This is an attractive introductory work on differential equations, with extensive information in addition to what can be covered in a two-semester course. The order of the topics examined is slightly unusual in that Laplacians are covered after Fourier transforms and power series. The chapter on power series contains a section on hypergeometric equations, which could well be the first time that an introductory book on the subject goes that far. The book has plenty of exercises at the end of each section, and also at the end of each chapter. The solutions to some of these are included at the end of the book. Most chapters contain a few appendixes that are several pages long. Their subject is either related to the life and work of an exceptional mathematician (such as Newton, Euler, or Gauss) or pertains to an area of mathematics in which the theory of differential equations can be applied. The historical appendixes put the material in context, and explain which parts of the material were the most difficult to discover. The writing is pleasant and reader-friendly throughout. This work is an essential acquisition for all math libraries; no competing works have put the material in such a deep historical context.

--M. Bona, University of Florida

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