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Published draft of eoc/chapter2 for patrons
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Grant Sanderson
parent
97bbed1fb9
commit
075c68bdf9
1 changed files with 126 additions and 20 deletions
146
eoc/chapter2.py
146
eoc/chapter2.py
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@ -969,6 +969,42 @@ class VelocityAtIndividualPointsVsPairs(GraphCarTrajectory):
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self.play(Blink(randy))
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self.dither(2)
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class FirstRealWorld(TeacherStudentsScene):
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def construct(self):
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self.teacher_says("First, the real world.")
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self.change_student_modes(
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"happy", "hooray", "happy"
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)
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self.dither(3)
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class SidestepParadox(Scene):
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def construct(self):
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car = Car()
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car.shift(DOWN)
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show_speedometer = ShowSpeedometer(skip_animations = True)
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speedomoeter = show_speedometer.speedomoeter
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speedomoeter.next_to(car, UP)
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title = TextMobject(
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"Instantaneous", "rate of change"
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)
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title.to_edge(UP)
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cross = TexMobject("\\times")
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cross.replace(title[0], stretch = True)
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cross.set_fill(RED, opacity = 0.8)
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new_words = TextMobject("over a small time")
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new_words.next_to(title[1], DOWN)
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new_words.highlight(TIME_COLOR)
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self.add(title, car)
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self.play(Write(speedomoeter))
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self.dither()
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self.play(Write(cross))
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self.dither()
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self.play(Write(new_words))
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self.dither()
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class CompareTwoVerySimilarTimes(CompareTwoTimes):
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CONFIG = {
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"start_distance" : 20,
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@ -1334,6 +1370,7 @@ class SecantLineToTangentLine(GraphCarTrajectory, DefineTrueDerivative):
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self.remove(self.y_axis_label_mob, self.x_axis_label_mob)
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self.add_derivative_definition(self.y_axis_label_mob)
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self.add_graph()
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self.draw_axes()
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self.show_tangent_line()
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self.best_constant_approximation_around_a_point()
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@ -1404,7 +1441,7 @@ class SecantLineToTangentLine(GraphCarTrajectory, DefineTrueDerivative):
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double_smooth_graph_function,
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animate = False
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)
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self.label_graph(
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self.graph_label = self.label_graph(
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graph, "s(t)",
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proportion = 1,
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direction = DOWN+RIGHT,
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@ -1432,6 +1469,18 @@ class SecantLineToTangentLine(GraphCarTrajectory, DefineTrueDerivative):
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self.add(deriv_def)
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return deriv_def
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def draw_axes(self):
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self.x_axis.remove(self.x_axis_label_mob)
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self.y_axis.remove(self.y_axis_label_mob)
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self.play(Write(
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VGroup(
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self.x_axis, self.y_axis,
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self.graph, self.graph_label
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),
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run_time = 4
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))
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self.dither()
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def show_tangent_line(self):
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self.curr_time = self.start_time
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@ -1443,7 +1492,7 @@ class SecantLineToTangentLine(GraphCarTrajectory, DefineTrueDerivative):
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Transform(ds_dt_group, new_group).update(1)
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self.play(
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UpdateFromAlphaFunc(ds_dt_group, update_ds_dt_group),
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run_time = 8
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run_time = 15
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)
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self.dither()
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def update_as_tangent_line(ds_dt_group, alpha):
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@ -1666,6 +1715,11 @@ class TCubedExample(SecantLineToTangentLine):
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mob.save_state()
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mob.move_to(mob.target)
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nonzero_size = TextMobject("Nonzero size...for now")
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nonzero_size.highlight(TIME_COLOR)
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nonzero_size.next_to(dt, DOWN+2*RIGHT, buff = LARGE_BUFF)
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arrow = Arrow(nonzero_size, dt)
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rhs = TexMobject(
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"\\frac{s(2+dt) - s(2)}{dt}"
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)
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@ -1692,10 +1746,11 @@ class TCubedExample(SecantLineToTangentLine):
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self.play(ShowCreation(v_lines[0]))
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self.dither()
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self.play(
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dt.scale_in_place, 1.2,
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rate_func = there_and_back
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ShowCreation(arrow),
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Write(nonzero_size),
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)
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self.dither(2)
