diff options
Diffstat (limited to 'FSF-2020/calculus/series-and-transformations/Laplace Transformations')
14 files changed, 537 insertions, 0 deletions
diff --git a/FSF-2020/calculus/series-and-transformations/Laplace Transformations/README.md b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/README.md new file mode 100644 index 0000000..d4cd8bc --- /dev/null +++ b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/README.md @@ -0,0 +1,21 @@ +### Basic Intuition + + +### Solving D.E.intuition + + +### Unit Step Function +#### Part1 + +#### Part2 + +#### Part3 + + +### Dirac Delta Function +#### Part1 + +#### Part2 + +#### Part3 + diff --git a/FSF-2020/calculus/series-and-transformations/Laplace Transformations/file1_laplaceTransformBasic.py b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/file1_laplaceTransformBasic.py new file mode 100644 index 0000000..7a37ae8 --- /dev/null +++ b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/file1_laplaceTransformBasic.py @@ -0,0 +1,67 @@ +from manimlib.imports import * +import pylatex + +class depict(Scene): + def construct(self): + square=Square(side_length=2,fill_color=GREEN,fill_opacity=0.7) + inputText=TextMobject("$t$") + squareText=TextMobject("$f$") + outputText=TextMobject("$f($","$t$","$)$") + + inputText.scale(0.8) + outputText.scale(0.8) + inputText.shift(2.1*LEFT) + outputText.shift(1.5*RIGHT) + squareText.scale(1.2) + + outputText.set_color_by_tex_to_color_map({"$t$":RED}) + + self.play(ShowCreation(square)) + self.play(FadeIn(squareText)) + self.add(inputText) + self.wait(0.5) + self.play(ApplyMethod(inputText.shift,0.9*RIGHT)) + self.play(FadeOut(inputText),FadeIn(outputText)) + self.play(ApplyMethod(outputText.shift,1.5*RIGHT)) + self.wait(1) + + fOutGroup=VGroup(outputText,square,squareText) + self.play(ApplyMethod(fOutGroup.scale,0.6)) + self.play(ApplyMethod(fOutGroup.shift,5*LEFT)) + self.wait(0.8) + laplaceSquare=Square(side_length=3,fill_color=BLUE,fill_opacity=0.6) + laplaceText=TextMobject("$\mathscr{L}$") + outText=TextMobject("$F($","$s$","$)$") + outText.scale(0.8) + outText.set_color_by_tex_to_color_map({"$s$":RED}) + laplaceText.scale(1.5) + outText.shift(2*RIGHT) + self.play(ShowCreation(laplaceSquare)) + self.play(FadeIn(laplaceText)) + self.wait(0.5) + self.play(ApplyMethod(outputText.shift,RIGHT)) + self.play(FadeOut(outputText),FadeIn(outText)) + self.play(ApplyMethod(outText.shift,2*RIGHT)) + self.wait(1) + + updatedOutputText=TextMobject("$f($","$t$","$)$") + updatedOutputText.shift(2.5*LEFT) + updatedOutputText.set_color_by_tex_to_color_map({"$t$":RED}) + updatedInputText=TextMobject("$t$") + updatedInputText.shift(6*LEFT) + updatedInputText.scale(0.7) + updatedOutputText.scale(0.7) + + self.play(FadeIn(updatedInputText),FadeIn(updatedOutputText)) + self.wait(0.5) + + timeText=TextMobject("Time Domain") + frequencyText=TextMobject("Frequency Domain") + timeText.set_color(RED) + frequencyText.set_color(RED) + timeText.scale(0.35) + frequencyText.scale(0.35) + timeText.shift(2.5*LEFT+0.5*DOWN) + frequencyText.shift(4*RIGHT+0.5*DOWN) + self.play(Write(frequencyText),Write(timeText)) + self.wait(2)
