Merge branch 'master' into master

36 files changed, 565 insertions, 3 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
+![GIF1](gifs/basicIntuition.gif)
+
+### Solving D.E.intuition
+![GIF2](gifs/solvingDEintuition.gif)
+
+### Unit Step Function
+#### Part1
+![GIF3](gifs/unitStepFunction.gif)
+#### Part2
+![GIF4](gifs/UnitStepFunctionExample.gif)
+#### Part3
+![GIF5](gifs/LtransformUnitStepFunction.gif)
+
+### Dirac Delta Function
+#### Part1
+![GIF6](gifs/DiracFunction.gif)
+#### Part2
+![GIF7](gifs/DiracFunctionFormation.gif)
+#### Part3
+![GIF8](gifs/LtransformDiracFunction.gif)
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)
\ No newline at end of file
diff --git a/FSF-2020/calculus/series-and-transformations/Laplace Transformations/gifs/DiracFunction.gif b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/gifs/DiracFunction.gif
new file mode 100644
index 0000000..cb62ed2
--- /dev/null
+++ b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/gifs/DiracFunction.gif
diff --git a/FSF-2020/calculus/series-and-transformations/Laplace Transformations/gifs/DiracFunctionFormation.gif b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/gifs/DiracFunctionFormation.gif
new file mode 100644
index 0000000..23acbe9
--- /dev/null
+++ b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/gifs/DiracFunctionFormation.gif
diff --git a/FSF-2020/calculus/series-and-transformations/Laplace Transformations/gifs/LtransformDiracFunction.gif b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/gifs/LtransformDiracFunction.gif
new file mode 100644
index 0000000..b1d50b5
--- /dev/null
+++ b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/gifs/LtransformDiracFunction.gif
diff --git a/FSF-2020/calculus/series-and-transformations/Laplace Transformations/gifs/LtransformUnitStepFunction.gif b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/gifs/LtransformUnitStepFunction.gif
new file mode 100644
index 0000000..ccbd791
--- /dev/null
+++ b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/gifs/LtransformUnitStepFunction.gif
diff --git a/FSF-2020/calculus/series-and-transformations/Laplace Transformations/gifs/UnitStepFunctionExample.gif b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/gifs/UnitStepFunctionExample.gif
new file mode 100644
index 0000000..2b1c38f
--- /dev/null
+++ b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/gifs/UnitStepFunctionExample.gif
diff --git a/FSF-2020/calculus/series-and-transformations/Laplace Transformations/gifs/basicIntuition.gif b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/gifs/basicIntuition.gif
new file mode 100644
index 0000000..3b974bb
--- /dev/null
+++ b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/gifs/basicIntuition.gif
diff --git a/FSF-2020/calculus/series-and-transformations/Laplace Transformations/gifs/solvingDEintuition.gif b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/gifs/solvingDEintuition.gif
new file mode 100644
index 0000000..9883a8c
--- /dev/null
+++ b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/gifs/solvingDEintuition.gif
diff --git a/FSF-2020/calculus/series-and-transformations/Laplace Transformations/gifs/unitStepFunction.gif b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/gifs/unitStepFunction.gif
new file mode 100644
index 0000000..16757e1
--- /dev/null
+++ b/FSF-2020/calculus/series-and-transformations/Laplace Transformations/gifs/unitStepFunction.gif
diff --git a/FSF-2020/calculus/series-and-transformations/Power Series/PowerSeriesQuestions.pdf b/FSF-2020/calculus/series-and-transformations/Power Series/PowerSeriesQuestions.pdf
index 04ed6d5..9fc409b 100644
--- a/FSF-2020/calculus/series-and-transformations/Power Series/PowerSeriesQuestions.pdf
+++ b/FSF-2020/calculus/series-and-transformations/Power Series/PowerSeriesQuestions.pdf
diff --git a/FSF-2020/calculus/series-and-transformations/Power Series/README.md b/FSF-2020/calculus/series-and-transformations/Power Series/README.md
new file mode 100644
index 0000000..85c6fc4
--- /dev/null
+++ b/FSF-2020/calculus/series-and-transformations/Power Series/README.md
@@ -0,0 +1,14 @@
+#### PieChart
+![GIF1](gifs/file1_pieChart.gif)
+
+#### Convergence Intuition
+![GIF2](gifs/file2_convergence_Intuition.gif)
+
+#### Convergence of a function
+![GIF3](gifs/file3_convergence_of_a_function.gif)
