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:

• 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