Asymptotic expansion of Integrals, a very applied technique, is fundamental to my area of research: computational electromagnetics (CEM). I have read the review by one of the anonymous reviewer, and do agree fully with him/her. Professors Bleistien and Handelsman have done a remarkable job in exposing the asymptotic theory, as one of the parameters (in the exponent of the integrand) becomes large. This technique is fundamental to our understanding of "high-frequency" phenomena and in particular diffraction phenomena. Without repeating the contents of the preceding review, I must reiterate that a reasonably good knowledge in the theory of fundtions of a complex variable is essential for benefiting from this book. The book is presents a rigorous theory of a very useful and applied mathematical technique for electrical engineering (radars, em scattering, antenna theory) and is a must for those wishing to do some serious yet useful research in CEM. Very typically, the Green's functions for a e.m. b.v.p (boundary value problem), can be approximated by such techniques, which results in substantial savings of computer resources at higher frequencies. (It is one of the most useful books in my personal library.)
The book contains valuable information about a specialized area of applied mathematics. The material presented in this book is applicable to problems involving quantum and electromagtnetic scattering at high frequencies. In the area of radar technology, the radar cross-section of a target is calculated using asymptotic evaluation of Fourier integrals that appear in the final form of the electric and magnetic field vectors following a solution to the appropriate boundary value problem, starting with Maxwell's equations. To study the book, the reader must have had course on complex variables upto and including residue theory, infinite series, analytic continuation, conformal mapping and multivalued functions, plus a introductory knowledge of ordinary differential equations. Without discussing the contents of each chapter, I can only comment that they are most lucid and intellectually satisfying; in particular chaps. 7 and 9 are most useful to practical problems The contents of chapters 7 and 9 are widely applicable in various electrical engineering problems - short-pulse radars, high-frequnecy scattering, antenna theory and the like. The main advantage of using these asymptotic methods is that they reduce spectral integrals stemming from potential theory (Green's functions) are to " almost " closed form solutions that are not exact but computationally extremely helpful. In many cases, for example EM scattering by a circular cylinder, numerical results can only be obtained if asymptotic methods are applied at high frequencies. The use of asymptotic methods in engineering computation is primarily to reduce the c.p.u. time by several orders of magnitude as compared to exact calculations. This allows faster and more efficient solution to problems. The book is well organized and there are enough homework problems for the interested reader. A must pre-requisite for understanding the topic(s) is a reasonably good grasp of the theory functions of a complex variable, as mentioned at the begining of this review.
This Dover reprint comes complete with someone's handwritten annotations and underscorings, as can be seen already on p.2. See also p. 9, 12, etc. Essentially all the bibliographies of the chapters come with hooks, cf. e.g. p.40. I think Dover is overdoing it with the careless photographic reproduction.