Applied Partial Differential Equations

Book Description:
This textbook is for the standard, one-semester, junior-senior course that often goes by the title "Elementary Partial Differential Equations" or "Boundary Value Problems". The audience consists of students in mathematics, engineering, and the physical sciences. The topics include derivations of some of the standard models of mathematical physics (e. g. , the heat equation, the wave equation, and Laplace's equation) and methods for solving those equations on unbounded and bounded domains (transform methods and eigenfunction expansions). Prerequisites include multivariable calculus and elementary differential equations. The text differs from other texts in that it is a brief treatment (about 200 pages); yet it provides coverage of the main topics usually studied in the standard course as well as an introduction to using computer algebra packages to solve and understand partial differential equations. The many exercises help students sharpen their computational skills by encouraging them to think about concepts and derivations. The student who reads this book carefully and solves most of the problems will have a sound knowledge base for a second-year partial differential equations course where careful proofs are constructed or upper division courses in science and in engineering where detailed applications of partial differential equations are introduced.

Nice idea:
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."

Worth a look as a possible text for a course in partial differential equations:
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.

I though it was a good book:
This book, although plagued by mathmatical nuances, was in my oppinion, very good. The author supplies you with all of the information you need to complete the problems found at the end of each chapter and even supplies the solutions on his website (check the preface). Hence if a student were to need more examples... he could easily try a few problems and then check to see if his answers were correct. Also, it spends a great deal of time on separation of variables as a technique used for solving PDE's, something that I use often in many of my physics courses. In fact, its explanation of this topic would be worth the book's price alone.

Horrible Textbook:
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.