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self.play(*map(FadeOut, [arrow, nonzero_size]))
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self.play(Write(numerator))
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self.play(ShowCreation(v_lines[1]))
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self.dither()
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@ -1734,17 +1789,24 @@ class TCubedExample(SecantLineToTangentLine):
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])
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def brace_for_details(self):
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brace_yourself = TextMobject(
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"(Brace yourself for details)"
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morty = Mortimer()
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morty.next_to(self.rhs, DOWN, buff = LARGE_BUFF)
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self.play(FadeIn(morty))
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self.play(
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morty.change_mode, "hooray",
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morty.look_at, self.rhs
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)
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brace_yourself.next_to(
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self.lhs, DOWN,
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buff = LARGE_BUFF,
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aligned_edge = LEFT
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)
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self.play(FadeIn(brace_yourself))
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self.play(Blink(morty))
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self.dither()
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self.play(FadeOut(brace_yourself))
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self.play(
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morty.change_mode, "sassy",
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morty.look, OUT
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)
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self.play(Blink(morty))
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self.play(morty.change_mode, "pondering")
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self.dither()
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self.play(FadeOut(morty))
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def show_expansion(self):
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expression = TexMobject("""
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@ -1863,6 +1925,11 @@ class TCubedExample(SecantLineToTangentLine):
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new_group = self.get_ds_dt_group(new_dt)
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Transform(group, new_group).update(1)
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self.play(FadeOut(self.vertical_lines))
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self.secant_line_length = 10
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self.play(Transform(
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self.ds_dt_group,
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self.get_ds_dt_group(self.start_dt)
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))
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self.play(
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UpdateFromAlphaFunc(self.ds_dt_group, ds_dt_group_update),
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faders.fade, 0.7,
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@ -1900,13 +1967,23 @@ class TCubedExample(SecantLineToTangentLine):
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Write(approach_text)
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)
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self.dither(2)
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self.secant_line_length = 10
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self.play(Transform(
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self.ds_dt_group,
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self.get_ds_dt_group(self.end_dt)
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))
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self.dither()
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#Ephasize slope
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v_line = self.vertical_lines[0]
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slope_text = TextMobject("Slope = $12$")
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slope_text.highlight(VELOCITY_COLOR)
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slope_text.next_to(v_line.get_end(), LEFT)
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self.play(Write(slope_text))
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self.play(
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self.ds_dt_group.rotate_in_place, np.pi/24,
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rate_func = wiggle
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)
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self.play(ShowCreation(v_line))
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self.dither()
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self.play(FadeOut(v_line))
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self.play(FadeOut(slope_text))
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#Generalize to more t
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twos = [
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self.lhs[6],
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@ -2471,8 +2548,37 @@ class Chapter2PatreonThanks(PatreonThanks):
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]
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}
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class Thumbnail(SecantLineToTangentLine):
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def construct(self):
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self.setup_axes(animate = False)
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self.add_graph()
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self.curr_time = 6
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ds_dt_group = self.get_ds_dt_group(1)
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self.add(ds_dt_group)
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self.remove(self.x_axis_label_mob)
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self.remove(self.y_axis_label_mob)
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VGroup(*self.get_mobjects()).fade(0.4)
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title = TextMobject("Derivative paradox")
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title.scale_to_fit_width(2*SPACE_WIDTH-1)
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title.to_edge(UP)
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title.add_background_rectangle()
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title.gradient_highlight(GREEN, YELLOW)
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randy = Randolph(mode = "confused")
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randy.scale(1.7)
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randy.to_corner(DOWN+LEFT)
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randy.shift(RIGHT)
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deriv = TexMobject("\\frac{ds}{dt}(t)")
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VGroup(*deriv[:2]).highlight(DISTANCE_COLOR)
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VGroup(*deriv[3:5]).highlight(TIME_COLOR)
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deriv.scale(3)
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# deriv.next_to(randy, RIGHT, buff = 2)
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deriv.to_edge(RIGHT, buff = LARGE_BUFF)
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randy.look_at(deriv)
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self.add(title, randy, deriv)
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