Asymptotic Approximation of Integrals

This classic text remains the most up-to-date book to deal with asymptotic approximations of integrals.

R. Wong (Author)

9780898714975, Society for Industrial and Applied Mathematics

Paperback / softback, published 1 August 2001

184 pages
22.8 x 15.3 x 2.9 cm, 0.776 kg

Asymptotic methods are frequently used in many branches of both pure and applied mathematics, and this classic text remains the most up-to-date book dealing with one important aspect of this area, namely, asymptotic approximations of integrals. In this book, all results are proved rigorously, and many of the approximation formulas are accompanied by error bounds. A thorough discussion on multidimensional integrals is given, with references provided. Asymptotic Approximations of Integrals contains the 'distributional method', not available elsewhere. Most of the examples in this text come from concrete applications. Since its publication twelve years ago, significant developments have occurred in the general theory of asymptotic expansions, including smoothing of the Stokes phenomenon, uniform exponentially improved asymptotic expansions, and hyperasymptotics. These new concepts belong to the area now known as 'exponential asymptotics'. Expositions of these new theories are available in papers published in various journals, but not yet in book form.

Preface
1. Fundamental concepts of asymptotics
2. Classical procedures
3. Mellin transform techniques
4. The summability method
5. Elementary theory of distributions
6. The distributional approach
7. Uniform asymptotic expansions
8. Double integrals
9. Higher dimensional integrals
Bibliography
Symbol Index
Author index
Subject index.

Subject Areas: Mathematical modelling [PBWH], Applied mathematics [PBW], Numerical analysis [PBKS], Integral calculus & equations [PBKL]