Essential mathematics for applied fields / Richard M. Meyer

The preface states that "The purpose of this work is to provide... a wide spectrum of essential (non-measure-theoretic) mathematics for use by workers in a variety of applied fields''. To provide this background, "a prohibitive number of... mathematics courses'' would have to be studied if available. "Only calculus through differential equations'' is presumed. There is an extensive treatment of sequences and series of functions and the corresponding limit possibilities, leading to a discussion of Abelian and Tauberian theorems. Stieltjes integration is treated including its multidimensional form. Finite difference results are given which are analogous to the differential results of the calculus and differential equations with constant coefficients. The chapter on complex variables contains the essentials of a basic graduate course, and this is followed by four chapters on linear algebra dealing with matrices, determinants, vector spaces, linear equations and characteristic roots. The three concluding chapters are headed "Convex sets and convex functions'', "Max min problems'' and "Some basic inequalities''. A good deal of the presentation consists of a sequence of examples and exercises with references elsewhere or with answers or just hints at the end of the chapters. The emphasis on immediate mathematical examples is laudable, but this format is vulnerable in a number of ways: The relation of the topics with applications is not given and the references concern mathematical developments. (MSN)