# Asymptotic Analysis

## A Distributional Approach

• Ram P. Kanwal
Book

1. Front Matter
Pages i-ix
2. Ricardo Estrada, Ram P. Kanwal
Pages 1-42
3. Ricardo Estrada, Ram P. Kanwal
Pages 43-87
4. Ricardo Estrada, Ram P. Kanwal
Pages 88-150
5. Ricardo Estrada, Ram P. Kanwal
Pages 151-194
6. Ricardo Estrada, Ram P. Kanwal
Pages 195-232
7. Ricardo Estrada, Ram P. Kanwal
Pages 233-245
8. Back Matter
Pages 247-258

### Introduction

Asymptotic analysis is an old subject that has found applications in vari­ ous fields of pure and applied mathematics, physics and engineering. For instance, asymptotic techniques are used to approximate very complicated integral expressions that result from transform analysis. Similarly, the so­ lutions of differential equations can often be computed with great accuracy by taking the sum of a few terms of the divergent series obtained by the asymptotic calculus. In view of the importance of these methods, many excellent books on this subject are available [19], [21], [27], [67], [90], [91], [102], [113]. An important feature of the theory of asymptotic expansions is that experience and intuition play an important part in it because particular problems are rather individual in nature. Our aim is to present a sys­ tematic and simplified approach to this theory by the use of distributions (generalized functions). The theory of distributions is another important area of applied mathematics, that has also found many applications in mathematics, physics and engineering. It is only recently, however, that the close ties between asymptotic analysis and the theory of distributions have been studied in detail [15], [43], [44], [84], [92], [112]. As it turns out, generalized functions provide a very appropriate framework for asymptotic analysis, where many analytical operations can be performed, and also pro­ vide a systematic procedure to assign values to the divergent integrals that often appear in the literature.

### Keywords

Kernel Moment Power Taylor series calculus derivative differential equation distribution generalized function integral perturbation perturbation theory

#### Authors and affiliations

• 1
• Ram P. Kanwal
• 2
1. 1.Escuela de MatemáticaUniversidad de Costa RicaSan JoséCosta Rica
2. 2.Department of MathematicsThe Pennsylvania State UniversityUniversity ParkUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4684-0029-8
• Copyright Information Birkhäuser Boston 1994
• Publisher Name Birkhäuser Boston
• eBook Packages
• Print ISBN 978-1-4684-0031-1
• Online ISBN 978-1-4684-0029-8
• Buy this book on publisher's site