auto-update(nvim): 2025-02-27 20:53:38

documents/by-course/math-6a/course-notes/main.typ

@@ -274,9 +274,11 @@ the directional derivative is zero.
 
 ]
 
-= Midterm 2 review
+= Speedrun
 
-I literally forgot everything...time to cram.
+In this chapter I wrote up notes for the entirety of the course, starting from
+week 1, ending at week 8, because I skipped 80% of the classes up to the
+midterm.
 
 == Vector review
 
@@ -1078,3 +1080,31 @@ ignore it.
 
 Now we just compare our four candidates and find the greatest (or least) for
 optimization!
+
+=== Notes from Week 7 section
+
+We have a function $f : RR^n -> RR$ that is subject to a constraint $g : RR^n -> RR^c$, where $c$ is our number of constraints. It's really a vector of $c$ constraints,
+$
+  g = vec(g_1,g_2,dots.v,g_c)
+$
+
+Idea: define the so-called *Lagrangian* $cal(L) = f + (g,lambda)$.
+
+#theorem[
+  If $f$ and $g$ are "nice" (partials continuous), there are no redundant constraints, and it's not overconstrained ($"Rank" Dif g = c < n$). Then any optimal solution that respects $g = 0$ solves $gradient f = lambda dot Dif g$.
+]
+
+= Lecture #datetime(day: 27, year: 2025, month:2).display()
+
+== Volume
+
+Any 3D shape can be built recursively of atomic objects.
+
+#exercise[
+  Derive formulae for the volume of a pyramid and cone.
+]
+
+Schley what are you doing???
+
+== Signed area and volume
+