.play(ReplacementTransform(thirdApprox[2],thirdApprox[3])) - self.wait(0.6) - self.play(ReplacementTransform(thirdApprox[3],thirdApprox[4])) - self.wait(1.5) - self.play(ReplacementTransform(bottomText6,bottomText7)) - self.wait(1.5) - self.play(ReplacementTransform(bottomText7,bottomText8),ReplacementTransform(thirdApprox[4],secondGraph)) - self.play(ReplacementTransform(generalized_eq_coeff[2],coeff[2])) - self.wait(2) - - textFinal=TextMobject("And so on..!") - textFinal.scale(0.7) - textFinal.shift(4.5*RIGHT+2.5*DOWN) - self.play(ReplacementTransform(bottomText8,textFinal)) - self.wait(2.5) - - finalFormula=TextMobject("Hence","$T_{ n }(x)$","=","$f(0)+f'(0)x+\\frac { f''(0) }{ 2! }x^2+..+\\frac { { f }^{ n }(0) }{ n! } { x }^{ n }$") - finalFormula.scale(0.8) - finalFormula.set_color_by_tex_to_color_map({"$T_{ n }(x)$":GREEN,"$f(0)+f'(0)x+\\frac { f''(0) }{ 2! }x^2+..+\\frac { { f }^{ n }(0) }{ n! } { x }^{ n }$":RED}) - - self.play(FadeOut(self.axes),FadeOut(textFinal),FadeOut(secondGraph),FadeOut(trTextGrup),FadeOut(mainfunction),FadeOut(fx),FadeOut(coeff[0]),FadeOut(coeff[1]),FadeOut(coeff[2])) - self.play(Write(finalFormula)) - self.wait(2) - # self.play(ReplacementTransform(secondApprox[2],secondApprox[3])) - # self.wait(0.5) - # self.play(ReplacementTransform(secondApprox[3],secondApprox[4])) - # self.wait(0.5) - # self.play(ReplacementTransform(secondApprox[4],secondApprox[5])) - # self.wait(0.5) - # self.play(ReplacementTransform(secondApprox[0],secondApprox[0])) - # self.wait(0.5) - # self.play(ReplacementTransform(secondApprox[0],secondApprox[0])) - # self.wait(0.5) - - - - -- cgit