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-rw-r--r--FSF-2020/series-and-transformations/Taylor Series/TaylorSeriesQuestions.pdfbin119804 -> 0 bytes
-rw-r--r--FSF-2020/series-and-transformations/Taylor Series/script1.py198
-rw-r--r--FSF-2020/series-and-transformations/Taylor Series/script2.py195
-rw-r--r--FSF-2020/series-and-transformations/Taylor Series/script3.py111
-rw-r--r--FSF-2020/series-and-transformations/Taylor Series/script4.py82
5 files changed, 0 insertions, 586 deletions
diff --git a/FSF-2020/series-and-transformations/Taylor Series/TaylorSeriesQuestions.pdf b/FSF-2020/series-and-transformations/Taylor Series/TaylorSeriesQuestions.pdf
deleted file mode 100644
index 2096f52..0000000
--- a/FSF-2020/series-and-transformations/Taylor Series/TaylorSeriesQuestions.pdf
+++ /dev/null
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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)
-
-
-
-
diff --git a/FSF-2020/series-and-transformations/Taylor Series/script2.py b/FSF-2020/series-and-transformations/Taylor Series/script2.py
deleted file mode 100644
index b5d0a53..0000000
--- a/FSF-2020/series-and-transformations/Taylor Series/script2.py
+++ /dev/null
@@ -1,195 +0,0 @@
-from manimlib.imports import*
-import math
-
-
-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("at $a=1$")
- text.scale(0.7)
- text.shift(DOWN)
-
- shiftText=TextMobject("(Here we shift the origin to the point $x=1$)")
- shiftText.scale(0.6)
- shiftText.shift(2.4*DOWN)
-
-
- self.play(Write(equation))
- self.wait(0.5)
- self.play(FadeIn(text))
- self.wait(0.7)
- self.play(Write(shiftText))
- self.wait(0.7)
- self.play(FadeOut(equation),FadeOut(text),FadeOut(shiftText))
-
-
-def formFormula(coeff_list,variable_list):
- coeff_list=[TextMobject("${ a }_{ 0 }$"),TextMobject("${ a }_{ 1 }$"),TextMobject("${ a }_{ 2 }$")]
- variable_list=[TextMobject("+"),TextMobject("${ (x-1) }$+"),TextMobject("${ (x-1) }^{ 2 }$")]
- 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 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("$e^{-1}$"),TextMobject("$f'(x)$"),TextMobject("$\\frac { f''(x) }{ 2! } $")]
- coeff[0].shift(3.33*UP+3.65*RIGHT)
- coeff[0].scale(0.45)
- coeff[1].shift(3.33*UP+4.13*RIGHT)
- coeff[1].scale(0.275)
- coeff[2].shift(3.33*UP+5.36*RIGHT)
- coeff[2].scale(0.28)
-
- for obj in coeff:
- obj.set_color(GOLD_A)
-
- firstApprox=[self.get_graph(lambda x:math.exp(-1),color=BLUE,x_min=-5.5,x_max=5.5)]
- secondApprox=[self.get_graph(lambda x:math.exp(-1)-2*(x-1)*math.exp(-1),color=BLUE,x_min=-5.5,x_max=5.5),
- self.get_graph(lambda x:math.exp(-1)+3*(x-1)*math.exp(-1),color=BLUE,x_min=-5.5,x_max=5.5),
- self.get_graph(lambda x:math.exp(-1)-4*(x-1)*math.exp(-1),color=BLUE,x_min=-5.5,x_max=5.5)]
- thirdApprox=[self.get_graph(lambda x:math.exp(-1)-2*(x-1)*math.exp(-1)-2*math.exp(-1)*(x-1)**2,color=BLUE,x_max=5.5,x_min=-5.5),
- self.get_graph(lambda x:math.exp(-1)-2*(x-1)*math.exp(-1)-0.1*math.exp(-1)*(x-1)**2,color=BLUE,x_max=5.5,x_min=-5.5),
- self.get_graph(lambda x:math.exp(-1)-2*(x-1)*math.exp(-1),color=BLUE,x_max=5.5,x_min=-5.5),
- self.get_graph(lambda x:math.exp(-1)-2*(x-1)*math.exp(-1)+0.5*math.exp(-1)*(x-1)**2,color=BLUE,x_max=5.5,x_min=-5.5),
- self.get_graph(lambda x:math.exp(-1)-2*(x-1)*math.exp(-1)+2*math.exp(-1)*(x-1)**2,color=BLUE,x_max=5.5,x_min=-5.5)]
-
- firstGraph=self.get_graph(lambda x:math.exp(-1),color=BLUE,x_min=-5.5,x_max=5.5)
- secondGraph=self.get_graph(lambda x:math.exp(-1)-2*(x-1)*math.exp(-1),color=BLUE,x_min=-5.5,x_max=5.5)
- thirdGraph=self.get_graph(lambda x:math.exp(-1)-2*(x-1)*math.exp(-1)+math.exp(-1)*(x-1)**2,color=BLUE,x_max=5.5,x_min=-5.5)
-
- bottomText1=TextMobject("Apply","$f(1)=T_{n}(1)$")
- bottomText2=TextMobject("This gives","$a_{ 0 }=e^{-1}$")
- bottomText3=TextMobject("Now it could be of","any slope!")
