Latest scenes for Fourier series video

active_projects/diffyq/all_part4_scenes.py

@@ -40,6 +40,13 @@ SCENES_IN_ORDER = [
     YouSaidThisWasEasier,
     AskAboutComplexNotVector,
     SimpleComplexExponentExample,
+    LooseWithLanguage,
+    DemonstrateAddingArrows,
+    TRangingFrom0To1,
+    LabelRotatingVectors,
+    IntegralTrick,
+    SwapIntegralAndSum,
+    FootnoteOnSwappingIntegralAndSum,
 
     # Oldies
     # FourierSeriesIllustraiton,

active_projects/diffyq/part2/fourier_series.py

@@ -97,7 +97,6 @@ class FourierCirclesScene(Scene):
             phase = np.log(coefficient).imag
         vector.rotate(phase, about_point=ORIGIN)
         vector.freq = freq
-        vector.phase = phase
         vector.coefficient = coefficient
         vector.center_func = center_func
         vector.add_updater(self.update_vector)
@@ -105,12 +104,13 @@ class FourierCirclesScene(Scene):
 
     def update_vector(self, vector, dt):
         time = self.get_vector_time()
-        vector.set_angle(
+        coef = vector.coefficient
-            vector.phase + time * vector.freq * TAU
+        freq = vector.freq
-        )
+        phase = np.log(coef).imag
-        vector.shift(
+
-            vector.center_func() - vector.get_start()
+        vector.set_length(abs(coef))
-        )
+        vector.set_angle(phase + time * freq * TAU)
+        vector.shift(vector.center_func() - vector.get_start())
         return vector
 
     def get_circles(self, vectors):

active_projects/diffyq/part4/complex_functions.py

@@ -672,3 +672,32 @@ class SimpleComplexExponentExample(ClarifyInputAndOutput):
         )
         input_line.add_numbers(*range(0, 30, 5))
         return input_line
+
+
+class TRangingFrom0To1(SimpleComplexExponentExample):
+    CONFIG = {
+        "input_space_rect_config": {
+            "width": 6,
+            "height": 2,
+        },
+    }
+
+    def construct(self):
+        self.setup_input_space()
+        self.setup_input_trackers()
+
+        self.play(
+            self.input_tracker.set_value, 1,
+            run_time=10,
+            rate_func=linear
+        )
+
+    def get_input_line(self, rect):
+        result = ClarifyInputAndOutput.get_input_line(self, rect)
+        result.stretch(0.9, 0)
+        result.set_stroke(width=2)
+        for sm in result.get_family():
+            if isinstance(sm, DecimalNumber):
+                sm.stretch(1 / 0.9, 0)
+                sm.set_stroke(width=0)
+        return result

active_projects/diffyq/part4/pi_creature_scenes.py

@@ -156,3 +156,36 @@ class YouSaidThisWasEasier(TeacherStudentsScene):
         )
         self.look_at(self.screen)
         self.wait(3)
+
+
+class LooseWithLanguage(TeacherStudentsScene):
+    def construct(self):
+        terms = VGroup(
+            TextMobject("``Complex number''"),
+            TextMobject("``Vector''"),
+        )
+        colors = [YELLOW, BLUE]
+        for term, color in zip(terms, colors):
+            term.set_color(color)
+
+        terms.scale(1.5)
+        terms.arrange(DOWN, buff=LARGE_BUFF)
+        terms.to_edge(UP)
+        terms.match_x(self.students)
+
+        self.teacher_says(
+            "Loose with\\\\language",
+            bubble_kwargs={"width": 3, "height": 3},
+            run_time=2,
+        )
+        self.play(
+            FadeInFrom(terms[1], DOWN),
+            self.get_student_changes(
+                "thinking", "pondering", "erm",
+                look_at_arg=terms,
+            )
+        )
+        self.play(FadeInFromDown(terms[0]))
+        self.wait()
+        self.play(Swap(*terms))
+        self.wait(3)

