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| author | G Sri Harsha | 2020-07-08 13:03:45 +0530 |
|---|---|---|
| committer | GitHub | 2020-07-08 13:03:45 +0530 |
| commit | 1d2d4a240f7df65865237fd0108abf1132263a4f (patch) | |
| tree | bd6b0948a9e525a2ac12c6173dd058db81ec8bae /FSF-2020/calculus/series-and-transformations | |
| parent | 19916e39ad44abf72c9e73f8df1984e11612d3bf (diff) | |
| download | FSF-mathematics-python-code-archive-1d2d4a240f7df65865237fd0108abf1132263a4f.tar.gz FSF-mathematics-python-code-archive-1d2d4a240f7df65865237fd0108abf1132263a4f.tar.bz2 FSF-mathematics-python-code-archive-1d2d4a240f7df65865237fd0108abf1132263a4f.zip | |
implemented changes
Diffstat (limited to 'FSF-2020/calculus/series-and-transformations')
| -rw-r--r-- | FSF-2020/calculus/series-and-transformations/Taylor Series/video2_TaylorExpansionGeneralForm.py | 98 |
1 files changed, 65 insertions, 33 deletions
diff --git a/FSF-2020/calculus/series-and-transformations/Taylor Series/video2_TaylorExpansionGeneralForm.py b/FSF-2020/calculus/series-and-transformations/Taylor Series/video2_TaylorExpansionGeneralForm.py index c177ab4..75f200d 100644 --- a/FSF-2020/calculus/series-and-transformations/Taylor Series/video2_TaylorExpansionGeneralForm.py +++ b/FSF-2020/calculus/series-and-transformations/Taylor Series/video2_TaylorExpansionGeneralForm.py @@ -7,7 +7,7 @@ class intro(Scene): 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=TextMobject("about $x=1$") text.scale(0.7) text.shift(DOWN) @@ -41,7 +41,7 @@ def formFormula(coeff_list,variable_list): return expansion,coeff_list -class graphScene(GraphScene): +class graphScene(GraphScene,MovingCameraScene): CONFIG = { "x_min": -8, "x_max": 8, @@ -55,6 +55,9 @@ class graphScene(GraphScene): "exclude_zero_label": True, "x_labeled_nums": range(-8, 8, 1), } + 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) @@ -62,7 +65,7 @@ class graphScene(GraphScene): equation=TextMobject("$f(x)=$","${ e }^{ -x^{ 2 } }$") equation.scale(0.55) equation.set_color_by_tex_to_color_map({"${ e }^{ -x^{ 2 } }$":RED}) - text=TextMobject("$a=1$") + text=TextMobject("about $x=1$") text.scale(0.55) equation.shift(3.39*UP+5*LEFT) text.shift(3*UP+5*LEFT) @@ -80,7 +83,7 @@ class graphScene(GraphScene): trTextGrup.scale(0.5) trTextGrup.to_corner(UP+RIGHT) self.play(Write(trTextGrup)) - self.setup_axes(animate=True) + self.setup_axes(animate=True,scalee=1) fx=TextMobject("${ e }^{ -x^{ 2 } }$") fx.scale(0.5) @@ -91,29 +94,29 @@ class graphScene(GraphScene): 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) + coeff[0].shift(4.1*y_each_unit*UP+5.15*RIGHT*x_each_unit) + coeff[0].scale(0.3) + coeff[1].shift(4*y_each_unit*UP+5.7*RIGHT*x_each_unit) + coeff[1].scale(0.2) + coeff[2].shift(4*y_each_unit*UP+7.3*RIGHT*x_each_unit) + coeff[2].scale(0.18) 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)] + firstApprox=[self.get_graph(lambda x:math.exp(-1),color=BLUE,x_min=-3,x_max=4)] + secondApprox=[self.get_graph(lambda x:math.exp(-1)-2*(x-1)*math.exp(-1),color=BLUE,x_min=-3,x_max=4), + self.get_graph(lambda