- #show graphs of second approx
- bottomText4=TextMobject("Hence","apply","$f'(1)=T_{n}'(1)$")
- #final graph
- bottomText5=TextMobject("This gives","$a_{ 1 }=-2e^{-1}$")
- bottomText6=TextMobject("Since the rate of change of this slope","could vary")
- #show third approx graphs
- bottomText7=TextMobject("Hence also","apply","$f''(1)=T_{ n }''(1)$")
- #final graph
- bottomText8=TextMobject("This gives","$a_{ 2 }=e^{-1}$")
-
- bottomText1.set_color_by_tex_to_color_map({"Apply":YELLOW})
- bottomText2.set_color_by_tex_to_color_map({"$a_{ 0 }=e^{-1}$":BLUE})
- bottomText3.set_color_by_tex_to_color_map({"any slope!":YELLOW})
- bottomText4.set_color_by_tex_to_color_map({"apply":YELLOW})
- bottomText5.set_color_by_tex_to_color_map({"$a_{ 1 }=-2e^{-1}$":BLUE})
- bottomText6.set_color_by_tex_to_color_map({"could vary":YELLOW})
- bottomText7.set_color_by_tex_to_color_map({"apply":YELLOW})
- bottomText8.set_color_by_tex_to_color_map({"$a_{ 2 }=e^{-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[2]))
- # self.wait(0.5)
- # self.play(ReplacementTransform(secondApprox[2],secondApprox[0]))
- self.wait(1)
- self.play(ReplacementTransform(bottomText3,bottomText4),FadeOut(secondApprox[2]))
- self.wait(1)
- self.play(Write(secondGraph),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(secondGraph,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[1],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],thirdGraph))
- 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(1)+f'(1)(x-1)+\\frac { f''(1) }{ 2! }(x-1)^2+..+\\frac { { f }^{ n }(1) }{ n! } { (x-1) }^{ n }$")
- finalFormula.scale(0.8)
- finalFormula.set_color_by_tex_to_color_map({"$T_{ n }(x)$":GREEN,"$f(1)+f'(1)(x-1)+\\frac { f''(1) }{ 2! }(x-1)^2+..+\\frac { { f }^{ n }(1) }{ n! } { (x-1) }^{ n }$":RED})
-
- self.play(FadeOut(self.axes),FadeOut(textFinal),FadeOut(thirdGraph),FadeOut(trTextGrup),FadeOut(mainfunction),FadeOut(fx),FadeOut(coeff[0]),FadeOut(coeff[1]),FadeOut(coeff[2]))
- self.play(Write(finalFormula))
- self.wait(2) \ No newline at end of file
diff --git a/FSF-2020/series-and-transformations/Taylor Series/script3.py b/FSF-2020/series-and-transformations/Taylor Series/script3.py
deleted file mode 100644
index a2870d4..0000000
--- a/FSF-2020/series-and-transformations/Taylor Series/script3.py
+++ /dev/null
@@ -1,111 +0,0 @@
-from manimlib.imports import*
-import math
-
-
-class graphScene(GraphScene):
- CONFIG = {
- "x_min": -8,
- "x_max": 8,
- "y_min": -8,
- "y_max": 8,
- "graph_origin": ORIGIN,
- "function_color": RED,
- "axes_color": GREEN,
- "x_axis_label": "$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)
-
- self.setup_axes(animate=True)
-
- lnx=self.get_graph(lambda x:math.log2(x),color=RED,x_min=0.01,x_max=8)
-
- bottomText1=TextMobject("Apply $f(x)=T_{n}(x)$")
- bottomText2=TextMobject("Then apply $f'(x)=T_{n}'(x)$")
- bottomText3=TextMobject("Then apply $f''(x)=T_{n}''(x)$")
- bottomText4=TextMobject("and so on..")
