Graduate Level PDE Book?

Question

I'm looking for a good textbook on PDE's for a first course at the graduate level of applied mathematics. Specifically I need one that:

Introduces theory and applications of partial differential equations, including existence, uniqueness, stability, regularity, and solution construction and approximation procedures.

I need one that's primary focus is PDE's, and not just having a few chapters on them. Thank you for any help you can offer.

Answer 1

Cheap? That's gonna be hard. Some of the better books that I recommend:

More introductory level:

Robert McOwen, Partial Differential Equations: Methods and Applications

Slightly more advanced:

Fritz John, Partial Differential Equations (Volume 1 of the Springer-Verlag applied mathematical sciences series)

More about theory:

Lawrence Evans, Partial Differential Equations

Cheaper, slightly outdated:

Farlow, PDE for Scientists and Engineers (There is a Dover version out there that you can pick up for < 20 bucks).

Numerical:

Tveito and Winther, Introduction to Partial Differentail Equations: a Computational Approach

The problem is that most Good Books for theory of PDEs (ones that talk about existence, uniqueness, regularity) do not talk too much about numerical and approximation methods, and vice versa.