active_projects/diffyq/part4/staging.py

@@ -6,7 +6,7 @@ from active_projects.diffyq.part2.wordy_scenes import WriteHeatEquationTemplate
 class FourierSeriesFormula(Scene):
     def construct(self):
         formula = TexMobject(
-            "c_{n} = \\int_0^1 e^{-2\\pi i {n} {t}}f({t})d{t}",
+            "c_{n} = \\int_0^1 e^{-2\\pi i {n} {t}}f({t}){dt}",
             tex_to_color_map={
                 "{n}": RED,
                 "{t}": YELLOW,
@@ -1111,3 +1111,103 @@ class AskAboutComplexNotVector(Scene):
         self.wait()
         self.play(ShowCreationThenFadeAround(i_part))
         self.wait()
+
+
+class SwapIntegralAndSum(Scene):
+    def construct(self):
+        self.perform_swap()
+        self.show_average_of_individual_terms()
+
+    def perform_swap(self):
+        tex_config = {
+            "tex_to_color_map": {
+                "=": WHITE,
+                "\\int_0^1": WHITE,
+                "{t}": PINK,
+                "{dt}": interpolate_color(PINK, WHITE, 0.25),
+                "{\\cdot 1}": YELLOW,
+                "{0}": YELLOW,
+                "{1}": YELLOW,
+                "{2}": YELLOW,
+            },
+        }
+        int_ft = TexMobject(
+            "\\int_0^1 f({t}) {dt}",
+            **tex_config
+        )
+        int_sum = TexMobject(
+            """
+            =
+            \\int_0^1 \\left(
+            \\cdots +
+            c_{\\cdot 1}e^{{\\cdot 1} \\cdot 2\\pi i {t}} +
+            c_{0}e^{{0} \\cdot 2\\pi i {t}} +
+            c_{1}e^{{1} \\cdot 2\\pi i {t}} +
+            c_{2}e^{{2} \\cdot 2\\pi i {t}} +
+            \\cdots
+            \\right){dt}
+            """,
+            **tex_config
+        )
+        sum_int = TexMobject(
+            """
+            = \\cdots +
+            \\int_0^1
+            c_{\\cdot 1}e^{{\\cdot 1} \\cdot 2\\pi i {t}}
+            {dt} +
+            \\int_0^1
+            c_{0}e^{{0} \\cdot 2\\pi i {t}}
+            {dt} +
+            \\int_0^1
+            c_{1}e^{{1} \\cdot 2\\pi i {t}}
+            {dt} +
+            \\int_0^1
+            c_{2}e^{{2} \\cdot 2\\pi i {t}}
+            {dt} +
+            \\cdots
+            """,
+            **tex_config
+        )
+
+        self.fix_minuses(int_sum)
+        self.fix_minuses(sum_int)
+
+        # top_line = VGroup(int_ft, int_sum)
+        # top_line.arrange(RIGHT, buff=SMALL_BUFF)
+        # top_line.set_width(FRAME_WIDTH - 1)
+        # top_line.to_corner(UL)
+
+
+        group = VGroup(int_ft, int_sum, sum_int)
+        group.arrange(
+            DOWN, buff=MED_LARGE_BUFF,
+            aligned_edge=LEFT
+        )
+        group.set_width(FRAME_WIDTH - 1)
+        group.to_corner(UL)
+        int_ft.align_to(int_sum[1], LEFT)
+        int_ft.shift(0.2 * RIGHT)
+
+        self.add(int_ft)
+        self.add(int_sum)
+        self.add(sum_int)
+
+    def show_average_of_individual_terms(self):
+        pass
+
+    #
+    def fix_minuses(self, tex_mob):
+        for mob in tex_mob.get_parts_by_tex("{\\cdot 1}"):
+            minus = TexMobject("-")
+            minus.match_style(mob[0])
+            minus.set_width(
+                3 * mob[0].get_width(),
+                stretch=True,
+            )
+            minus.move_to(mob, LEFT)
+            mob.submobjects[0] = minus
+
+
+class FootnoteOnSwappingIntegralAndSum(Scene):
+    def construct(self):
+        pass