Required Texts

Partial Differential Equations, Methods and Applications by Robert McOwen, Prentice Hall, Inc., New Jersey 1996 (MCOWEN)
An excellent presentation of the theoretical side of the subject with an interspersing of examples and methods. Tends to emphasize the properties of solutions of PDEs as they flow from smoothes/non-smoothness features. For this course only Chapters 1-5 are covered. The remainder of the book is an introduction to research questions in PDEs and would be excellent for a second course in the subject, one that emphasizes the functional analytic side of the discipline.

Supplementary Texts

Theoretical Treatments

Partial Differential Equations by Fritz John, Springer-Verlag, Inc., New York 1982 (4th Edition) (JOHN)
In many ways this text is a better discussion of the theory than MCOWEN since it provides more detail and additional aspects of the materials for our course. In addition it does not go very far into functional analytic methods. Excellent place to go for an additional treatment of a subject presented in MCOWEN.

Partial Differential Equations, An Introduction by Bernard Epstein, Robert E. Kreiger Publ. Co., Malabar, Florida 1983 (3rd Edition) (EPSTEIN)
Another excellent theoretical treatment of the subject, especially with extended discussions of rigorous arguments. Covers the classical material corresponding to Chapters 1 - 5 of MCOWEN (plus basic functional analysis of Banach and Hilbert spaces), but covers that material in more depth. Terrible short on practical exercises.

Treatments of Methods and Applications

Partial Differential Equations, Theory and Technique by George Carrier and Carl Pearson, Academic Press, Inc., New York 1988 (2nd Edition) (CARRIER & PEARSON)
The hallmark applications and methods text. Excellent source for worked examples, extra problems and extended discussions of techniques. Also covers several advanced techniques such as perturbations methods and numerical methods.

Elementary Applied Partial Differential Equations, with Fourier Series and Boundary Value Problems by Richard Haberman, Prentice-Hall, Inc., New Jersey 1983 (HABERMAN)
If you would like a book with a modern presentation but which concentrates on methods and calculations, this is the one for you. It doesn't discuss the general classification of 2nd order problems, or any of the theory that is part of such a discussion, so the presentation is thin on general principles and concepts. But it does a good job at discussing methods, especially if they relate to fourier type analysis.

Partial Differential Equations of Mathematical Physics by Tyn Myint-U, North Holland, Inc., New York 1980 (MYINT-U)
An excellent overall treatment of classical PDEs together with practical examples. Might be used as an alternate text for a course such as ours, but MCOWEN gives a slightly more general and rigorous discussion. There are a good number of problems to test one's skills.