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)

PS5: Q1 should define the thermal conductivity as k not kappa.

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

Correction to lectures 16 when I wrote “Is $\exp(\cos x)$ periodic? (No)”. Oops. It is periodic. Note that $\exp(f(x+L)) = \exp(f(x))$.