\ No newline at end of file diff --git a/FSF-2020/calculus/series-and-transformations/Laplace Transformations/file2_differentialEqSimplification.py b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/file2_differentialEqSimplification.py new file mode 100644 index 0000000..33e9173 --- /dev/null +++ b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/file2_differentialEqSimplification.py @@ -0,0 +1,78 @@ +from manimlib.imports import * +import pylatex + +class scene(Scene): + def construct(self): + normalSq=Square(side_length=2,fill_color=BLUE,fill_opacity=0.6) + normalSqText=TextMobject("$\mathscr{L}$") + inputText=TextMobject("$f($","$y'(t)$","$)$") + outputText=TextMobject("$F($","$s$","$)$") + + inputText.scale(0.7) + outputText.scale(0.7) + inputText.shift(2.5*LEFT) + outputText.shift(1.7*RIGHT) + normalSq.scale(1.2) + + inputText.set_color_by_tex_to_color_map({"$y'(t)$":RED}) + outputText.set_color_by_tex_to_color_map({"$s$":RED}) + + self.play(ShowCreation(normalSq)) + self.play(FadeIn(normalSqText)) + self.add(inputText) + self.wait(0.5) + self.play(ApplyMethod(inputText.shift,0.7*RIGHT)) + self.play(FadeOut(inputText),FadeIn(outputText)) + self.play(ApplyMethod(outputText.shift,RIGHT)) + self.wait(1) + + group1=VGroup(outputText,normalSq,normalSqText) + self.play(ApplyMethod(group1.scale,0.6)) + self.play(ApplyMethod(group1.shift,4.7*LEFT)) + self.wait(0.6) + + inverseSq=Square(side_length=3,fill_color=GREEN,fill_opacity=0.6) + inverseSqText=TextMobject("$\mathscr{L}^{ -1 }$") + outText=TextMobject("$f($","$y(t)$","$)$") + inverseSqText.scale(0.7) + outText.scale(0.7) + outText.set_color_by_tex_to_color_map({"$y(t)$":RED}) + self.play(ShowCreation(inverseSq)) + self.play(FadeIn(inverseSqText)) + self.wait(0.5) + outText.shift(2*RIGHT) + self.play(ApplyMethod(outputText.shift,RIGHT)) + self.play(FadeOut(outputText),FadeIn(outText)) + self.play(ApplyMethod(outText.shift,2*RIGHT)) + self.wait(1) + + updatedOutputText=TextMobject("$F($","$s$","$)$") + updatedOutputText.shift(2.5*LEFT) + updatedInputText=TextMobject("$f($","$y'(t)$","$)$") + updatedInputText.shift(6*LEFT) + updatedInputText.scale(0.7) + updatedOutputText.scale(0.7) + updatedOutputText.set_color_by_tex_to_color_map({"$s$":RED}) + updatedInputText.set_color_by_tex_to_color_map({"$y'(t)$":RED}) + + self.play(FadeIn(updatedInputText),FadeIn(updatedOutputText)) + self.wait(0.5) + + deText=TextMobject("Differential Equation") + deinterTexta=TextMobject("Transformed D.E") + deinterTextb=TextMobject("(Easy to simplify)!") + deOutText=TextMobject("Solution of D.E") + deText.set_color(RED) + deinterTexta.set_color(RED) + deOutText.set_color(RED) + deinterTextb.set_color(PURPLE_C) + deText.scale(0.35) + deinterTexta.scale(0.35) + deinterTextb.scale(0.35) + deOutText.scale(0.35) + deText.shift(6*LEFT+0.5*DOWN) + deinterTexta.shift(2.6*LEFT+0.5*DOWN) + deinterTextb.shift(2.6*LEFT+0.8*DOWN) + deOutText.shift(4*RIGHT+0.5*DOWN) + self.play(Write(deText),Write(deinterTexta),Write(deinterTextb),Write(deOutText)) + self.wait(2) diff --git a/FSF-2020/calculus/series-and-transformations/Laplace Transformations/file3_unitStepFunction.py b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/file3_unitStepFunction.py new file mode 100644 index 0000000..53c5f14 --- /dev/null +++ b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/file3_unitStepFunction.py @@ -0,0 +1,168 @@ +from manimlib.imports import * +import math +import pylatex + +class intro(GraphScene,Scene): + CONFIG = { + "x_min": -8, + "x_max": 8, + "y_min": -5, + "y_max": 5, + "graph_origin": ORIGIN+DOWN, + "function_color": RED, + "axes_color": GREEN, + "x_axis_label": "$t$", + "y_axis_label": "$\mu_{c}(t)$", + "exclude_zero_label": True, + "y_axis_height":4, + "x_axis_width":7 + } + def setup(self): + GraphScene.setup(self) + Scene.setup(self) + def construct(self): + introText=TextMobject("Unit","Step","Function") + introText.set_color_by_tex_to_color_map({"Unit":BLUE,"Step":YELLOW}) + introText.scale(0.8) + self.play(Write(introText)) + self.wait(0.5) + self.play(ApplyMethod(introText.shift,3*UP)) + formulaa=TextMobject("$\mu _{ c }(t)=0\quad$","$t<c$") + formulab=TextMobject("$\mu _{ c }(t)=1\quad$","$t\ge c$") + formulaa.set_color_by_tex_to_color_map({"$t<c$":RED}) + formulab.set_color_by_tex_to_color_map({"$t\ge c$":RED}) + formulaa.scale(0.8) + formulab.scale(0.8) + formulab.shift(0.5*DOWN) + self.play(FadeIn(formulaa),FadeIn(formulab)) + self.wait(1) + + self.play(FadeOut(formulaa),FadeOut(formulab)) + + 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) + + self.setup_axes(animate=True) + self.wait(0.8) + + c=TextMobject("c") + c.scale(0.5) + c.set_color(RED) + c.shift(self.graph_origin+3*x_each_unit*RIGHT+y_each_unit*0.4*DOWN) + self.play(Write(c)) + smallCircle=Circle(radius=0.03,fill_color=WHITE,color=WHITE) + smallCircle.shift(self.graph_origin+3*x_each_unit*RIGHT) + downLine=Line(start=self.graph_origin,end=self.graph_origin+RIGHT*3*x_each_unit,color=BLUE) + upLine=Line(start=self.graph_origin+3*x_each_unit*RIGHT+y_each_unit*UP,end=self.graph_origin+8*x_each_unit*RIGHT+y_each_unit*UP,color=BLUE) + + self.play(Write(downLine)) + self.play(Write(smallCircle)) + self.play(Write(upLine)) + self.wait(1.5) + self.play(FadeOut(self.axes),FadeOut(smallCircle),FadeOut(c),FadeOut(upLine),FadeOut(downLine),FadeOut(introText)) + self.wait(0.5) + + +class example(GraphScene): + CONFIG = { + "x_min": -3, + "x_max": 8, + "y_min": -4, + "y_max": 5, + "graph_origin": ORIGIN+LEFT+DOWN, + "function_color": RED, + "axes_color": GREEN, + "x_axis_label": "$t$", + "y_axis_label": "$y$", + "exclude_zero_label": True, + "y_axis_height":4, + "x_axis_width":6 + } + 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) + + text1=TextMobject("Consider the","formation","of","following graph!"," (a part of $f(t))$") + text1.set_color_by_tex_to_color_map({"following graph!":BLUE,"formation":YELLOW}) + text1.scale(0.6) + ft=TextMobject("$f(t)$") + ftminusc=TextMobject("$f(t-c)$") + final=TextMobject("$\mu_{c}(t)f(t-c)$") + ft.set_color(PURPLE_C) + ftminusc.set_color(PURPLE_C) + final.set_color(PURPLE_C) + c=TextMobject("c") + c.scale(0.5) + c.set_color(RED) + c.shift(self.graph_origin+RIGHT*x_each_unit*3+DOWN*y_each_unit*0.5) + ft.scale(0.5) + ftminusc.scale(0.5) + final.scale(0.5) + + self.play(Write(text1)) + self.play(ApplyMethod(text1.shift,3*UP)) + + self.setup_axes(animate=True) + y=self.get_graph(lambda x:(math.pow((x-3),3)/3)-math.pow((x-3),2)-(x-3)+3,x_min=3,x_max=7,color=RED) + f=self.get_graph(lambda x:(math.pow(x,3)/3)-math.pow(x,2)-x+3,x_min=-2,x_max=4,color=RED) + yFull=self.get_graph(lambda x:(math.pow((x-3),3)/3)-math.pow((x-3),2)-(x-3)+3,x_min=1,x_max=7,color=RED) + + self.play(Write(c)) + self.play(ShowCreation(y)) + self.wait(1) + self.play(FadeOut(self.axes),FadeOut(y),FadeOut(c)) + + belowText1=TextMobject("Consider its","normal form",", $f(t)$") + belowText1.set_color_by_tex_to_color_map({"normal form":BLUE}) + belowText2=TextMobject("Shift it to","x=c") + belowText2.set_color_by_tex_to_color_map({"x=c":RED}) + belowText3a=TextMobject("Now to remove the","left