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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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