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Diffstat (limited to 'FSF-2020/series-and-transformations/Taylor Series/script3.py')
| -rw-r--r-- | FSF-2020/series-and-transformations/Taylor Series/script3.py | 111 |
1 files changed, 111 insertions, 0 deletions
diff --git a/FSF-2020/series-and-transformations/Taylor Series/script3.py b/FSF-2020/series-and-transformations/Taylor Series/script3.py new file mode 100644 index 0000000..a2870d4 --- /dev/null +++ b/FSF-2020/series-and-transformations/Taylor Series/script3.py @@ -0,0 +1,111 @@ +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)
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