Prerequisites/lecture notes for V. Arnold's PDE

Question

I could not understand Lectures on Partial Differential Equations pass the first chapter, even if I have taken a course in pure math PDE (proving that convolving with the heat kernel is actually convergent, mean value property, maximum principle, etc), and another two courses in Lagrangian and Hamiltonian physics.

Arnold's verdict that it's good for undergrad students seems too optimistic. I think one reason for its difficulty is that it has too little explicit calculation and examples. Many statements are like implicit exercises I can't solve.

So what are prerequisites for studying V. Arnold's PDE? Maybe there is a set of lecture notes that expand on this textbook to make it readable, and supply with exercises and solutions?

Answer 1

Vladimir Arnold generally wrote his books at the standard of his own students, who were Russian. Different countries/regions have different standards for what counts as undergraduate-level preparation. Arnold's book would not be amiss in a graduate course on PDEs.

Skimming through the first chapter, Arnold seems to assume that the reader is fairly comfortable with differential geometric language, such as transversality. That is consistent with what I know of his other books as well. I would treat differential geometry/topology as one of the prerequisites for this book.