### Synopses & Reviews

"...The authors of this remarkable book are among the very few who have faced up to the challenge of explaining what an asymptotic expansion is, and of systematizing the handling of asymptotic series. The idea of using distributions is an original one, and we recommend that you read the book...[it] should be on your bookshelf if you are at all interested in knowing what an asymptotic series is." -"The Bulletin of Mathematics Books" (Review of the 1st edition) ** "...The book is a valuable one, one that many applied mathematicians may want to buy. The authors are undeniably experts in their field...most of the material has appeared in no other book." -"SIAM News" (Review of the 1st edition) This book is a modern introduction to asymptotic analysis intended not only for mathematicians, but for physicists, engineers, and graduate students as well. Written by two of the leading experts in the field, the text provides readers with a firm grasp of mathematical theory, and at the same time demonstrates applications in areas such as differential equations, quantum mechanics, noncommutative geometry, and number theory. Key features of this significantly expanded and revised second edition: * addition of a new chapter and many new sections * wide range of topics covered, including the Ces.ro behavior of distributions and their connections to asymptotic analysis, the study of time-domain asymptotics, and the use of series of Dirac delta functions to solve boundary value problems * novel approach detailing the interplay between underlying theories of asymptotic analysis and generalized functions * extensive examples and exercises at the end of each chapter * comprehensive bibliography and index This work is an excellent tool for the classroom and an invaluable self-study resource that will stimulate application of asymptotic

#### Review

"This is not just a 'Second Edition' of some monograph in the usual sense, but a revised and largely expanded version of

*Asymptotic Analysis: A Distributional Approach* (1994) by the same authors.... A completely new chapter on the Cesáro behavior of distributions has been added; moreover there are several new sections, among them respective problem sections at the end of each chapter. Finally, a large number of recent results and additional examples have been included.... Even more than its predecessor, this book presents an interesting and carefully written introduction into the theory and applications of asymptotic analysis based on distribution theory."

**--MONATSHEFTE FÜR MATHEMATIK (Review of the Second Edition)**

"The authors of this remarkable book are among the very few that have faced up to the challenge of explaining what an asymptotic expansion is, and of systematizing the handling of asymptotic series. The idea of using distributions is an original one, and we recommend that you read the book...[it] should be on your bookshelf if you are at all interested in knowing what an asymptotic series is." ** **

**--THE BULLETIN OF MATHEMATICS BOOKS (Review of the First Edition)**

". . . the book is a valuable one, one that many applied mathematicians may want to buy. The authors are undeniably experts in their field . . . most of the material has appeared in no other book." ** **

**--SIAM REVIEW (Review of the First Edition)**

#### Synopsis

Written by two leading experts, this book provides readers with a firm grasp asymptotic analysis, and demonstrates applications in areas such as differential equations and quantum mechanics.

#### Synopsis

Key features of this significantly expanded second edition: - addition of several new chapters and sections, including a presentation of time-domain asymptotics needed for the understanding of wavelet theory - extensive examples and problem sets - useful bibliography and index. This book is a modern introduction to asymptotic analysis intended not only for mathematicians, but for physicists, engineers, and graduate students as well. Written by two of the leading experts in the field, the text provides readers with a firm grasp of mathematical theory, and at the same time demonstrates applications in areas such as differential equations, quantum mechanics, noncommutative geometry, and number theory. "...The authors of this remarkable book are among the very few who have faced up to the challenge of explaining what an asymptotic expansion is, and of systematizing the handling of asymptotic series. The idea of using distributions is an original one, and we recommend that you read the book...[it] should be on your bookshelf if you are at all interested in knowing what an asymptotic series is." ¿ "The Bulletin of Mathematics Books" (Review of the 1st edition) "...The book is a valuable one, one that many applied mathematicians may want to buy. The authors are undeniably experts in their field...most of the material has appeared in no other book." ¿ "SIAM News" (Review of the 1st edition) Table of contents Preface 1. Basic Results in Asymptotics 2. Introduction to the Theory of Distributions 3. A Distributional Theory for Asymptotic Expansions 4. The Asymptotic Expansion of Multi-Dimensional Generalized Functions 5. The Asymptotic Expansion of Certain Series Considered by Ramamujan 6. The Cesaro Behavior of Distributions 7. Series of Dirac Delta Functions References Index

### Table of Contents

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. Ces