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**[Lucas' Notes for Lecture 3](/SummerCourseHeatWave.pdf)**
+# Unanswered Questions
+
Below are answers to some questions that came up during the lecture. If anyone remembers other unanswered questions please post them here as well, and hopefully they'll get answered.
-# Heat Equation With Nonperiodic Boundary Conditions
+## Heat Equation With Nonperiodic Boundary Conditions
Suppose instead of having a metal ring we had a metal rod of length $L$, and we kept the ends of the rod at constant temperatures $u_0$ and $u_L$. How might we solve the heat equation in this context?
@@ -67,5 +69,5 @@ In fact, every function of the kind described above does have a Fourier sine exp
## Convergence for not-so-nice Fourier series.
-How do we know that the Fourier series of a square wave or sawtooth function converge?
+How do we know that the Fourier series of a square wave or sawtooth function converges?