An Introduction to Partial Differential Equations

This book was the primary textbook for my first year graduate PDE's class (I am an Applied Math student). The supplementary textbook was the one written by Strauss, which is the traditional undergraduate leveled text. My background is in Physics so I have seen PDE's before, just not in any detail as this. As a textbook, I liked it. It was easy to read through and the hints in the back of the book were helpful when I was having a tough time solving the problems (some of which are quite difficult, others less so). I can say that I learned enough PDE's to be able to solve them properly if I were to see a PDE lying around in a, say, physics book! You will learn solving techniques reading through this book. This text, unfortunately, is far from thorough, as the other reviewer has pointed out. This is an Applied Math textbook, NOT a Pure Math textbook! I had Evans' book with me the whole time and they were worlds apart! I tried to go through Evans' book along-side after reviewing a subject (like The Method of Characteristics) from P&R and it was a challenge. You won't become an expert in PDE theory using this book. It is most certainly an introduction. You don't see one bit of Sobolev spaces in the entire text; the treatment of shocks and conservation laws are left to a minimum, you don't even see a statement about the Reimann Problem (which comes up in research today)! Yes, there are many application but one thing I find tragic (coming from physics) is that the *interpretation* is kept to a minimum as well! Many "applied" mathematicians feel free to do this, I find, and it irks me to no end. The chapters on Separation of Variables and Sturm-Liouville theory is not complete either - this is to be expected since the topic can span multiple books by themselves. They do a good job of *introducing* you to the material, however. I found myself always looking up other texts for another point of view and, perhaps, an interpretation or a better understanding of some results. For Separation of Variable and a view of Sturm-Liouville problems from a different angle, I whole-heartedly recommend taking a look at Churchill and Brown's "Fourier Series and Boundary Value Problems" and "Fourier Analysis" by Korner. I find the treatment of Characteristcs to be done better and more intuitively by Zauderer. Uniqueness proofs are a strength of P&R and the only other book I found to be as easy to read regarding them is the one by Strauss. All in all, this is a good book, don't get me wrong, it's just that you won't become an expert in the field. If you want a working knowledge of PDE's, I would recommend this book, Erich Zauderer's book, and Churchill and Brown's (excellent) book on Fourier Series; all of them to be read together.