RefreshOnDerivativeDefinition in eoc7

animation/simple_animations.py

@@ -178,6 +178,26 @@ class SmoothedVectorizedHomotopy(Homotopy):
         submob.make_smooth()
 
 
+class ApplyWave(Homotopy):
+    CONFIG = {
+        "direction" : DOWN,
+        "amplitude" : 0.2,
+        "run_time" : 1,
+    }
+    def __init__(self, mobject, **kwargs):
+        digest_config(self, kwargs, locals())
+        left_x = mobject.get_left()[0]
+        right_x = mobject.get_right()[0]
+        vect = self.amplitude*self.direction
+        def homotopy(x, y, z, t):
+            start_point = np.array([x, y, z])
+            alpha = (x-left_x)/(right_x-left_x)
+            power = np.exp(2*(alpha-0.5))
+            nudge = there_and_back(t**power)
+            return np.array([x, y, z]) + nudge*vect
+        Homotopy.__init__(self, homotopy, mobject, **kwargs)
+
+
 class PhaseFlow(Animation):
     CONFIG = {
         "virtual_time" : 1,

eoc/chapter7.py

@@ -0,0 +1,350 @@
+from helpers import *
+
+from mobject.tex_mobject import TexMobject
+from mobject import Mobject
+from mobject.image_mobject import ImageMobject
+from mobject.vectorized_mobject import *
+
+from animation.animation import Animation
+from animation.transform import *
+from animation.simple_animations import *
+from animation.playground import *
+from topics.geometry import *
+from topics.characters import *
+from topics.functions import *
+from topics.fractals import *
+from topics.number_line import *
+from topics.combinatorics import *
+from topics.numerals import *
+from topics.three_dimensions import *
+from topics.objects import *
+from scene import Scene
+from scene.zoomed_scene import ZoomedScene
+from scene.reconfigurable_scene import ReconfigurableScene
+from camera import Camera
+from mobject.svg_mobject import *
+from mobject.tex_mobject import *
+
+from topics.common_scenes import OpeningQuote, PatreonThanks
+
+from eoc.graph_scene import *
+
+class Chapter7OpeningQuote(OpeningQuote):
+    CONFIG = {
+        "quote" : [
+            " Calculus required ",
+            "continuity",
+            ", and ",
+            "continuity ",
+            "was supposed to require the ",
+            "infinitely little",
+            "; but nobody could discover what the ",
+            "infinitely little",
+            " might be. ",
+        ],
+        "quote_arg_separator" : "",
+        "highlighted_quote_terms" : {
+            "continuity" : BLUE,
+            "infinitely" : GREEN,
+        },
+        "author" : "Bertrand Russell",
+    }
+
+class ThisVideo(TeacherStudentsScene):
+    def construct(self):
+        series = VideoSeries()
+        series.to_edge(UP)
+        deriv_videos = VGroup(*series[1:6])
+        this_video = series[6]
+        integral_videos = VGroup(*series[7:9])
+        video_groups = [deriv_videos, this_video, integral_videos]
+
+        braces = map(Brace, video_groups)
+        deriv_brace, this_brace, integral_brace = braces
+
+        tex_mobs = [
+            TexMobject(*args)
+            for args in [
+                ("{df ", " \\over \\, ", " dx}"),
+                ("\\lim_{h \\to 0}",),
+                ("\\int ", "f(x)", "\\,dx"),
+            ]
+        ]
+        deriv_tex, this_tex, integral_tex = tex_mobs
+        for tex_mob, brace in zip(tex_mobs, braces):
+            tex_mob.highlight_by_tex("f", GREEN)
+            tex_mob.highlight_by_tex("dx", YELLOW)
+            tex_mob.next_to(brace, DOWN)
+        integral_tex.shift(LARGE_BUFF*RIGHT)
+
+        lim_to_deriv_arrow = Arrow(this_tex, deriv_tex, color = WHITE)
+
+        self.add(series)
+        for index in 0, 2:
+            videos = video_groups[index]
+            brace = braces[index]
+            tex_mob = tex_mobs[index]
+            self.play(ApplyWave(
+                videos,
+                apply_function_kwargs = {"maintain_smoothness" : False}
+            ))
+            self.play(
+                GrowFromCenter(brace),
+                Write(tex_mob, run_time = 2)
+            )
+            self.dither()
