A Distributional Approach to Asymptotics

Theory and Applications

  • Ricardo Estrada
  • Ram P. Kanwal

Part of the Birkhäuser Advanced Texts book series (BAT)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Ricardo Estrada, Ram P. Kanwal
    Pages 1-52
  3. Ricardo Estrada, Ram P. Kanwal
    Pages 53-105
  4. Ricardo Estrada, Ram P. Kanwal
    Pages 107-186
  5. Ricardo Estrada, Ram P. Kanwal
    Pages 187-248
  6. Ricardo Estrada, Ram P. Kanwal
    Pages 249-296
  7. Ricardo Estrada, Ram P. Kanwal
    Pages 297-396
  8. Ricardo Estrada, Ram P. Kanwal
    Pages 397-432
  9. Back Matter
    Pages 433-454

About this book

Introduction

"...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

Keywords

Boundary value problem Derivative Fourier series Taylor series Wavelet asymptotic analysis differential equation distribution theory generalized functions geometry mechanics number theory quantum mechanics

Authors and affiliations

  • Ricardo Estrada
    • 1
  • Ram P. Kanwal
    • 2
  1. 1.Escuela de MatemáticaUniversidad de Costa RicaSan JoséCosta Rica
  2. 2.Department of MathematicsPennsylvania State UniversityUniversity ParkUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-8130-2
  • Copyright Information Birkhäuser Boston 2002
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6410-1
  • Online ISBN 978-0-8176-8130-2
  • About this book