-
- bottomText1.scale(0.5)
- bottomText2.scale(0.5)
- bottomText3.scale(0.5)
- bottomText4.scale(0.5)
-
- bottomText1.shift(3*RIGHT+2*DOWN)
- bottomText2.shift(3*RIGHT+2*DOWN)
- bottomText3.shift(3*RIGHT+2*DOWN)
- bottomText4.shift(3*RIGHT+2*DOWN)
-
- equations=[self.get_graph(lambda x:math.log2(2),color=BLUE),
- self.get_graph(lambda x:math.log2(2)+(x-2)/2,color=BLUE),
- self.get_graph(lambda x:math.log2(2)+(x-2)/2-((x-2)**2)/8,color=BLUE),
- self.get_graph(lambda x:math.log2(2)+(x-2)/2-((x-2)**2)/8+((x-2)**3)/24,color=BLUE),
- self.get_graph(lambda x:math.log2(2)+(x-2)/2-((x-2)**2)/8+((x-2)**3)/24-((x-2)**4)/64,color=BLUE),
- self.get_graph(lambda x:math.log2(2)+(x-2)/2-((x-2)**2)/8+((x-2)**3)/24-((x-2)**4)/64+((x-2)**5)/160,color=BLUE),
- self.get_graph(lambda x:math.log2(2)+(x-2)/2-((x-2)**2)/8+((x-2)**3)/24-((x-2)**4)/64+((x-2)**5)/160-((x-2)**6)/384,color=BLUE)]
-
- terms=[TextMobject("$T_{n}:=$"),TextMobject("$ln(2)$"),TextMobject("$+\\frac { x-2 }{ 2 } $"),TextMobject("$-\\frac { (x-2)^{2} }{ 8 }$"),TextMobject("+..")]
- for obj in terms:
- obj.scale(0.5)
-
- terms[0].shift(3*UP+3*RIGHT)
- terms[1].next_to(terms[0],buff=0.1)
- terms[2].next_to(terms[1],buff=0.1)
- terms[3].next_to(terms[2],buff=0.1)
- terms[4].next_to(terms[3],buff=0.1)
-
- self.play(ShowCreation(lnx))
- self.wait(1)
- self.play(Write(bottomText1))
- self.wait(0.5)
- self.play(ShowCreation(equations[0]),Write(terms[0]),Write(terms[1]))
- self.wait(1)
- self.play(ReplacementTransform(bottomText1,bottomText2))
- self.wait(0.5)
- self.play(ReplacementTransform(equations[0],equations[1]),Write(terms[2]))
- self.wait(1)
- self.play(ReplacementTransform(bottomText2,bottomText3))
- self.wait(0.5)
- self.play(ReplacementTransform(equations[1],equations[2]),Write(terms[3]))
- self.wait(1)
- self.play(ReplacementTransform(bottomText3,bottomText4),Write(terms[4]))
- self.wait(1.5)
-
- self.play(FadeOut(terms[0]),FadeOut(terms[1]),FadeOut(terms[2]),FadeOut(terms[3]),FadeOut(terms[4]),FadeOut(bottomText4))
-
- dline=DashedLine(start=ORIGIN+8*y_each_unit*UP,end=ORIGIN+8*y_each_unit*DOWN)
- dline.shift(ORIGIN+x_each_unit*4*RIGHT)
-
- bottomText5=TextMobject("Here","after $x=4$",", the graph","continuously diverges away","from $ln(x)$")
- bottomText5.scale(0.3)
- bottomText5.shift(4.5*RIGHT+2*DOWN)
- bottomText5.set_color_by_tex_to_color_map({"after $x=4$":YELLOW,"continuously diverges away":BLUE})
-
- self.play(Write(bottomText5),Write(dline))
- self.wait(1)
- self.play(ReplacementTransform(equations[2],equations[3]))
- self.wait(0.3)
- self.play(ReplacementTransform(equations[3],equations[4]))
- self.wait(0.3)
- self.play(ReplacementTransform(equations[4],equations[5]))
- self.wait(0.3)
- self.play(ReplacementTransform(equations[5],equations[6]),FadeOut(bottomText5))
- self.wait(1)
-
- circle=Circle(radius=ORIGIN+x_each_unit*2,color=PURPLE_E)
- circle.shift(ORIGIN+RIGHT*x_each_unit*2)
- radiusLine=Line(start=ORIGIN+x_each_unit*RIGHT*2,end=ORIGIN+x_each_unit*4*RIGHT,color=PURPLE_E)
- radius=TextMobject("$R$")
- radius.set_color(RED)
- radius.scale(0.5)