part","of","$c$,") + belowText3a.set_color_by_tex_to_color_map({"left part":YELLOW,"$c$,":YELLOW}) + belowText3b=TextMobject("multiply it with the","unit step function",", $\mu_{c}(t)$") + belowText3b.set_color_by_tex_to_color_map({"unit step function":BLUE}) + belowText1.scale(0.4) + belowText2.scale(0.4) + belowText3a.scale(0.4) + belowText3b.scale(0.4) + belowText1.shift(2.7*DOWN+4*RIGHT) + belowText2.shift(2.7*DOWN+4*RIGHT) + belowText3a.shift(2.7*DOWN+4*RIGHT) + belowText3b.shift(3.1*DOWN+4*RIGHT) + self.setup_axes(animate=True) + self.play(Write(belowText1)) + self.play(ShowCreation(f)) + ft.shift(1.5*RIGHT+UP*0.8) + self.play(FadeIn(ft)) + self.play(ReplacementTransform(belowText1,belowText2)) + ftminusc.shift(3.5*RIGHT+UP*0.8) + self.play(ReplacementTransform(f,yFull),ReplacementTransform(ft,ftminusc),Write(c)) + self.wait(1) + + self.play(ReplacementTransform(belowText2,belowText3a)) + self.play(Write(belowText3b)) + final.shift(3.7*RIGHT+UP*0.8) + self.play(ReplacementTransform(ftminusc,final),ReplacementTransform(yFull,y)) + + finalText=TextMobject("We got our required Graph!") + finalText.scale(0.55) + finalText.shift(2.7*DOWN+4*RIGHT) + self.play(FadeOut(belowText3b),ReplacementTransform(belowText3a,finalText)) + self.wait(1.5) + + self.play(FadeOut(finalText),FadeOut(text1)) + + graphGrup=VGroup(self.axes,c,final,y) + self.play(ApplyMethod(graphGrup.scale,0.45)) + box=Square(side_length=2,fill_color=BLUE,fill_opacity=0.7) + boxtext=TextMobject("$\mathscr{L}$") + boxtext.scale(0.8) + self.play(ApplyMethod(graphGrup.shift,5.5*LEFT+UP)) + self.play(ShowCreation(box),Write(boxtext)) + outText=TextMobject("${ e }^{ -cs }F(s)$") + outText.set_color(GREEN) + outText.scale(0.65) + outText.shift(2*RIGHT) + self.play(ApplyMethod(graphGrup.shift,2*RIGHT)) + self.play(FadeOut(graphGrup),FadeIn(outText)) + self.play(ApplyMethod(outText.shift,RIGHT)) + self.wait(2) diff --git a/FSF-2020/calculus/series-and-transformations/Laplace Transformations/file4_diracBasic.py b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/file4_diracBasic.py new file mode 100644 index 0000000..0c7f8e4 --- /dev/null +++ b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/file4_diracBasic.py @@ -0,0 +1,61 @@ +from manimlib.imports import * +import math +import pylatex + +class intro(GraphScene,Scene): + CONFIG = { + "x_min": -9, + "x_max": 9, + "y_min": -5, + "y_max": 5, + "graph_origin": ORIGIN+DOWN, + "function_color": RED, + "axes_color": GREEN, + "x_axis_label": "$x$", + "y_axis_label": "$\delta (x)$", + "y_axis_height":4, + "x_axis_width":7 + } + def setup(self): + GraphScene.setup(self) + Scene.setup(self) + def construct(self): + introText=TextMobject("Dirac","Delta","Function") + introText.set_color_by_tex_to_color_map({"Dirac":BLUE,"Delta":YELLOW}) + introText.scale(0.8) + self.play(Write(introText)) + self.wait(0.5) + self.play(ApplyMethod(introText.shift,3*UP)) + formulaa=TextMobject("$\delta (x)=\infty$","$x=0$") + formulab=TextMobject("$\delta (x)=0$","$x\\neq 0$") + formulaa.set_color_by_tex_to_color_map({"$x=0$":RED}) + formulab.set_color_by_tex_to_color_map({"$x\\neq 0$":RED}) + formulaa.scale(0.8) + formulab.scale(0.8) + formulab.shift(0.5*DOWN) + self.play(FadeIn(formulaa),FadeIn(formulab)) + self.wait(1) + + self.play(FadeOut(formulaa),FadeOut(formulab)) + + 