From b7d0db731712d3603f5c18cffbf19cc1e81f9a42 Mon Sep 17 00:00:00 2001 From: G Sri Harsha Date: Tue, 26 May 2020 14:35:15 +0530 Subject: Rename script5.py to video5_UniformConvergence.py --- .../Power Series/script5.py | 136 --------------------- .../Power Series/video5_UniformConvergence.py | 136 +++++++++++++++++++++ 2 files changed, 136 insertions(+), 136 deletions(-) delete mode 100644 FSF-2020/calculus/series-and-transformations/Power Series/script5.py create mode 100644 FSF-2020/calculus/series-and-transformations/Power Series/video5_UniformConvergence.py (limited to 'FSF-2020/calculus') diff --git a/FSF-2020/calculus/series-and-transformations/Power Series/script5.py b/FSF-2020/calculus/series-and-transformations/Power Series/script5.py deleted file mode 100644 index e9681aa..0000000 --- a/FSF-2020/calculus/series-and-transformations/Power Series/script5.py +++ /dev/null @@ -1,136 +0,0 @@ -from manimlib.imports import * -import math - -class uniformlyConvergent(Scene): - def construct(self): - introText1=TextMobject("Again consider the","above","example") - introText2=TextMobject("Let","$g(x)=\\frac { 1 }{ 1+{ x }^{ 2 } }$","and","x=0.5 $\in$(-1,1)") - introText3=TextMobject("Lets analyse..","!") - introText1.scale(0.8) - introText2.scale(0.7) - introText3.scale(0.9) - introText3.shift(DOWN) - introText1.set_color_by_tex_to_color_map({"above":YELLOW}) - introText2.set_color_by_tex_to_color_map({"$g(x)=\\frac { 1 }{ 1+{ x }^{ 2 } }$":BLUE,"x=0.5 $\in$(-1,1)":YELLOW}) - introText3.set_color_by_tex_to_color_map({"!":GREEN}) - self.play(Write(introText1)) - self.wait(0.5) - self.play(FadeOut(introText1)) - self.play(Write(introText2)) - self.play(FadeIn(introText3)) - self.wait(2) - - -def gety(x,n): - ans=0 - for i in range(0,n+1): - if(i%2==0): - ans+=(math.pow(x,2*i)) - else: - ans-=(math.pow(x,2*i)) - return ans - -def makeSeries(x,points,x_each_unit,y_each_unit): - p=0 - for point in points: - y=gety(x,p) - point.shift(ORIGIN+RIGHT*x_each_unit*p+UP*y_each_unit*y) - p+=1 - -def makeLines(x,numPoints,x_each_unit,y_each_unit): - lines=[0]*numPoints - for i in range(0,numPoints-1): - y=gety(x,i) - y_next=gety(x,i+1) - lines[i]=Line(start=ORIGIN+RIGHT*x_each_unit*i+UP*y_each_unit*y,end=ORIGIN+RIGHT*x_each_unit*(i+1)+UP*y_each_unit*y_next,color=RED) - return lines - -class graphScene(GraphScene,MovingCameraScene): - CONFIG = { - "x_min": -6, - "x_max": 6, - "y_min": -5, - "y_max": 5, - "graph_origin": ORIGIN, - "function_color": RED, - "axes_color": GREEN, - "x_axis_label": "$k$", - "y_axis_label": "$f(\\frac{1}{2})_k$", - "exclude_zero_label": True, - "x_axis_width":7, - "y_axis_height":7 - } - - def setup(self): - GraphScene.setup(self) - MovingCameraScene.setup(self) - - - 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) - sequence=TextMobject("$1$ , $1-(0.5)^2$ , $1-(0.5)^2+(0.5)^4..