Partial Differential Equations

This is a Dover reprint of a book originally published in 1969. As evidenced by its inclusion in the MAA's list of recommendations for undergraduate libraries, it's a good book. At the time of publication, V. Komkov wrote in Mathematical Reviews:

The approach is thoroughly modern. The prerequisites are rather high: at least two semesters of functional analysis plus some prior course in elementary differential equations. On the other hand the reviewer, who has taught a course using this text, found out that students who studied this text have acquired a high level of maturity in this field.

The text blends exposition and some insight into research problems in a lucid manner. This book should be on the shelf of every mathematician working on differential equations.

The prerequisites in question are described in the preface as "the theory of Lebesgue integration" and "the very basic concepts of Banach spaces." The author points out that some familiarity with "classical methods for solving the Laplace equation and the heat equation under the usual boundary conditions" might be useful as motivation.

As always, the Dover edition is fairly priced and well produced.