+        self.play(self.get_teacher().change_mode, "raise_right_hand")
+        self.play(
+            this_video.highlight, YELLOW,
+            GrowFromCenter(this_brace)
+        )
+        self.play(Write(this_tex))
+        self.dither()
+        self.play(ShowCreation(lim_to_deriv_arrow))
+        self.change_student_modes(*["happy"]*3)
+        self.dither(2)
+
+class ApproachWordToLim(PiCreatureScene):
+    CONFIG = {
+        "dx_color" : GREEN
+    }
+    def construct(self):
+        limit_expression = self.get_limit_expression()
+        limit_expression.next_to(
+            self.pi_creature, LEFT, aligned_edge = UP
+        )
+
+        evaluated_expressions = self.get_evaluated_expressions()
+        evaluated_expressions.to_edge(UP)
+        brace = Brace(evaluated_expressions[0][-1], DOWN)
+        question = TextMobject("What does this ``approach''?")
+        question.next_to(brace, DOWN)
+
+        expression = evaluated_expressions[0]
+        self.add(expression, brace, question)
+        self.change_mode("raise_right_hand")
+        for next_expression in evaluated_expressions[1:]:
+            next_expression.move_to(expression, RIGHT)
+            self.play(Transform(expression, next_expression))
+            self.dither(0.5)
+        self.play(
+            Write(limit_expression),
+            self.pi_creature.change_mode, "pondering"
+        )
+        self.play(Indicate(limit_expression[0]))
+        self.dither(2)
+
+    def get_limit_expression(self):
+        lim = TexMobject("\\lim_", "{dx", " \\to 0}")
+        lim.highlight_by_tex("dx", self.dx_color)
+        ratio = self.get_expression("dx")
+        ratio.next_to(lim, RIGHT)
+        limit_expression = VGroup(lim, ratio)
+        return limit_expression
+
+    def get_evaluated_expressions(self):
+        result = VGroup()
+        for num_zeros in range(1, 6):
+            dx_str = "0." + "0"*num_zeros + "1"
+            expression = self.get_expression(dx_str)            
+            dx = float(dx_str)
+            ratio = ((2+dx)**3-2**3)/dx
+            ratio_mob = TexMobject("%.6f\\dots"%ratio)
+            group = VGroup(expression, TexMobject("="), ratio_mob)
+            group.arrange_submobjects(RIGHT)
+            result.add(group)
+        return result
+
+    def get_expression(self, dx):
+        result = TexMobject(
+            "{(2 + ", str(dx), ")^3 - 2^3 \\over", str(dx)
+        )
+        result.highlight_by_tex(dx, self.dx_color)
+        return result
+
+class RefreshOnDerivativeDefinition(GraphScene):
+    CONFIG = {
+        "start_x" : 2,
+        "dx" : 0.7,
+        "df_color" : YELLOW,
+        "dx_color" : GREEN,
+        "secant_line_color" : MAROON_B,
+    }
+    def construct(self):
+        self.setup_axes()
+        def func(x):
+            u = 0.3*x - 1.5
+            return -u**3 + 5*u + 7
+        graph = self.get_graph(func)
+        graph_label = self.get_graph_label(graph)
+        start_x_v_line, nudged_x_v_line = [
+            self.get_vertical_line_to_graph(
+                self.start_x + nudge, graph, 
+                line_class = DashedLine,
+                color = RED
+            )
+            for nudge in 0, self.dx
+        ]
+        ss_group = self.get_secant_slope_group(
+            self.start_x, graph,
+            dx = self.dx,
+            dx_label = "dx",
+            df_label = "df",
+            df_line_color = self.df_color,
+            dx_line_color = self.dx_color,
+            secant_line_color = self.secant_line_color,
+        )
+        derivative = TexMobject(
+            "{df", "\\over \\,", "dx}", "(", str(self.start_x), ")"
+        )
+        derivative.highlight_by_tex("df", self.df_color)
+        derivative.highlight_by_tex("dx", self.dx_color)
+        derivative.highlight_by_tex(str(self.start_x), RED)
+        df = derivative.get_part_by_tex("df")
+        dx = derivative.get_part_by_tex("dx")
+        input_x = derivative.get_part_by_tex(str(self.start_x))
+        derivative.move_to(self.coords_to_point(7, 4))
+        deriv_brace = Brace(derivative)
