this. I was happy with it, I was even surprised that I was happy with it, I expected it to be one of those typical non-sensical physics books. But this one actually have proofs* in it . Do not let the title fool you, it has a lot of stuff in it, it is only "basic" if it compare it to advanced mathematical books on PDE's as opposed to physics books on PDE's.
*)And by "proofs" I mean real proofs, not some hand-waving that is presented in physics books.