Applied Partial Differential Equations (Undergraduate Texts in Mathematics)

This book has two flaws. The first is the classic pitfall of mathematicians trying to reach an audience who are interested in mathematics largely as a tool rather than an end in itself. The author or instructor teaches a pure math course and inserts "application chapters," or pauses between boardfuls of algebra to mumble, "...and this represents a vibrating drumhead." The second is that the book is just too thin. The explanations are very brief, the material is arguably not complete, and there aren't enough examples or problems. While I share the author's taste for minimalism, PDE's are a big subject, and you need a bigger book than this to do them justice.

A general problem with applied PDE courses and books (including this one) is that they fail to give adequate consideration to finite difference methods. Any course in the 21st century should give at least parity to these methods, as they are immeasurably more useful in the real world than eigenfunction expansions or Duhamel's principle. I give the book three stars because the author has succeeded to the extent possible given the constraints he placed upon himself, but I can't recommend it to someone who actually wants to learn applied PDE's; instead, I would recommend DuChateau and Zachmann for a comprehensive and understandable treatment for $20 less.

On the other hand, if you want physical intuition and running code, pick up Garcia, "Numerical Methods for Physics." If you are a mathematician trying to figure out how to write an applied book, drop everything and buy H.M. Schey's "Div, Grad, Curl and All That."

In my opinion, courses in partial differential equations should be offered more often in undergraduate curricula. Many of the problems encountered in the world are solved using partial differential equations rather than ordinary differential equations. This book would be a good text for a course in partial differential equations; it begins with a chapter on the physical origins of partial differential equations and contains descriptions of the mathematical models of the physical events. The sections of the chapter are:

*) Mathematical models
*) Conservation laws
*) Diffusion
*) PDEs in biology
*) Vibrations and acoustics
*) Quantum mechanics
*) Heat flow in three dimensions
*) Laplace's equation
*) Classification of PDEs

A small set of exercises are included at the end of each section, although no solutions are included. The level of discourse is rigorous, yet well within the bounds of the advanced undergraduate with calculus and a course in ordinary differential equations behind them. If you are scheduled to teach or are pondering a course in partial differential equations, then this is a book you should consider as a possible text.

well even if it doesn't cover all the methods of solving PDE. it still a great book, it explains the origin of each problem and the way to attack it.
i think this book is goo for someone who is seeking to understand PDE but not used a course book (other books are better for courses).

Very little explanation of how to apply the theory to the problems at the end of each chapter. Not good for people who are not super math students.