====== Errata for the 2019-20' MA20223 materials ======

==== Typed notes ====

  * 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.