+        dx_to_0 = TexMobject("dx", "\\to 0")
+        dx_to_0.highlight_by_tex("dx", self.dx_color)
+        dx_to_0.next_to(deriv_brace, DOWN)
+
+        #Introduce graph
+        self.play(ShowCreation(graph))
+        self.play(Write(graph_label, run_time = 1))
+        self.play(Write(derivative))
+        self.dither()
+        input_copy = input_x.copy()
+        self.play(
+            input_copy.next_to, 
+            self.coords_to_point(self.start_x, 0),
+            DOWN
+        )
+        self.play(ShowCreation(start_x_v_line))
+        self.dither()
+
+        #ss_group_development
+        self.play(
+            ShowCreation(ss_group.dx_line),
+            ShowCreation(ss_group.dx_label),
+        )
+        self.dither()
+        self.play(ShowCreation(ss_group.df_line))
+        self.play(Write(ss_group.df_label))
+        self.dither(2)
+        self.play(
+            ReplacementTransform(ss_group.dx_label.copy(), dx),
+            ReplacementTransform(ss_group.df_label.copy(), df),
+            run_time = 2
+        )
+        self.play(ShowCreation(ss_group.secant_line))
+        self.dither()
+
+        #Let dx approach 0
+        self.play(
+            GrowFromCenter(deriv_brace),
+            Write(dx_to_0),
+        )
+        self.animate_secant_slope_group_change(
+            ss_group,
+            target_dx = 0.01,
+            run_time = 5,
+        )
+        self.dither()
+
+        #Write out fuller limit
+        new_deriv = TexMobject(
+            "{f", "(", str(self.start_x), "+", "dx", ")", 
+            "-", "f", "(", str(self.start_x), ")",
+            "\\over \\,", "dx"
+        )
+        new_deriv.highlight_by_tex("dx", self.dx_color)
+        new_deriv.highlight_by_tex("f", self.df_color)
+        new_deriv.highlight_by_tex(str(self.start_x), RED)
+        deriv_to_new_deriv = dict([
+            (
+                VGroup(derivative.get_part_by_tex(s)), 
+                VGroup(*new_deriv.get_parts_by_tex(s))
+            )
+            for s in ["f", "over", "dx", "(", str(self.start_x), ")"]
+        ])
+        covered_new_deriv_parts = list(it.chain(*deriv_to_new_deriv.values()))
+        uncovered_new_deriv_parts = filter(
+            lambda part : part not in covered_new_deriv_parts,
+            new_deriv
+        )
+        new_deriv.move_to(derivative)
+        new_brace = Brace(new_deriv, DOWN)
+
+        self.animate_secant_slope_group_change(
+            ss_group,
+            target_dx = self.dx,
+            run_time = 2
+        )
+        self.play(ShowCreation(nudged_x_v_line))
+        self.dither()
+        self.play(*[
+            ReplacementTransform(*pair, run_time = 2)
+            for pair in deriv_to_new_deriv.items()
+        ]+[
+            Transform(deriv_brace, new_brace),
+            dx_to_0.next_to, new_brace, DOWN
+        ])
+        self.play(Write(VGroup(*uncovered_new_deriv_parts), run_time = 2))
+        self.dither()
+
+        #Introduce limit notation
+        lim = TexMobject("\\lim").scale(1.3)
+        dx_to_0.generate_target()
+        dx_to_0.target.scale(0.7)
+        dx_to_0.target.next_to(lim, DOWN, buff = SMALL_BUFF)
+        lim_group = VGroup(lim, dx_to_0.target)
+        lim_group.move_to(new_deriv, LEFT)
+
+        self.play(
+            ReplacementTransform(deriv_brace, lim),
+            MoveToTarget(dx_to_0),
+            new_deriv.next_to, lim_group, RIGHT,
+            run_time = 2
+        )
+        for sf, color in (1.2, YELLOW), (1/1.2, WHITE):
+            self.play(
+                lim.scale_in_place, sf,
+                lim.highlight, color,
+                submobject_mode = "lagged_start"
+            )
+        self.dither(2)
+        self.animate_secant_slope_group_change(
+            ss_group, target_dx = 0.01,
+            run_time = 5,
+            added_anims = [
+                Transform(nudged_x_v_line, start_x_v_line, run_time = 5)
+            ]
+        )
+        self.dither(2)
+
+
+
+
+
+
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+

