diff options
Diffstat (limited to 'FSF-2020/calculus/intro-to-calculus/fundamental-theorem-of-calculus/fundamental1.py')
| -rw-r--r-- | FSF-2020/calculus/intro-to-calculus/fundamental-theorem-of-calculus/fundamental1.py | 72 |
1 files changed, 72 insertions, 0 deletions
diff --git a/FSF-2020/calculus/intro-to-calculus/fundamental-theorem-of-calculus/fundamental1.py b/FSF-2020/calculus/intro-to-calculus/fundamental-theorem-of-calculus/fundamental1.py new file mode 100644 index 0000000..fd40347 --- /dev/null +++ b/FSF-2020/calculus/intro-to-calculus/fundamental-theorem-of-calculus/fundamental1.py @@ -0,0 +1,72 @@ +from manimlib.imports import * + +class funda1(GraphScene, MovingCameraScene): + def setup(self): + MovingCameraScene.setup(self) + GraphScene.setup(self) + CONFIG = { + "y_max": 5, + "x_max": 8, + "x_min": 0, + "y_min": 0, + "x_axis_width": 10, + "y_axis_height": 5, + "init_dx":0.5, + "x_axis_label":"$t$", + "y_axis_label":"$F(x)$", + "graph_origin": ORIGIN+2*DOWN+6*LEFT, + } + def construct(self): + self.setup_axes() + def func(x): + return 0.1*(x)*(x-3)*(x-7)+3 + + graph1 = self.get_graph(func, x_min = 0, x_max = 7) + graph2 = self.get_graph(func, x_min = 5, x_max = 6) + sqr = Square(side_length = 15.0).move_to(np.array([0.5,-1.5,0])) + line1 = self.get_vertical_line_to_graph(1,graph1,DashedLine, color = PINK) + line2 = self.get_vertical_line_to_graph(5,graph1,DashedLine, color = PINK) + line3 = self.get_vertical_line_to_graph(6,graph1,DashedLine, color = PINK) + line4 = self.get_vertical_line_to_graph(5.01,graph1,DashedLine, color = PINK) + t1 = TextMobject("a").next_to(line1, DOWN) + t2 = TextMobject("x").next_to(line2, DOWN) + t3 = TextMobject("x+h").next_to(line3, DOWN) + text1 = TexMobject(r"\int _{ a }^{ x+h }{ f(t)dt }").move_to(np.array([3,2,0])).scale(0.7) + text2 = TexMobject(r"\int _{ a }^{ x }{ f(t)dt }").move_to(np.array([1,2,0])).scale(0.7) + text3 = TexMobject(r"= \int _{ x }^{ x+h }{ f(t)dt }").move_to(np.array([3,2,0])).scale(0.7) + text4 = TexMobject(r"h \rightarrow 0").move_to(np.array([1,-1.5,0])).scale(0.8) + text5 = TexMobject(r"F^{ ' }\left( x \right)=\lim _{ h\rightarrow 0 }{ \frac { f(x).h }{ h } }").move_to(np.array([1,-1.5,0])).scale(0.2) + text6 = TexMobject(r"F^{ ' }\left( x \right)=f(x)").move_to(np.array([1,-1.5,0])).scale(0.2) + minus = TextMobject("-").move_to(np.array([0.2,2,0])) + group = VGroup(line1, line2, line3, t1, t2, t3) + brace1 = Brace(line2, LEFT).scale(0.35) + br1text = brace1.get_text(r"$f(x)$").next_to(brace1, 1.001*LEFT+1*RIGHT).scale(0.1) + brgrp = VGroup(brace1, br1text) + flat_rectangles1 = self.get_riemann_rectangles(self.get_graph(lambda x : 0),dx=self.init_dx,start_color=invert_color(PURPLE),end_color=invert_color(ORANGE)) + riemann_rectangles_list3 = self.get_riemann_rectangles_list(graph1, 8, max_dx=self.init_dx, power_base=2, start_color = GREEN, end_color=GREEN, x_min =1, x_max = 6) + riemann_rectangles_list1 = self.get_riemann_rectangles_list(graph1,8,max_dx=self.init_dx,power_base=2,start_color=PURPLE,end_color=BLUE_A,x_min = 1, x_max = 5) + riemann_rectangles_list2 = self.get_riemann_rectangles_list(graph1,8,max_dx=self.init_dx,power_base=2,start_color=RED,end_color=RED,x_min = 5, x_max = 6) + riemann_rectangles_list4 = self.get_riemann_rectangles_list(graph1,8,max_dx=self.init_dx,power_base=2,start_color=RED,end_color=RED,x_min = 5, x_max = 5.01) + + self.add(graph1) + self.play(ReplacementTransform(flat_rectangles1,riemann_rectangles_list3[7]), ShowCreation(text1)) + self.wait(3) + self.play(ShowCreation(group)) + self.wait(1) + self.play(ReplacementTransform(flat_rectangles1,riemann_rectangles_list2[7]), ReplacementTransform(flat_rectangles1,riemann_rectangles_list1[7])) + self.play(FadeOut(riemann_rectangles_list3[7])) + self.wait(2) + self.play(ApplyMethod(text1.shift, 4*LEFT), ShowCreation(minus), ShowCreation(text2), ShowCreation(text3)) + self.play(FadeOut(riemann_rectangles_list1[7])) + self.wait(3) + self.camera_frame.save_state() + self.play(self.camera_frame.set_width,2.25,self.camera_frame.move_to,sqr,run_time = 2) + self.wait(2) + self.play(ReplacementTransform(riemann_rectangles_list2[7], riemann_rectangles_list4[7]), FadeOut(riemann_rectangles_list2[7]), ReplacementTransform(line3, line4), FadeOut(line3), ShowCreation(text4)) + self.wait(2) + self.play(ShowCreation(brgrp)) + self.wait(2) + self.play(ReplacementTransform(text4, text5)) + self.wait(2) + self.play(ReplacementTransform(text5, text6)) + self.wait(5)
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