Problem book for differential equations?? Are there?

Question

Is there a problem book which gathers the most relevant exercises in differential equations (historical problems, eventually providing counter-examples for some theorems and properties if some conditions are neglected)? I'm interested in both ODE and PDE.

Thanks a lot!

Answer 1

I recently visited Springer press and found this title Principles of Partial Differential Equations. It belongs to a series called Problem Books in Mathematics. https://www.amazon.com/Principles-Partial-Differential-Equations-Mathematics/dp/1441910956

According to the the publisher:

This concise book covers the classical tools of PDE theory used in today's science and engineering: characteristics, the wave propagation, the Fourier method, distributions, Sobolev spaces, fundamental solutions, and Green's functions. The approach is problem-oriented, giving the reader an opportunity to master solution techniques. The theoretical part is rigorous and with important details presented with care. Hints are provided to help the reader restore the arguments to their full rigor. Many examples from physics are intended to keep the book intuitive and to illustrate the applied nature of the subject. The book is useful for a higher-level undergraduate course and for self-study.