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) + + self.setup_axes(animate=True) + self.wait(0.8) + + functionUpLine=Line(start=self.graph_origin,end=self.graph_origin+UP*y_each_unit*5,color=RED) + functionDownLine=Line(start=self.graph_origin+UP*y_each_unit*5,end=self.graph_origin,color=RED) + functinLeftLine=Line(start=self.graph_origin+LEFT*x_each_unit*9,end=self.graph_origin,color=RED) + functionRightLine=Line(start=self.graph_origin,end=self.graph_origin+RIGHT*x_each_unit*9,color=RED) + functionUpLine.shift(0.02*LEFT) + functionRightLine.shift(0.02*RIGHT) + + self.play(ShowCreation(functinLeftLine)) + self.play(ShowCreation(functionUpLine)) + self.play(ShowCreation(functionDownLine)) + self.play(ShowCreation(functionRightLine)) + self.wait(1.5) + + self.play(FadeOut(self.axes),FadeOut(introText),FadeOut(functinLeftLine),FadeOut(functionRightLine),FadeOut(functionUpLine),FadeOut(functionDownLine)) + self.wait(0.5) diff --git a/FSF-2020/calculus/series-and-transformations/Laplace Transformations/file5_formationDiracDeltaFunction.py b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/file5_formationDiracDeltaFunction.py new file mode 100644 index 0000000..565a7cb --- /dev/null +++ b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/file5_formationDiracDeltaFunction.py @@ -0,0 +1,142 @@ +from manimlib.imports import * +import math +import pylatex + +def func(x,t): + if(x>-t and x<t): + return 1/(2*t) + else: + return 0 + + +class formation(GraphScene): + CONFIG = { + "x_min": -7, + "x_max": 7, + "y_min": -2, + "y_max": 2, + "graph_origin": ORIGIN, + "function_color": RED, + "axes_color": GREEN, + "x_axis_label": "$t$", + "y_axis_label": "$y$", + "y_labeled_nums":range(-2,3), + "y_axis_height":4, + "x_axis_width":7 + } + 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) + + text1=TextMobject("Consider the","following function's graph!") + text1.set_color_by_tex_to_color_map({"following function's graph!":BLUE}) + text1.scale(0.6) + + equation1=TextMobject("$\delta _{ \\tau }(t)=\\frac { 1 }{ 2\\tau } \quad$","$-\\tau <t<\\tau$") + equation2=TextMobject("$\delta _{ \\tau }(t)=0\quad \quad$","$t\in (-\infty ,-\\tau ]\cup [\\tau ,\infty )$") + equation1.scale(0.7) + equation2.scale(0.7) + equation1.shift(0.2*UP) + equation2.shift(0.4*DOWN+RIGHT*0.8) + equation1.set_color_by_tex_to_color_map({"$-\\tau <t<\\tau$":RED}) + equation2.set_color_by_tex_to_color_map({"$t\in (-\infty ,-\\tau ]\cup [\\tau ,\infty )$":RED}) + + self.play(Write(text1)) + self.play(ApplyMethod(text1.shift,3*UP)) + self.play(Write(equation1)) + self.play(Write(equation2)) + self.wait(1) + + self.play(FadeOut(equation1),FadeOut(equation2)) + self.wait(0.5) + + pointes1=TextMobject("$-\\tau$") + pointes2=TextMobject("$\\tau$") + pointes1.set_color(RED) + pointes2.set_color(RED) + pointes1.scale(0.65) + pointes2.scale(0.65) + + bottomText1=TextMobject("Here","$\int _{ -\infty }^{ \infty }{ \delta _{ \\tau }(t)dt }$","=","$1$") + bottomText2=TextMobject("Now as","$\\tau \\rightarrow 0$") + bottomText3=TextMobject("We get our","Dirac Function!") + bottomText4=TextMobject("i.e.","$\lim _{ \\tau \\rightarrow 0 }{ \delta _{ \\tau }(t)}$","$=$","$\delta (t)$") + textFinal=TextMobject("Area=1") + bottomText1.set_color_by_tex_to_color_map({"$\int _{ -\infty }^{ \infty }{ \delta _{ \\tau }(t)dt }$":BLUE,"$1$":YELLOW}) + textFinal.set_color(PURPLE_B) + bottomText2.set_color_by_tex_to_color_map({"$\\tau \\rightarrow 0$":YELLOW}) + bottomText3.set_color_by_tex_to_color_map({"Dirac