x:math.exp(-1)+3*(x-1)*math.exp(-1),color=BLUE,x_min=-3,x_max=4), + self.get_graph(lambda x:math.exp(-1)-4*(x-1)*math.exp(-1),color=BLUE,x_min=-3,x_max=4)] + 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=4,x_min=-3), + 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=4,x_min=-3), + self.get_graph(lambda x:math.exp(-1)-2*(x-1)*math.exp(-1),color=BLUE,x_max=4,x_min=-3), + 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=4,x_min=-3), + 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=4,x_min=-3)] - 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) + firstGraph=self.get_graph(lambda x:math.exp(-1),color=BLUE,x_min=-3,x_max=4) + secondGraph=self.get_graph(lambda x:math.exp(-1)-2*(x-1)*math.exp(-1),color=BLUE,x_min=-3,x_max=4) + 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=4,x_min=-3) bottomText1=TextMobject("Apply","$f(1)=T_{n}(1)$") bottomText2=TextMobject("This gives","$a_{ 0 }=e^{-1}$") @@ -147,16 +150,42 @@ class graphScene(GraphScene): 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) + # 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) + bottomText2.shift(5*RIGHT*x_each_unit+2.5*DOWN*y_each_unit) + bottomText3.shift(5*RIGHT*x_each_unit+2.5*DOWN*y_each_unit) + bottomText4.shift(5*RIGHT*x_each_unit+2.5*DOWN*y_each_unit) + bottomText5.shift(5*RIGHT*x_each_unit+2.5*DOWN*y_each_unit) + bottomText6.shift(5.7*RIGHT*x_each_unit+2.5*DOWN*y_each_unit) + bottomText7.shift(5.7*RIGHT*x_each_unit+2.5*DOWN*y_each_unit) + bottomText8.shift(5.7*RIGHT*x_each_unit+2.5*DOWN*y_each_unit) + + bottomText2.scale(0.7) + bottomText3.scale(0.7) + bottomText4.scale(0.7) + bottomText5.scale(0.7) + bottomText6.scale(0.7) + bottomText7.scale(0.7) + bottomText8.scale(0.7) self.play(Write(bottomText1)) - self.wait(1) + self.wait(0.8) + self.camera_frame.save_state() + self.play(self.camera_frame.set_width, 8, + self.camera_frame.move_to, x_each_unit*UP+x_each_unit*2*RIGHT, + ApplyMethod(trTextGrup.move_to,4*y_each_unit*UP+6.1*RIGHT*x_each_unit), + ApplyMethod(bottomText1.move_to,5.4*RIGHT*x_each_unit+2.5*DOWN*y_each_unit), + ApplyMethod(equation.shift,1.39*DOWN+2*RIGHT+RIGHT*x_each_unit*2), + ApplyMethod(text.shift,1.39*DOWN+2*RIGHT+RIGHT*x_each_unit*2),) + self.play(ApplyMethod(text.scale,0.5),ApplyMethod(equation.scale,0.5),ApplyMethod(bottomText1.scale,0.6),ApplyMethod(trTextGrup.scale,0.7)) + self.play(ApplyMethod(text.shift,0.25*UP)) + self.wait(0.6) + self.play(ShowCreation(firstApprox[0]),ReplacementTransform(bottomText1,bottomText2)) #change coeff in tn(x) self.play(ReplacementTransform(generalized_eq_coeff[0],coeff[0])) @@ -193,10 +222,13 @@ class graphScene(GraphScene): self.wait(2) textFinal=TextMobject("And so on..!") - textFinal.scale(0.7) - textFinal.shift(4.5*RIGHT+2.5*DOWN) + textFinal.scale(0.35) + textFinal.shift(5.7*RIGHT*x_each_unit+2.5*DOWN*y_each_unit) self.play(ReplacementTransform(bottomText8,textFinal)) - self.wait(2.5) + self.wait(1) + self.play(FadeOut(equation),FadeOut(text)) + self.play(self.camera_frame.set_width, 15, + self.camera_frame.move_to, 0) 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) |