diff options
Diffstat (limited to 'FSF-2020/calculus/intro-to-calculus/introderivative')
3 files changed, 190 insertions, 0 deletions
diff --git a/FSF-2020/calculus/intro-to-calculus/introderivative/derivative1.py b/FSF-2020/calculus/intro-to-calculus/introderivative/derivative1.py new file mode 100644 index 0000000..79a6fc6 --- /dev/null +++ b/FSF-2020/calculus/intro-to-calculus/introderivative/derivative1.py @@ -0,0 +1,55 @@ +from manimlib.imports import * +class derivative1(GraphScene, Scene): + def setup(self): + GraphScene.setup(self) + CONFIG = { + "y_max" : 4, + "y_min" : -2, + "x_max" : 4, + "x_min" : -2, + "y_tick_frequency" : 1, + "x_tick_frequency" : 1, + "axes_color" : WHITE, + "num_graph_anchor_points": 3000, #this is the number of points that graph manim + "graph_origin" : ORIGIN+2*DOWN+4*LEFT, + "x_labeled_nums": list(range(-2,5)), + "y_labeled_nums": list(range(-2,5)), + "x_axis_label":"$x$", + "y_axis_label":r"$f(x)=y= 3-\frac { 3 }{ 2 } x$", + "x_axis_width": 5, + "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) + + text1 = TextMobject("") + text2 = TexMobject("{y}_{2}-{y}_{1}") + text2 = TexMobject("{x}_{2}-{x}_{1}") + text3 = TexMobject(r"m\quad =\frac { { y }_{ 2 }-{ y }_{ 1 } }{ { x }_{ 2 }-{ x }_{ 1 } }").move_to(np.array([3,0,0])) + text4 = TexMobject(r"m\quad =\frac { 3 }{ -2 }").move_to(np.array([3,0,0])) + text5 = TexMobject(r"m\quad =\quad -1.5").move_to(np.array([3,0,0])) + self.setup_axes() + graph_1 = self.get_graph(lambda x : 3-1.5*x, color = GREEN_SCREEN, x_min = -1, x_max = 3) + graph_2 = self.get_graph(lambda x : 3.1-1.5*x, color = ORANGE, x_min = 0, x_max = 2) + dot1 = Dot() + dot2 = SmallDot(self.graph_origin+1.7*RIGHT, color = PINK) + dot3 = SmallDot(self.graph_origin+2.5*UP, color = RED_B) + vec1 = Vector(2.5*DOWN, color = PINK).shift(self.graph_origin+2.5*UP) + vec2 = Vector(1.7*RIGHT, color = RED_B).shift(self.graph_origin) + brace1 = Brace(vec1, LEFT) + brace2 = Brace(vec2, DOWN) + br1text = brace1.get_text(r"${y}_{2}-{y}_{1}$").next_to(brace1, LEFT) + br2text = brace2.get_text(r"${x}_{2}-{x}_{1}$").next_to(brace2, DOWN) + self.play(ShowCreation(graph_1), ShowCreation(dot2), ShowCreation(dot3)) + self.play(MoveAlongPath(dot1, graph_2), ShowCreation(vec1), ShowCreation(vec2), run_time = 3) + self.wait(1) + self.play(ShowCreation(brace1), ShowCreation(brace2)) + self.play(ShowCreation(br1text), ShowCreation(br2text)) + self.wait(2) + self.play(GrowFromCenter(text3)) + self.wait(2.5) + self.play(ReplacementTransform(text3, text4)) + self.wait(2) + self.play(ReplacementTransform(text4, text5)) + self.wait(2) diff --git a/FSF-2020/calculus/intro-to-calculus/introderivative/derivative2.py b/FSF-2020/calculus/intro-to-calculus/introderivative/derivative2.py new file mode 100644 index 0000000..d6aab15 --- /dev/null +++ b/FSF-2020/calculus/intro-to-calculus/introderivative/derivative2.py @@ -0,0 +1,78 @@ +from manimlib.imports import * +class derivative2(GraphScene, MovingCameraScene): + def setup(self): + GraphScene.setup(self) + MovingCameraScene.setup(self) + CONFIG = { + "y_max" : 100, + "y_min" : 0, + "x_max" : 10, + "x_min" : 0, + "y_tick_frequency" : 100, + "x_tick_frequency" : 10, + "axes_color" : WHITE, + "num_graph_anchor_points": 3000, #this is the number of points that graph manim + "graph_origin" : ORIGIN, + "x_labeled_nums": None,#list(range(0,11)), + "y_labeled_nums": None,#list(range(0,101))[::10], + "x_axis_label":"$x$", + "y_axis_label":"$f(x)$", + "x_axis_width": 5, + "y_axis_height": 5, + "start_x" : 2, + "start_dx" : 6, + "df_color" : YELLOW, + "dx_color" : GREEN, + "secant_line_color" : MAROON_B, + "zoomed_camera_frame_starting_position": ORIGIN+2*DOWN+6*LEFT, + } + def construct(self): + self.setup() + self.camera_frame.save_state() + self.graph_origin = ORIGIN+2*DOWN+6*LEFT + self.setup_axes() + graph23 = self.get_graph(lambda x : x**2+7, color = GREEN_SCREEN, x_min = 0, x_max = 10) + graph24 = self.get_graph(lambda x : x**2+7, color = GREEN_SCREEN, x_min = 8, x_max = 2.01) + line_1 = DashedVMobject(Line(np.array([-5,-2,0]), np.array([-5,-1.42,0]))) + textdef = TextMobject("") + text1 = TexMobject("{ x }_{ 0 }").move_to(np.array([-5,-2.2,0])) + text2 = TextMobject("The line becomes tangential to the curve").move_to(self.graph_origin+RIGHT+0.5*UP).scale(0.01) + text3 = TexMobject(r"\frac { df }{ dx } =\frac { f({ x }_{ 0 }+h)-f({ x }_{ 0 }) }{ h-0 }").move_to(2*RIGHT) + text4 = TexMobject(r"\frac { df }{ dx } =\lim _{ h\rightarrow 0 }{ \frac { f({ x }_{ 0 }+h)-f({ x }_{ 0 }) }{ h } }").move_to(2*RIGHT) + squareobj = Square(side_length = 15).move_to(self.graph_origin+RIGHT+0.53*UP) + ss_group = self.get_secant_slope_group( + self.start_x, graph23, + dx = self.start_dx, + dx_label = "h", + df_label = "df", + df_line_color = self.df_color, + dx_line_color = self.dx_color, + secant_line_color = self.secant_line_color, + dot_df_top = True, + dot_dx_start = True, + dot_df_top_label = "Q", + dot_dx_start_label = "P", + secant_line_length = 8 + ) + self.play(ShowCreation(graph23)) + self.wait() + self.play(ShowCreation(ss_group.secant_line)) + self.add(text1) + self.play(ShowCreation(line_1)) + self.wait(3) + self.play(ShowCreation(ss_group.dx_line)) + self.play(ShowCreation(ss_group.dx_label)) + self.play(ShowCreation(ss_group.df_line)) + self.play(Write(ss_group.df_label)) + self.play(ShowCreation(ss_group.dot_df_top), ShowCreation(ss_group.dot_dx_start)) + self.play(ShowCreation(ss_group.dot_df_top_label), ShowCreation(ss_group.dot_dx_start_label)) + self.wait() + self.play(ShowCreation(text3)) + self.wait(2) + self.play(ReplacementTransform(text3, text4)) + self.animate_secant_slope_group_change(ss_group, target_dx = 0.01, run_time = 5) + self.wait(2) + self.play(self.camera_frame.set_width,0.2,self.camera_frame.move_to,squareobj,run_time = 2) + self.wait() + self.play(ShowCreation(text2)) + self.wait(3) diff --git a/FSF-2020/calculus/intro-to-calculus/introderivative/derivative3.py b/FSF-2020/calculus/intro-to-calculus/introderivative/derivative3.py new file mode 100644 index 0000000..ebbacb1 --- /dev/null +++ b/FSF-2020/calculus/intro-to-calculus/introderivative/derivative3.py @@ -0,0 +1,57 @@ +from manimlib.imports import * +class derivative3(GraphScene, Scene): + def setup(self): + Scene.setup(self) + #ZoomedScene.setup(self) + CONFIG = { + "y_max" : 8, + "y_min" : 0, + "x_max" : 11, + "x_min" : 0, + "y_tick_frequency" : 1, + "x_tick_frequency" : 1, + "axes_color" : WHITE, + "num_graph_anchor_points": 3000, #this is the number of points that graph manim + "graph_origin" : ORIGIN+3*DOWN+6.5*LEFT, + "x_labeled_nums": list(range(0,12))[::1], + "y_labeled_nums": list(range(0,9))[::1], + "x_axis_label":"$t$", + "y_axis_label":"$s$", + "x_axis_width": 5, + "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) + + self.setup_axes() + graph_1 = self.get_graph(lambda x : -(x-2)**2+4, color = GOLD_A, x_min = 0, x_max = 1.5) + graph_2 = self.get_graph(lambda x : 1*x+2.25, color = GOLD_A, x_min = 1.5, x_max = 5) + graph_3 = self.get_graph(lambda x : 7.25, color = GOLD_A, x_min = 5, x_max = 8) + graph_4 = self.get_graph(lambda x : -3.625*x + 36.25, color = GOLD_A, x_min = 8, x_max = 10) + + self.y_max = 5 + self.x_max = 10 + self.x_min = 0 + self.y_min = -5 + self.x_labeled_nums = list(range(0,11)) + self.y_labeled_nums = list(range(-5,6))[::1] + self.x_axis_label = r"$t$" + self.y_axis_label = r"$v$" + self.y_tick_frequency = 1 + self.x_tick_frequency = 1 + self.graph_origin = ORIGIN+1*RIGHT + self.setup_axes() + graph_5 = self.get_graph(lambda x : 2*(x-2)+4, color = GREEN_SCREEN, x_min = 0, x_max = 1.5) + graph_6 = self.get_graph(lambda x : 3, color = GREEN_SCREEN, x_min = 1.5, x_max = 5) + graph_7 = self.get_graph(lambda x : 0, color = GREEN_SCREEN, x_min = 5, x_max = 8) + graph_8 = self.get_graph(lambda x : -3.625, color = GREEN_SCREEN, x_min = 8, x_max = 10) + line1 = DashedVMobject(Line(self.graph_origin+2.5*RIGHT, self.graph_origin+2.5*RIGHT+1.5*UP)) + line2 = DashedVMobject(Line(self.graph_origin+4*RIGHT, self.graph_origin+4*RIGHT+1.835*DOWN)) + self.play(ShowCreation(graph_1), ShowCreation(graph_5), run_time = 3) + self.play(ShowCreation(graph_2), ShowCreation(graph_6), run_time = 3) + self.add(line1) + self.play(ShowCreation(graph_3), ShowCreation(graph_7), run_time = 3) + self.add(line2) + self.play(ShowCreation(graph_4), ShowCreation(graph_8), run_time = 3) + self.wait(3) |