$") - sequence.set_color(RED) - sequence.scale(0.35) - sequence.to_edge(UP+RIGHT) - formula=TextMobject("$f(x)_{ k }=\sum _{ i=0 }^{ k }{ (-1)^{ i }(x)^{ 2i } } $") - formula.set_color(PURPLE_C) - formula.scale(0.4) - formula.shift(5.3*RIGHT+3*UP) - fLine=Line(start=ORIGIN+x_each_unit*6*LEFT,end=ORIGIN+x_each_unit*6*RIGHT) - fLine.shift(ORIGIN+(4/5)*y_each_unit*UP) - fLineText=TextMobject("$g(0.5)=\\frac { 4 }{ 5 } $") - fLineText.set_color(RED) - fLineText.scale(0.3) - fLineText.shift(UP*1.2*y_each_unit+RIGHT*x_each_unit+4*LEFT) - points=[Dot(radius=0.03,color=BLUE) for i in range(0,6)] - makeSeries(0.5,points,x_each_unit,y_each_unit) - lines=makeLines(0.5,6,x_each_unit,y_each_unit) - - - self.add(sequence) - self.add(formula) - self.setup_axes(animate=True) - self.play(Write(fLine)) - self.add(fLineText) - for p in points: - self.add(p) - for p in range(0,5): - self.play(Write(lines[p])) - self.wait(0.5) - self.camera_frame.save_state() - self.camera_frame.set_width(0.6) - self.play(self.camera_frame.move_to, points[0]) - self.wait(0.4) - self.play(self.camera_frame.move_to, points[1]) - self.wait(0.4) - self.play(self.camera_frame.move_to, points[2]) - self.wait(0.3) - self.play(self.camera_frame.move_to, points[3]) - self.wait(1) - self.play(self.camera_frame.move_to,ORIGIN) - self.camera_frame.set_width(14) - self.wait(1) - - explanation1=TextMobject("Since the series","converges","to") - explanation1.set_color_by_tex_to_color_map({"converges":YELLOW}) - explanation2=TextMobject("$\\frac {4}{5}$") - explanation2.set_color(BLUE) - explanation3=TextMobject("Hence","$\\forall \epsilon>0$,","$\exists k$","such that,") - explanation3.set_color_by_tex_to_color_map({"$\\forall \epsilon>0$":BLUE,"$\exists k$":YELLOW}) - explanation4=TextMobject("$\left| { f\left( \\frac { 1 }{ 2 } \\right) }_{ k }-\\frac { 4 }{ 5 } \\right| <$","$\epsilon$") - explanation4.set_color_by_tex_to_color_map({"$\epsilon$":RED}) - explanation1.scale(0.5) - explanation3.scale(0.5) - explanation1.shift(1.8*DOWN+3.5*RIGHT) - explanation2.shift(2.4*DOWN+3.5*RIGHT) - explanation3.shift(1.8*DOWN+3.5*RIGHT) - explanation4.shift(2.4*DOWN+3.5*RIGHT) - - self.play(Write(explanation1)) - self.play(FadeIn(explanation2)) - self.wait(1) - self.play(FadeOut(explanation1),FadeOut(explanation2)) - self.play(Write(explanation3)) - self.play(Write(explanation4)) - self.wait(2) diff --git a/FSF-2020/calculus/series-and-transformations/Power Series/video5_UniformConvergence.py b/FSF-2020/calculus/series-and-transformations/Power Series/video5_UniformConvergence.py new file mode 100644 index 0000000..e9681aa --- /dev/null +++ b/FSF-2020/calculus/series-and-transformations/Power Series/video5_UniformConvergence.py @@ -0,0 +1,136 @@ +from manimlib.imports import * +import math + +class uniformlyConvergent(Scene): + def construct(self): + introText1=TextMobject("Again consider the","above","example") + introText2=TextMobject("Let","$g(x)=\\frac { 1 }{ 1+{ x }^{ 2 } }$","and","x=0.5 $\in$(-1,1)") + introText3=TextMobject("Lets analyse..","!") + introText1.scale(0.8) + introText2.scale(0.7) + introText3.scale(0.9) + introText3.shift(DOWN) + introText1.set_color_by_tex_to_color_map({"above":YELLOW}) + introText2.set_color_by_tex_to_color_map({"$g(x)=\\frac { 1 }{ 1+{ x }^{ 2 } }$":BLUE,"x=0.5 $\in$(-1,1)":YELLOW}) + introText3.set_color_by_tex_to_color_map({"!":GREEN}) + self.play(Write(introText1)) + self.wait(0.5) + self.play(FadeOut(introText1)) + self.play(Write(introText2)) + self.play(FadeIn(introText3)) + self.wait(2) + + +def gety(x,n): + ans=0 + for i in range(0,n+1): + if(i%2==0): + ans+=(math.pow(x,2*i)) + else: + ans-=(math.pow(x,2*i)) + return ans + +def makeSeries(x,points,x_each_unit,y_each_unit): + p=0 + for point in