Asymptotic Approximation of Integrals

Erscheinungsjahr 2001
ISBN: 978-0-89871-497-5
Verlag: Society for Industrial and Applied Mathematics

Buch, Englisch, Band 34, 184 Seiten, Format (B × H): 152 mm x 228 mm, Gewicht: 776 g

Reihe: Classics in Applied Mathematics

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.

Autoren/Hrsg.

Wong, R.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematische Analysis Integralrechnungen- und -gleichungen

Inhaltsverzeichnis

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.