Solution Techniques for Elementary Partial Differential Equations

See our review of the second edition. This third edition is a modest update, with a small amount of additional material, examples, and exercises, and some rearrangement of the text.

This is a leisurely cookbook of PDE solution methods, aimed at engineering students. The approach is very traditional. There is no numerical work. There is a great deal of Mathematica code, although in my opinion this does not add much to the text. Mathematica knows all the cookbook methods too, and the code merely asks for the exact solution to the example problem. These are described as “verifications”, but they do raise the question: Why do we need to learn these techniques, when Mathematica already knows them?

There is a small amount of instructor support material on the publisher’s web site, consisting of a solutions manual a set of viewgraphs based on the text. I did not examine these.

This book is well-done, and has comprehensive coverage of explicit solution methods, and many students will benefit from the completely written-out solutions. On the other hand, it may be overkill for many students to have a whole book on this subject, when engineering math books (such as Kreyszig’s Advanced Engineering Mathematics) also have good coverage, although more concise and not as extensive as the present book.

On the third hand, there is more to PDEs today than explicit solutions, and most engineering students will also want to learn qualitative methods and numerical methods. Surprisingly, the Schaum’s Outline of Partial Differential Equations (Paul DuChateau & David W. Zachmann, McGraw-Hill, 3^rd edition, 2011) is much more up-to-date than the present book, as well as being much cheaper at $20. It covers generally the same topics, although at less length, but also has a lot on difference equation methods, the finite element method, and qualitative behavior of elliptic, hyperbolic, and parabolic PDEs.

Allen Stenger is a math hobbyist and retired software developer. He is an editor of the Missouri Journal of Mathematical Sciences. His personal web page is allenstenger.com. His mathematical interests are number theory and classical analysis.