+
+#### Radius and IntervalOfConvergence
+![GIF4](gifs/file4_radius_and_intervalOfConvergence.gif)
+
+#### Uniform Convergence
+![GIF5](gifs/file5_UniformConvergence.gif)
diff --git a/FSF-2020/calculus/series-and-transformations/Power Series/gifs/file1_pieChart.gif b/FSF-2020/calculus/series-and-transformations/Power Series/gifs/file1_pieChart.gif
new file mode 100644
index 0000000..f102f6d
--- /dev/null
+++ b/FSF-2020/calculus/series-and-transformations/Power Series/gifs/file1_pieChart.gif
diff --git a/FSF-2020/calculus/series-and-transformations/Power Series/gifs/file2_convergence_Intuition.gif b/FSF-2020/calculus/series-and-transformations/Power Series/gifs/file2_convergence_Intuition.gif
new file mode 100644
index 0000000..9463ac2
--- /dev/null
+++ b/FSF-2020/calculus/series-and-transformations/Power Series/gifs/file2_convergence_Intuition.gif
diff --git a/FSF-2020/calculus/series-and-transformations/Power Series/gifs/file3_convergence_of_a_function.gif b/FSF-2020/calculus/series-and-transformations/Power Series/gifs/file3_convergence_of_a_function.gif
new file mode 100644
index 0000000..836e044
--- /dev/null
+++ b/FSF-2020/calculus/series-and-transformations/Power Series/gifs/file3_convergence_of_a_function.gif
diff --git a/FSF-2020/calculus/series-and-transformations/Power Series/gifs/file4_radius_and_intervalOfConvergence.gif b/FSF-2020/calculus/series-and-transformations/Power Series/gifs/file4_radius_and_intervalOfConvergence.gif
new file mode 100644
index 0000000..e8dbff4
--- /dev/null
+++ b/FSF-2020/calculus/series-and-transformations/Power Series/gifs/file4_radius_and_intervalOfConvergence.gif
diff --git a/FSF-2020/calculus/series-and-transformations/Power Series/gifs/file5_UniformConvergence.gif b/FSF-2020/calculus/series-and-transformations/Power Series/gifs/file5_UniformConvergence.gif
new file mode 100644
index 0000000..44cd78b
--- /dev/null
+++ b/FSF-2020/calculus/series-and-transformations/Power Series/gifs/file5_UniformConvergence.gif
diff --git a/FSF-2020/calculus/series-and-transformations/Power Series/script1.py b/FSF-2020/calculus/series-and-transformations/Power Series/video1_pieChart.py
index 28eb07c..28eb07c 100644
--- a/FSF-2020/calculus/series-and-transformations/Power Series/script1.py
+++ b/FSF-2020/calculus/series-and-transformations/Power Series/video1_pieChart.py
diff --git a/FSF-2020/calculus/series-and-transformations/Power Series/script2.py b/FSF-2020/calculus/series-and-transformations/Power Series/video2_convergence_Intuition.py
index 72356c6..72356c6 100644
--- a/FSF-2020/calculus/series-and-transformations/Power Series/script2.py
+++ b/FSF-2020/calculus/series-and-transformations/Power Series/video2_convergence_Intuition.py
diff --git a/FSF-2020/calculus/series-and-transformations/Power Series/script3.py b/FSF-2020/calculus/series-and-transformations/Power Series/video3_convergence_of_a_function.py
index f710f42..f710f42 100644
--- a/FSF-2020/calculus/series-and-transformations/Power Series/script3.py
+++ b/FSF-2020/calculus/series-and-transformations/Power Series/video3_convergence_of_a_function.py
diff --git a/FSF-2020/calculus/series-and-transformations/Power Series/script4.py b/FSF-2020/calculus/series-and-transformations/Power Series/video4_radius_and_intervalOfConvergence.py
index 412d20c..412d20c 100644
--- a/FSF-2020/calculus/series-and-transformations/Power Series/script4.py
+++ b/FSF-2020/calculus/series-and-transformations/Power Series/video4_radius_and_intervalOfConvergence.py
diff --git a/FSF-2020/calculus/series-and-transformations/Power Series/script5.py b/FSF-2020/calculus/series-and-transformations/Power Series/video5_UniformConvergence.py
index e9681aa..e9681aa 100644
--- a/FSF-2020/calculus/series-and-transformations/Power Series/script5.py
+++ b/FSF-2020/calculus/series-and-transformations/Power Series/video5_UniformConvergence.py
diff --git a/FSF-2020/calculus/series-and-transformations/Taylor Series/README.md b/FSF-2020/calculus/series-and-transformations/Taylor Series/README.md
new file mode 100644
index 0000000..ce3b088
--- /dev/null
+++ b/FSF-2020/calculus/series-and-transformations/Taylor Series/README.md
@@ -0,0 +1,11 @@
+#### Example of Taylors expansion
+![GIF1](gifs/file1_Example_TaylorExpansion.gif)
+
+#### Taylor Series GeneralForm
+![GIF2](gifs/file2_TaylorExpansionGeneralForm.gif)