eoc/graph_scene.py

@@ -251,6 +251,7 @@ class GraphScene(Scene):
             df_label, (if applicable)
             secant_line, (if applicable)
         )
+        with attributes of those names.
         """
         kwargs = locals()
         kwargs.pop("self")

mobject/tex_mobject.py

@@ -110,28 +110,23 @@ class TexMobject(SVGMobject):
         self.submobjects = new_submobjects
         return self
 
-    def get_part_by_tex(self, tex, substring = True, return_all_parts = False):
+    def get_parts_by_tex(self, tex, substring = True):
         def test(tex1, tex2):
             return tex1 == tex2 or (substring and tex1 in tex2)
+
         if not hasattr(self, "expression_parts"):
             if test(tex, self.get_tex_string()):
                 return self
-            return None
-        all_parts = [
+            return []
+        return [
             submob
             for submob, part_tex in zip(self.split(), self.expression_parts)
             if test(tex, part_tex)
         ]
-        if return_all_parts:
-            return all_parts
-        else:
-            if len(all_parts) > 0:
-                return all_parts[0]
-            else:
-                return None
 
-    def get_parts_by_tex(self, tex, **kwargs):
-        return self.get_part_by_tex(tex, return_all_parts = True, **kwargs)
+    def get_part_by_tex(self, tex, **kwargs):
+        all_parts = self.get_parts_by_tex(tex, **kwargs)
+        return all_parts[0] if all_parts else None
 
     def highlight_by_tex(self, tex, color, **kwargs):
         parts_to_color = self.get_parts_by_tex(tex, **kwargs)

topics/common_scenes.py

@@ -18,6 +18,7 @@ class OpeningQuote(Scene):
             """that contains all the 
             germs of generality."""
         ],
+        "quote_arg_separator" : " ",
         "highlighted_quote_terms" : {
             "special case" : BLUE
         },
@@ -25,7 +26,7 @@ class OpeningQuote(Scene):
         "fade_in_kwargs" : {
             "submobject_mode" : "lagged_start",
             "rate_func" : None,
-            "lag_factor" : 3,
+            "lag_factor" : 4,
             "run_time" : 5,
         },
     }
@@ -39,14 +40,15 @@ class OpeningQuote(Scene):
         self.dither()
 
     def get_quote(self, max_width = 2*SPACE_WIDTH-1):
+        text_mobject_kwargs = {
+            "alignment" : "",
+            "arg_separator" : self.quote_arg_separator,
+        }
         if isinstance(self.quote, str):
-            quote = TextMobject(
-                "``%s''"%self.quote.strip(),
-                alignment = "",
-            )
+            quote = TextMobject("``%s''"%self.quote.strip(), **text_mobject_kwargs)
         else:
             words = ["``"] + list(self.quote) + ["''"]
-            quote = TextMobject(*words, alignment = "")
+            quote = TextMobject(*words, **text_mobject_kwargs)
             ##TODO, make less hacky
             quote[0].shift(0.2*RIGHT)
             quote[-1].shift(0.2*LEFT)