points: + y=gety(x,p) + point.shift(ORIGIN+RIGHT*x_each_unit*p+UP*y_each_unit*y) + p+=1 + +def makeLines(x,numPoints,x_each_unit,y_each_unit): + lines=[0]*numPoints + for i in range(0,numPoints-1): + y=gety(x,i) + y_next=gety(x,i+1) + lines[i]=Line(start=ORIGIN+RIGHT*x_each_unit*i+UP*y_each_unit*y,end=ORIGIN+RIGHT*x_each_unit*(i+1)+UP*y_each_unit*y_next,color=RED) + return lines + +class graphScene(GraphScene,MovingCameraScene): + CONFIG = { + "x_min": -6, + "x_max": 6, + "y_min": -5, + "y_max": 5, + "graph_origin": ORIGIN, + "function_color": RED, + "axes_color": GREEN, + "x_axis_label": "$k$", + "y_axis_label": "$f(\\frac{1}{2})_k$", + "exclude_zero_label": True, + "x_axis_width":7, + "y_axis_height":7 + } + + def setup(self): + GraphScene.setup(self) + MovingCameraScene.setup(self) + + + 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) + sequence=TextMobject("$1$ , $1-(0.5)^2$ , $1-(0.5)^2+(0.5)^4..$") + sequence.set_color(RED) + sequence.scale(0.35) + sequence.to_edge(UP+RIGHT) + formula=TextMobject("$f(x)_{ k }=\sum _{ i=0 }^{ k }{ (-1)^{ i }(x)^{ 2i } } $") + formula.set_color(PURPLE_C) + formula.scale(0.4) + formula.shift(5.3*RIGHT+3*UP) + fLine=Line(start=ORIGIN+x_each_unit*6*LEFT,end=ORIGIN+x_each_unit*6*RIGHT) + fLine.shift(ORIGIN+(4/5)*y_each_unit*UP) + fLineText=TextMobject("$g(0.5)=\\frac { 4 }{ 5 } $") + fLineText.set_color(RED) + fLineText.scale(0.3) + fLineText.shift(UP*1.2*y_each_unit+RIGHT*x_each_unit+4*LEFT) + points=[Dot(radius=0.03,color=BLUE) for i in range(0,6)] + makeSeries(0.5,points,x_each_unit,y_each_unit) + lines=makeLines(0.5,6,x_each_unit,y_each_unit) + + + self.add(sequence) + self.add(formula) + self.setup_axes(animate=True) + self.play(Write(fLine)) + self.add(fLineText) + for p in points: + self.add(p) + for p in range(0,5): + self.play(Write(lines[p])) + self.wait(0.5) + self.camera_frame.save_state() + self.camera_frame.set_width(0.6) + self.play(self.camera_frame.move_to, points[0]) + self.wait(0.4) + self.play(self.camera_frame.move_to, points[1]) + self.wait(0.4) + self.play(self.camera_frame.move_to, points[2]) + self.wait(0.3) + self.play(self.camera_frame.move_to, points[3]) + self.wait(1) + self.play(self.camera_frame.move_to,ORIGIN) + self.camera_frame.set_width(14) + self.wait(1) + + explanation1=TextMobject("Since the series","converges","to") + explanation1.set_color_by_tex_to_color_map({"converges":YELLOW}) + explanation2=TextMobject("$\\frac {4}{5}$") + explanation2.set_color(BLUE) + explanation3=TextMobject("Hence","$\\forall \epsilon>0$,","$\exists k$","such that,") + explanation3.set_color_by_tex_to_color_map({"$\\forall \epsilon>0$":BLUE,"$\exists k$":YELLOW}) + explanation4=TextMobject("$\left| { f\left( \\frac { 1 }{ 2 } \\right) }_{ k }-\\frac { 4 }{ 5 } \\right| <$","$\epsilon$") + explanation4.set_color_by_tex_to_color_map({"$\epsilon$":RED}) + explanation1.scale(0.5) + explanation3.scale(0.5) + explanation1.shift(1.8*DOWN+3.5*RIGHT) + explanation2.shift(2.4*DOWN+3.5*RIGHT) + explanation3.shift(1.8*DOWN+3.5*RIGHT) + explanation4.shift(2.4*DOWN+3.5*RIGHT) + + self.play(Write(explanation1)) + self.play(FadeIn(explanation2)) + self.wait(1) + self.play(FadeOut(explanation1),FadeOut(explanation2)) + self.play(Write(explanation3)) + self.play(Write(explanation4)) + self.wait(2) -- cgit