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--- vpde_errata [2020/04/04 21:30]
trinh [Solutions]
+++ vpde_errata [2020/04/30 20:43] (current)
trinh
@@ Line 22: / Line 22: @@
   * PS4 Q4  $dx$  and  $dy$  transposed
   * PS6 Q1. The function  $\sin(x)\exp(-\cos(x^2))$  is indeed not periodic but not for the reasons stated in the solutions. The point here is that  $\cos(x^2)$  is not a periodic function. You can verify this either by checking whether it's possible that  $(x+L)^2 = x^2 + n\pi$  independent of  $x$ , or simply by plotting the  $\cos($ x^2)$ and observing its behaviour, particularly near the origin.
+  * **PS9 Q2:** There is a missing factor of  $p$  on the bottom here. See Lecture 29.
+  * **PS9 Q4:** Looks like axes were doubled here. //(Courtesy RA, HC)//
+  * **PS10 Q2:** Looks like there are a few  $\kappa$ s missing on the right hand side (I count three); **Q3** In the redefinition of the energy (above "So now you are back to...") there is a extra d/dt that should not be there.
 ==== Lectures ====
   * Correction to {{ :ma20223:ma20223-Week6.pdf |lectures 16}} when I wrote "Is  $\exp(\cos x)$  periodic? (No)". Oops. It is periodic. Note that  $\exp(f(x+L)) = \exp(f(x))$ . A similar gaff appears in the solutions of PS6.
+==== Past exams ====
+  * 2017-18 exam Q4d. The index should start from  $n = 1$  once the  $2n+1$  shift is done.

Trinh @ Bath