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--- vpde_errata [2020/03/04 09:18]
trinh created
+++ vpde_errata [2020/04/30 20:43] (current)
trinh
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 ====== Errata for the 2019-20' MA20223 materials ======
-===== Typed notes =====
+==== Typed notes ====
-  * The Corollary 8.4 on convex sets should specify that "if every **non-trivial straight line that intersects the interior** of  $\Omega$  intersects  $\partial\Omega$  at two points at most".
+  * The Corollary 8.4 on convex sets should specify that "if every straight line (**that includes a point on the interior of  $\Omega$ **) intersects  $\partial\Omega$  at two points at most".
+  * There were some typos in the derivation of the wave equation in Chap. 10. It should instead look like this:
+{{ ::ma20223:typo2020_03_04.png?nolink&600 |}}
+  * Chap. 12 and the Definition 12.8 of the even extension on p.56 should read  $x\in[0, L]$  instead of  $x\in[0, \pi]$
+  * Example 15.4 should read  $0 < x < \pi$  instead of  $0 < x < 2$ . //(Courtesy DH)//
+  * Eqn (16.7) should have  $\lambda^2$  instead of  $\lambda$  on the equation for  $G$ . //(Courtesy DH)//
+  * Theorem 18.3 should read the initial conditions of  $u(x, 0) = f(x)$  and  $u_t(x, 0) = g(x)$ . //(Courtesy RA)//
+==== Problem sets ====
+  * PS5: Q1 should define the thermal conductivity as k not kappa.
 ==== Solutions ====
   * PS3: Bottom of the first page  $\partial \phi$  should be  $\nabla \phi$
+  * PS3: Index notation needs to be removed from the main solutions in 19-20' delivery since the topic has been moved to the Appendix. Students are still free to use the technique if they learn it (as noted in lectures).
   * 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

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