1. First-order equations

Reading guide

In Section 1, we present in detail the case of a PDE that directly generalizes Cauchy-Lipschitz theory. The case of Hamiltonian dynamics will also be present in several sections, as one of the red threads of our presentation.

Section 2 introduces the Schrödinger equation both for its own sake and because it has historically been a driving force behind the development of functional analysis.

Sections 3, 4 and 5 introduce the more classical, second-order elliptic and parabolic operators, with a view to dealing with significantly more macroscopic issues.

The wave equation, the subject of Section 1 of