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”.

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