diff options
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, 0 insertions, 111 deletions
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)
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