Heat equation scenes up to ShowPartialDerivativeSymbols

active_projects/ode/all_part2_scenes.py

@@ -38,6 +38,7 @@ ALL_SCENE_CLASSES = [
     ShowCubeFormation,
     CompareInputsOfGeneralCaseTo1D,
     ContrastXChangesToTChanges,
+    ShowPartialDerivativeSymbols,
     TransitionToTempVsTime,
     ShowNewton,
     ShowCupOfWater,

active_projects/ode/part2/heat_equation.py

@@ -1023,6 +1023,7 @@ class ContrastXChangesToTChanges(TalkThrough1DHeatGraph):
         plane = self.input_plane
         plane_copy = plane.copy()
         plane_copy.set_color(BLUE_E)
+        plane_copy.shift(SMALL_BUFF * 0.5 * OUT)
 
         plane_copy1 = plane_copy.copy()
         plane_copy1.stretch(0.01, 1, about_edge=DOWN)

active_projects/ode/part2/wordy_scenes.py

@@ -11,6 +11,105 @@ class TodaysTargetWrapper(Scene):
         pass
 
 
+class ShowPartialDerivativeSymbols(Scene):
+    def construct(self):
+        t2c = {
+            "{x}": GREEN,
+            "{t}": PINK,
+        }
+        d_derivs, del_derivs = VGroup(*[
+            VGroup(*[
+                TexMobject(
+                    "{" + sym, "T", "\\over", sym, var + "}",
+                    "(", "{x}", ",", "{t}", ")",
+                ).set_color_by_tex_to_color_map(t2c)
+                for var in ("{x}", "{t}")
+            ])
+            for sym in ("d", "\\partial")
+        ])
+        dTdx, dTdt = d_derivs
+        delTdelx, delTdelx = del_derivs
+        dels = VGroup(*it.chain(*[
+            del_deriv.get_parts_by_tex("\\partial")
+            for del_deriv in del_derivs
+        ]))
+
+        dTdx.to_edge(UP)
+        self.play(FadeInFrom(dTdx, DOWN))
+        self.wait()
+        self.play(ShowCreationThenFadeAround(dTdx[3:5]))
+        self.play(ShowCreationThenFadeAround(dTdx[:2]))
+        self.wait()
+
+        dTdt.move_to(dTdx)
+        self.play(
+            dTdx.next_to, dTdt, RIGHT, {"buff": 1.5},
+            dTdx.set_opacity, 0.5,
+            FadeInFromDown(dTdt)
+        )
+        self.wait()
+
+        for m1, m2 in zip(d_derivs, del_derivs):
+            m2.move_to(m1)
+
+        pd_words = TextMobject("Partial derivatives")
+        pd_words.next_to(del_derivs, DOWN, MED_LARGE_BUFF)
+
+        self.play(
+            Write(pd_words),
+            dTdx.set_opacity, 1,
+            run_time=1,
+        )
+        self.wait()
+        self.play(
+            ReplacementTransform(d_derivs, del_derivs)
+        )
+        self.play(
+            LaggedStartMap(
+                ShowCreationThenFadeAround,
+                dels,
+                surrounding_rectangle_config={
+                    "color": BLUE,
+                    "buff": 0.5 * SMALL_BUFF,
+                    "stroke_width": 2,
+                }
+            )
+        )
+        self.wait()
+
+        num_words = VGroup(*[
+            TextMobject(
+                "Change in $T$\\\\caused by {}",
+                "$\\partial$", "${}$".format(var),
+                arg_separator="",
+            ).set_color_by_tex_to_color_map(t2c)
+            for var in ("{x}", "{t}")
+        ])
+        num_words.scale(0.8)
+        for word, deriv in zip(num_words, del_derivs):
+            num = deriv[:2]
+            word.move_to(num, UP)
+            word.to_edge(UP, buff=MED_SMALL_BUFF)
+            deriv.rect = SurroundingRectangle(
+                num,
+                buff=SMALL_BUFF,
+                stroke_width=2,
+            )
+            deriv.rect.mob = num
+            deriv.rect.add_updater(lambda r: r.move_to(r.mob))
+
+        self.play(
+            Write(num_words[1]),
+            VGroup(del_derivs, pd_words).shift, DOWN,
+            ShowCreation(del_derivs[1].rect),
+        )
+        self.play(
+            Write(num_words[0]),
+            ShowCreation(del_derivs[0].rect),
+        )
+        self.wait()
+
+
 class WriteHeatEquation(Scene):
     CONFIG = {
         "tex_mobject_config": {