ABSTRACT
I. Introduction 216II. General Handbooks 216III. Special and Generalized Functions 217A. Advanced undergraduate 217B. Advanced undergraduate/beginning graduate 217C. Graduate 218D. Advanced graduate 218E. Specialist 218IV. Ordinary Differential Equations 219A. Undergraduate 219B. Advanced undergraduate 219C. Advanced undergraduate/beginning graduate 221D. Advanced undergraduate/graduate 222E. Beginning graduate 223F. Beginning graduate/specialist 223G. Graduate 224H. Graduate/specialist 226I. Advanced graduate/specialist 227J. Specialist 228V. Partial Differential Equations 229A. Undergraduate 229B. Advanced undergraduate 229C. Advanced undergraduate/beginning graduate 231 215
D. Beginning graduate 232E. Graduate 234F. Graduate/specialist 234G. Advanced graduate 235H. Specialist 236
Mathematics is a venerable science whose branch is incontestably the thickest. The immensely diverse and seemingly fragmented mathematical literature, especially since the 1980s, reflects the manifold offshoots of mathematics’ major roots (logic, geometry, algebra, and analysis). Of course, this trend only mirrors the information production and needs of mathematicians and other scientists whose intellectual efforts have substantial mathematical content. Notably, in the last 15 years, the vast majority of new monographs and journal titles in mathematics or allied fields have had an “applied” spin/feel to them. Indeed, the techniques of differential equations weave their way through diverse disciplines, creating interfaces to facilitate enhanced understanding or extend theories.The reviewed books were selected on the basis of currency and usability from the perspective of a variety of audience types. The reviews are separated into two broad categories: ordinary differential equations (ODEs) and partial differential equations (PDEs). In each category the reviews’ audience type is described and arranged from beginner to specialist. Each review ends with a brief summary statement, and the review number(s), if available, from Mathematical Reviews (www.ams.org/mathscinet). To complement the reviews of books in differential equations, there are reviews of selected handbooks and monographs on special and generalized functions.No attempt has been made to provide a comprehensive list of newsgroups, websites, encyclopedias, journals, or databases relevant to differential equations. However, a first good approach would be to consult your local library’s librarian, or the numerous resources available off the homepages of the American Mathematical Society (www.ams.org), the Society of Industrial and Applied Mathematics (www.siam.org), or the European Mathematical Society (www.emis.de). II. GENERAL HANDBOOKS
PL Sachdev. A Compendium on Nonlinear Ordinary Differential Equations.New York: John Wiley, 1997.