Function!":RED}) + bottomText4.set_color_by_tex_to_color_map({"$\lim _{ \\tau \\rightarrow 0 }{ \delta _{ \\tau }(t)}$":BLUE,"$\delta (t)$":YELLOW}) + + bottomText1.scale(0.6) + bottomText2.scale(0.6) + bottomText3.scale(0.6) + bottomText4.scale(0.6) + textFinal.scale(0.9) + + bottomText1.shift(4*RIGHT+3*DOWN) + bottomText2.shift(4*RIGHT+3*DOWN) + bottomText3.shift(4*RIGHT+3*DOWN) + bottomText4.shift(4*RIGHT+3*DOWN) + textFinal.shift(5*RIGHT+2*UP) + + self.setup_axes(animate=True) + + graphs=[ + self.get_graph(lambda x:func(x,3),x_min=-7,x_max=7,color=RED), + self.get_graph(lambda x:func(x,2),x_min=-7,x_max=7,color=RED), + self.get_graph(lambda x:func(x,1),x_min=-7,x_max=7,color=RED), + self.get_graph(lambda x:func(x,0.5),x_min=-7,x_max=7,color=RED), + self.get_graph(lambda x:func(x,0.3),x_min=-7,x_max=7,color=RED), + self.get_graph(lambda x:func(x,0.15),x_min=-7,x_max=7,color=RED), + self.get_graph(lambda x:func(x,0.05),x_min=-7,x_max=7,color=RED), + self.get_graph(lambda x:func(x,0.01),x_min=-7,x_max=7,color=RED) + ] + pointes1.shift(self.graph_origin+3*LEFT*x_each_unit+0.4*DOWN*y_each_unit) + pointes2.shift(self.graph_origin+3*RIGHT*x_each_unit+0.4*DOWN*y_each_unit) + + functionUpLine=Line(start=self.graph_origin,end=self.graph_origin+UP*y_each_unit*2,color=RED) + functionDownLine=Line(start=self.graph_origin+UP*y_each_unit*2,end=self.graph_origin,color=RED) + functinLeftLine=Line(start=self.graph_origin+LEFT*x_each_unit*7,end=self.graph_origin,color=RED) + functionRightLine=Line(start=self.graph_origin,end=self.graph_origin+RIGHT*x_each_unit*7,color=RED) + functionUpLine.shift(0.02*LEFT) + functionRightLine.shift(0.02*RIGHT) + + self.play(Write(pointes1),Write(pointes2),ShowCreation(graphs[0])) + self.play(Write(bottomText1)) + self.wait(0.7) + + self.play(ReplacementTransform(bottomText1,bottomText2),Write(textFinal)) + self.wait(0.5) + self.play(ReplacementTransform(graphs[0],graphs[1]),ApplyMethod(pointes2.shift,LEFT*x_each_unit),ApplyMethod(pointes1.shift,RIGHT*x_each_unit)) + self.play(ReplacementTransform(graphs[1],graphs[2]),ApplyMethod(pointes2.shift,LEFT*x_each_unit),ApplyMethod(pointes1.shift,RIGHT*x_each_unit)) + self.wait(0.5) + self.play(ReplacementTransform(graphs[2],graphs[3]),FadeOut(pointes1),FadeOut(pointes2)) + self.play(ReplacementTransform(graphs[3],graphs[4])) + self.wait(1) + self.play(ReplacementTransform(bottomText2,bottomText3)) + self.wait(1) + self.play(FadeOut(graphs[4]),ReplacementTransform(bottomText3,bottomText4)) + self.wait(0.5) + self.play(ShowCreation(functinLeftLine)) + self.play(ShowCreation(functionUpLine)) + self.play(ShowCreation(functionDownLine)) + self.play(ShowCreation(functionRightLine)) + self.wait(2) + + self.play(FadeOut(bottomText4),FadeOut(textFinal)) + graphGrup=VGroup(self.axes,functinLeftLine,functionDownLine,functionRightLine,functionUpLine) + self.play(ApplyMethod(graphGrup.scale,0.5)) + box=Square(side_length=2,fill_color=BLUE,fill_opacity=0.6) + boxtext=TextMobject("$\mathscr{L}$") + boxtext.scale(0.8) + self.play(ApplyMethod(graphGrup.shift,4.9*LEFT)) + self.play(ShowCreation(box),Write(boxtext)) + outText=TextMobject("$f(0)$") + outText.set_color(GREEN) + outText.scale(0.65) + outText.shift(1.5*RIGHT) + self.play(ApplyMethod(graphGrup.shift,2*RIGHT)) + self.play(FadeOut(graphGrup),FadeIn(outText)) + self.play(ApplyMethod(outText.shift,RIGHT)) + self.wait(2)
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