Since the previous editions of this book have been used at senior undergraduate and first year graduate levels at many institutions in the United States and abroad, there is little doubt that the third edition will also be popular. The inclusion of new and recent examples and topics in PDE makes the book particularly useful to students of mathematics, sciences and engineering.
Although the author claims that the content of the book is modern, many of the results are not given in full generality. For instance, the function spaces where the solutions of equations are found are not fully modern (e.g., Lebesgue or Sobolev spaces); the reader interested in solving the problems in these more general spaces should consult other treatments. The author seems to have chosen this approach deliberately, in order to be accessible to an audience with an average mathematical background and who intend to pursue mathematical research by building on the material presented in the book. It makes the book easier to read, and yet the most important topics in applied mathematics are covered thoroughly.
What makes the book very attractive is the selection of topics from a wide range of areas, such as quantum mechanics, fluid dynamics, solid mechanics, calculus of variation, wave propagation, telecommunication, soliton dynamics, and nonlinear stability theory. The inclusion of topics from new and recent research articles in the above areas may well be a unique feature of this book. Naturally, it is not easy to cover all the above areas in a volume, but the author has been quite successful in presenting topics from different fields for students and researchers interested in applied partial differential equations.
A large number of examples and exercises is an excellent feature. The book is not free from typographical errors, such as the one on page 97, where the eigenvalue (lambda) does not appear in the differential equation displayed there.
Because the book can be used either as a textbook (with a careful selection of topics) or as a good reference for research in applied mathematics, physics, and engineering, it should find a place in a public library or personal library of every enthusiastic mathematician, physicist, and engineer.
Dhruba Adhikari is Assistant Professor of Mathematics at Southern Polytechnic State University, Marietta, Georgia.