diff options
Diffstat (limited to 'FSF-2020/calculus/intro-to-calculus/infinite-seq-and-series/taylorseries.py')
| -rw-r--r-- | FSF-2020/calculus/intro-to-calculus/infinite-seq-and-series/taylorseries.py | 67 |
1 files changed, 67 insertions, 0 deletions
diff --git a/FSF-2020/calculus/intro-to-calculus/infinite-seq-and-series/taylorseries.py b/FSF-2020/calculus/intro-to-calculus/infinite-seq-and-series/taylorseries.py new file mode 100644 index 0000000..2e9d423 --- /dev/null +++ b/FSF-2020/calculus/intro-to-calculus/infinite-seq-and-series/taylorseries.py @@ -0,0 +1,67 @@ +from manimlib.imports import * +class conv(GraphScene): + CONFIG = { + "y_max" : 10, + "y_min" : 0, + "x_max" : 5, + "x_min" : -1, + "y_tick_frequency" : 5, + "x_tick_frequency" : 1, + "axes_color" : WHITE, + "num_graph_anchor_points": 3000, + "graph_origin" : ORIGIN+2*DOWN+6*LEFT, + "x_labeled_nums": list(range(0,6)), + "y_labeled_nums": list(range(0,11))[::1], + "x_axis_label":"x", + "y_axis_label":"$f(x)$", + "x_axis_width": 9, + "y_axis_height": 5, + } + def construct(self): + XTD = self.x_axis_width/(self.x_max - self.x_min) + YTD = self.y_axis_height/(self.y_max - self.y_min) + texta = TexMobject(r"\text{Expressing }", r"{e}^{x}", r"\text{ as its Taylor series}") + self.play(FadeIn(texta)) + self.wait(3) + self.play(FadeOut(texta)) + self.setup_axes() + graph1 = self.get_graph(lambda x : (np.e)**x, x_min = -1, x_max = 5, color = PINK) + graph2 = self.get_graph(lambda x : 1+x, x_min = -1, x_max = 5, color = GREEN_SCREEN) + graph3 = self.get_graph(lambda x : 1+(x)+(x**2)/2, x_min = -1, x_max = 5, color = GREEN_SCREEN) + graph4 = self.get_graph(lambda x : 1+(x)+(x**2)/2+(x**3)/6, x_min = -1, x_max = 5, color = GREEN_SCREEN) + graph5 = self.get_graph(lambda x : 1+(x)+(x**2)/2+(x**3)/6+(x**4)/24, x_min = -1, x_max = 5, color = GREEN_SCREEN) + graph6 = self.get_graph(lambda x : 1+(x)+(x**2)/2+(x**3)/6+(x**4)/24+(x**5)/120, x_min = -1, x_max = 5, color = GREEN_SCREEN) + graph7 = self.get_graph(lambda x : 1+(x)+(x**2)/2+(x**3)/6+(x**4)/24+(x**5)/120+(x**6)/720, x_min = -1, x_max = 5, color = GREEN_SCREEN) + graph8 = self.get_graph(lambda x : 1+(x)+(x**2)/2+(x**3)/6+(x**4)/24+(x**5)/120+(x**6)/720+(x**7)/5040, x_min = -1, x_max = 5, color = GREEN_SCREEN) + texta = TexMobject(r"{e}^{x}").move_to(self.graph_origin+ 1*RIGHT+2*UP) + textb = TexMobject(r"\therefore {e}^{x}=").move_to(3.5*LEFT+0.5*DOWN) + text1 = TexMobject(r"1+x").move_to(4*RIGHT) + text2 = TexMobject(r"+\frac{{x}^{2}}{2!}").move_to(4*RIGHT) + text3 = TexMobject(r"+\frac{{x}^{3}}{3!}").move_to(4*RIGHT) + text4 = TexMobject(r"+\frac{{x}^{4}}{4!}").move_to(4*RIGHT) + text5 = TexMobject(r"+\frac{{x}^{5}}{5!}").move_to(4*RIGHT) + text6 = TexMobject(r"+\frac{{x}^{6}}{6!}").move_to(4*RIGHT) + text7 = TexMobject(r"+\frac{{x}^{7}}{7!}+...").move_to(4.5*RIGHT) + + self.play(ShowCreation(texta)) + self.play(ShowCreation(graph1)) + self.wait(3) + self.play(FadeOut(texta)) + self.play(ShowCreation(graph2)) + self.play(ShowCreation(text1)) + self.wait(3) + self.play(ReplacementTransform(graph2, graph3), ApplyMethod(text1.shift, 1*LEFT), ShowCreation(text2)) + self.wait(3) + self.play(ReplacementTransform(graph3, graph4), ApplyMethod(text1.shift, 1*LEFT), ApplyMethod(text2.shift, 1*LEFT), ShowCreation(text3)) + self.wait(3) + self.play(ReplacementTransform(graph4, graph5), ApplyMethod(text1.shift, 1*LEFT), ApplyMethod(text2.shift, 1*LEFT), ApplyMethod(text3.shift, 1*LEFT), ShowCreation(text4)) + self.wait(3) + self.play(ReplacementTransform(graph5, graph6), ApplyMethod(text1.shift, 1*LEFT), ApplyMethod(text2.shift, 1*LEFT), ApplyMethod(text3.shift, 1*LEFT), ApplyMethod(text4.shift, 1*LEFT), ShowCreation(text5)) + self.wait(3) + self.play(ReplacementTransform(graph6, graph7), ApplyMethod(text1.shift, 1*LEFT), ApplyMethod(text2.shift, 1*LEFT), ApplyMethod(text3.shift, 1*LEFT), ApplyMethod(text4.shift, 1*LEFT), ApplyMethod(text5.shift, 1*LEFT), ShowCreation(text6)) + self.wait(3) + self.play(ReplacementTransform(graph7, graph8),ApplyMethod(text1.shift, 1*LEFT), ApplyMethod(text2.shift, 1*LEFT), ApplyMethod(text3.shift, 1*LEFT), ApplyMethod(text4.shift, 1*LEFT), ApplyMethod(text5.shift, 1*LEFT), ApplyMethod(text6.shift, 1*LEFT), ShowCreation(text7)) + self.wait(3) + grp = VGroup(text1, text2, text3, text4, text5, text6, text7) + self.play(ApplyMethod(grp.shift, 0.5*DOWN), FadeIn(textb)) + self.wait(5)
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