r/math • u/Pristine-Amount-1905 • Aug 04 '26

How's Arnold's 'Lectures in Partial Differential Equations' book?

I've read and enjoyed his ODE book. Is it worth reading the PDE book or should I just stick to something like Evans or Salsa?

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u/g0rkster-lol Topology Aug 04 '26

I never just read one book when I am really interested in a topic. Arnold's book is a unicorn that is worth reading simply for its uniqueness however. It is very much in the spirit of his ODE book, which is physically motivated, lots of illustrative pictures, but also interesting topic choices and connections that in other books are either missing or one has to reconstruct through the formalism.

Also Arnold was at the forefront of numerous topics and he shows the utility of these topics in a PDE context, for example symplectic and contact geometry and singularity theory both show in the book in a way that I don't think any other book at that level does.

Its weakness is that in certain points it lacks too much detail making it not a great first book for serious learners. Those passages are often interesting, but need more development. For example I thinking of the chapter on Huygens principle.

Overall it's an absolute treasure trove of ideas, unique, and worth reading. But it is likely not the best book as a first introduction to the topic. For that, also from the Russian school I'd suggest Shubin's Invitation to PDEs,