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"...The authors of this remarkable book are among the very few whohave faced up to the challenge of explaining what an asymptoticexpansion is, and of systematizing the handling of asymptotic series.The idea of using distributions is an original one, and we recommendthat you read the book...[it] should be on your bookshelf if you areat all interested in knowing what an asymptotic series is." -"TheBulletin of Mathematics Books" (Review of the 1st edition) **"...The book is a valuable one, one that many applied mathematiciansmay want to buy. The authors are undeniably experts in theirfield...most of the material has appeared in no other book." -"SIAMNews" (Review of the 1st edition)This book is a modern introduction to asymptotic analysis intendednot only for mathematicians, but for physicists, engineers, andgraduate students as well. Written by two of the leading experts inthe field, the text provides readers with a firm grasp of mathematicaltheory, and at the same time demonstrates applications in areas suchas differential equations, quantum mechanics, noncommutative geometry,and number theory.Key features of this significantly expanded and revised secondedition: * addition of a new chapter and many new sections * widerange of topics covered, including the Ces.ro behavior ofdistributions and their connections to asymptotic analysis, the studyof time-domain asymptotics, and the use of series of Dirac deltafunctions to solve boundary value problems * novel approach detailingthe interplay between underlying theories of asymptotic analysis andgeneralized functions * extensive examples and exercises at the end ofeach chapter * comprehensive bibliography and indexThis work is an excellent tool for the classroom and an invaluableself-study resource that will stimulate application of asymptotic

A Distributional Approach to Asymptotics: Theory and Applications

Preface * 1. Basic Results in Asymptotics * 2. Introduction to the Theory of Distributions * 3. A Distributional Theory for Asymptotic Expansions * 4. Asymptotic Expansion of Multi-Dimensional Generalized Functions * 5. Asymptotic Expansion of Certain Series Considered by Ramanujan * 6. Cesaro Behavior of Distributions * 7. Series of Dirac Delta Functions * References * Index