Simone Calogero: Ordinary and Partial Differential Equations: An Introduction.

Version with hyperlinks suitable for screen reading (pdf). Requires Acrobate Reader (or similar)
Version without hyperlinks suitable for printing (pdf)

Remark: We skip the sections, proofs, etc., marked with (•)

Errata in the lecture notes (updated 21 Nov): pdf

Additional solutions of some selected exercises: pdf

Jupiter notebook with some relevant Python codes (ipynb)

Online resources (optional):

Several well written notes on ODEs and PDEs can be found here

A general introduction to ODEs (video)

Lagrangian ODEs and the variational principle (video)

Chaotic dynamics and the Lorenz attractor (video)

The trillion dollar PDE (video)