- radius.shift(ORIGIN+RIGHT*x_each_unit*2.45+DOWN*y_each_unit*0.6)
-
- self.play(FadeOut(equations[6]),Write(circle))
- self.wait(0.6)
- self.play(Write(radiusLine))
- self.play(FadeIn(radius))
- self.wait(2) \ No newline at end of file
diff --git a/FSF-2020/series-and-transformations/Taylor Series/script4.py b/FSF-2020/series-and-transformations/Taylor Series/script4.py
deleted file mode 100644
index 1f41c97..0000000
--- a/FSF-2020/series-and-transformations/Taylor Series/script4.py
+++ /dev/null
@@ -1,82 +0,0 @@
-from manimlib.imports import*
-import math
-
-
-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)
-
- self.setup_axes(animate=True)
- lnx=self.get_graph(lambda x:math.log2(x),color=RED,x_min=0.01,x_max=8)
- equation=self.get_graph(lambda x:math.log2(2)+(x-2)/2-((x-2)**2)/8+((x-2)**3)/24-((x-2)**4)/64+((x-2)**5)/160-((x-2)**6)/384,color=BLUE)
-
- terms=[TextMobject("$T_{n}:=$"),TextMobject("$ln(2)$"),TextMobject("$+\\frac { x-2 }{ 2 } $"),TextMobject("$-\\frac { (x-2)^{2} }{ 8 }$"),TextMobject("+..")]
- for obj in terms:
- obj.scale(0.5)
-
- terms[0].shift(3*UP+3*RIGHT)
- terms[1].next_to(terms[0],buff=0.1)
- terms[2].next_to(terms[1],buff=0.1)
- terms[3].next_to(terms[2],buff=0.1)
- terms[4].next_to(terms[3],buff=0.1)
-
- self.play(ShowCreation(lnx))
- self.wait(1)
- self.play(FadeIn(equation),FadeIn(terms[0]),FadeIn(terms[1]),FadeIn(terms[2]),FadeIn(terms[3]),FadeIn(terms[4]))
- self.wait(1)
-
- bottomText1=TextMobject("$R_{n}(x)=\\frac { d }{ dx } ($","area bounded","$)$")
-
- bottomText1.set_color_by_tex_to_color_map({"area bounded":ORANGE})
- #bottomText2.set_color_by_tex_to_color_map({"area bounded":BLUE})
- arrow=TextMobject("$\downarrow$")
- arrow.scale(2.5)
- arrow.shift(ORIGIN+x_each_unit*RIGHT*9.5+UP*y_each_unit)
- increasingText=TextMobject("Increases!")
- increasingText.set_color(GREEN)
- followupText=TextMobject("as n increase!")
- followupText.scale(0.3)
- followupText.shift(ORIGIN+x_each_unit*11*RIGHT+UP*y_each_unit*1.1)
- increasingText.shift(ORIGIN+x_each_unit*11*RIGHT+UP*y_each_unit*1.6)
- increasingText.scale(0.4)
-
- bottomText1.scale(0.5)
- #bottomText2.scale(0.5)
- #bottomText3.scale(0.5)
-
- bottomText1.shift(3.5*LEFT+2*DOWN)
- #bottomText2.shift(3.5*LEFT+2.4*DOWN)
- #bottomText3.shift(3.5*LEFT+2.8*DOWN)
-
- dline=DashedLine(start=ORIGIN+8*y_each_unit*UP,end=ORIGIN+8*y_each_unit*DOWN)
- dline.shift(ORIGIN+x_each_unit*4*RIGHT)
-
- area1=self.get_riemann_rectangles(lnx,x_max=8,x_min=4,dx=0.01,start_color=BLUE,end_color=RED,stroke_width=0,fill_opacity=0.8)
- area2=self.get_riemann_rectangles(equation,x_max=5.2,x_min=4,dx=0.025,start_color=BLACK,end_color=BLACK,stroke_width=0,fill_opacity=1)
-
- self.play(Write(dline))
- self.wait(0.5)
- self.play(ShowCreation(area1),ShowCreation(area2),Write(bottomText1))
- # self.play(Write(bottomText2))
- # self.play(FadeIn(bottomText3))
- self.play(Write(arrow))
- self.wait(0.7)
- self.play(Write(increasingText))
- self.play(FadeIn(followupText))
- self.wait(2)
- \ No newline at end of file
generated by cgit (git 2.34.1) at 2025-01-08 22:10:29 +0000