+
+#### Radius Of Convergence
+![GIF3](gifs/file3_radiusOfConvergence.gif)
+
+#### Divergence of a Remainder
+![GIF4](gifs/file4_DivergentRemainder.gif)
diff --git a/FSF-2020/calculus/series-and-transformations/Taylor Series/TaylorSeriesQuestions.pdf b/FSF-2020/calculus/series-and-transformations/Taylor Series/TaylorSeriesQuestions.pdf
index 2096f52..46d46e1 100644
--- a/FSF-2020/calculus/series-and-transformations/Taylor Series/TaylorSeriesQuestions.pdf
+++ b/FSF-2020/calculus/series-and-transformations/Taylor Series/TaylorSeriesQuestions.pdf
diff --git a/FSF-2020/calculus/series-and-transformations/Taylor Series/gifs/file1_Example_TaylorExpansion.gif b/FSF-2020/calculus/series-and-transformations/Taylor Series/gifs/file1_Example_TaylorExpansion.gif
new file mode 100644
index 0000000..ecd3272
--- /dev/null
+++ b/FSF-2020/calculus/series-and-transformations/Taylor Series/gifs/file1_Example_TaylorExpansion.gif
diff --git a/FSF-2020/calculus/series-and-transformations/Taylor Series/gifs/file2_TaylorExpansionGeneralForm.gif b/FSF-2020/calculus/series-and-transformations/Taylor Series/gifs/file2_TaylorExpansionGeneralForm.gif
new file mode 100644
index 0000000..e6d9171
--- /dev/null
+++ b/FSF-2020/calculus/series-and-transformations/Taylor Series/gifs/file2_TaylorExpansionGeneralForm.gif
diff --git a/FSF-2020/calculus/series-and-transformations/Taylor Series/gifs/file3_radiusOfConvergence.gif b/FSF-2020/calculus/series-and-transformations/Taylor Series/gifs/file3_radiusOfConvergence.gif
new file mode 100644
index 0000000..6b22d8d
--- /dev/null
+++ b/FSF-2020/calculus/series-and-transformations/Taylor Series/gifs/file3_radiusOfConvergence.gif
diff --git a/FSF-2020/calculus/series-and-transformations/Taylor Series/gifs/file4_DivergentRemainder.gif b/FSF-2020/calculus/series-and-transformations/Taylor Series/gifs/file4_DivergentRemainder.gif
new file mode 100644
index 0000000..2bb5185
--- /dev/null
+++ b/FSF-2020/calculus/series-and-transformations/Taylor Series/gifs/file4_DivergentRemainder.gif
diff --git a/FSF-2020/calculus/series-and-transformations/Taylor Series/script1.py b/FSF-2020/calculus/series-and-transformations/Taylor Series/video1_Example_TaylorExpansion.py
index e83eff8..e83eff8 100644
--- a/FSF-2020/calculus/series-and-transformations/Taylor Series/script1.py
+++ b/FSF-2020/calculus/series-and-transformations/Taylor Series/video1_Example_TaylorExpansion.py
diff --git a/FSF-2020/calculus/series-and-transformations/Taylor Series/script2.py b/FSF-2020/calculus/series-and-transformations/Taylor Series/video2_TaylorExpansionGeneralForm.py
index b5d0a53..f84cfe9 100644
--- a/FSF-2020/calculus/series-and-transformations/Taylor Series/script2.py
+++ b/FSF-2020/calculus/series-and-transformations/Taylor Series/video2_TaylorExpansionGeneralForm.py
@@ -192,4 +192,4 @@ class graphScene(GraphScene):
 
         self.play(FadeOut(self.axes),FadeOut(textFinal),FadeOut(thirdGraph),FadeOut(trTextGrup),FadeOut(mainfunction),FadeOut(fx),FadeOut(coeff[0]),FadeOut(coeff[1]),FadeOut(coeff[2]))
         self.play(Write(finalFormula))
-        self.wait(2)
\ No newline at end of file
+        self.wait(2)
diff --git a/FSF-2020/calculus/series-and-transformations/Taylor Series/script3.py b/FSF-2020/calculus/series-and-transformations/Taylor Series/video3_radiusOfConvergence.py
index a2870d4..a68afb6 100644
--- a/FSF-2020/calculus/series-and-transformations/Taylor Series/script3.py
+++ b/FSF-2020/calculus/series-and-transformations/Taylor Series/video3_radiusOfConvergence.py
@@ -108,4 +108,4 @@ class graphScene(GraphScene):
         self.wait(0.6)
         self.play(Write(radiusLine))
         self.play(FadeIn(radius))
-        self.wait(2)
\ No newline at end of file
+        self.wait(2)
diff --git a/FSF-2020/calculus/series-and-transformations/Taylor Series/script4.py b/FSF-2020/calculus/series-and-transformations/Taylor Series/video4_DivergentRemainder.py
index 1f41c97..5389039 100644
--- a/FSF-2020/calculus/series-and-transformations/Taylor Series/script4.py
+++ b/FSF-2020/calculus/series-and-transformations/Taylor Series/video4_DivergentRemainder.py
@@ -79,4 +79,4 @@ class graphScene(GraphScene):
         self.play(Write(increasingText))
         self.play(FadeIn(followupText))
         self.wait(2)
-        
\ No newline at end of file
+