Ordinary/Partial Diff Eq books? And any introductions to Green's functions?

[MissSilvy]

I took a class on ODEs and have used them in my physics classes fairly often, but I would like a book that I could go back and learn more about differential equations. Tenenbaum and Braun have been suggested but there are quite a lot of books out there, searching has

The second part is that I have an eye on eventually working up to Green's functions (before I get smashed by Jackson's Electrodynamics) and would like a book (or a few) that can get me from my current level of knowledge to there. Despite searching and talking to people that have done Jackson, I can't even seem to figure out what prior knowledge Green's functions even require. Any resources at all would be appreciated.

 

[Herr Malus]

Depends on what you want to learn about ODE's, if it's the theory behind it then all I can suggest is Lebovitz's book (my only real exposure). On the plus side, it's free and he updates it as he teaches. He's also a pretty fantastic teacher in my opinion. If you want pure application then basically take your pick. Boas has a decent enough set of sections on them, while for plug and chug problems you could take "Polking, Boggess and Arnold, Differential Equations with Boundary Value Problems, second edition, Pearson Prentice-Hall". Both these books have solutions manuals easily available online.

Now, about Green's Functions. Boas has, again in my opinion, a very sloppy introduction to the topic in her book and it is certainly not at the level of Jackson. But if you already own Boas it can't hurt to flip through. I've heard Weber is decent, but I've never used it. If you want the actual math theory behind Green's Functions (as Integral Kernel and whatnot) then I got my introduction from Strauss. If you're not familiar with math proofs then Strauss' intro probably won't work for you.