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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.
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First-order equations
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The Ultimate Scientific and Technical Reference