2001 / xvii + 543 pages / Softcover / ISBN: 978-0-898714-97-5 / List Price $106.00 / SIAM Member Price $74.20 / Order Code CL34
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 Asymptotic Approximations of Integrals, all results are proved rigorously, and many of the approximation formulas are accompanied by error bounds. A thorough discussion on multidimensional integrals is given, and references are provided. Asymptotic Approximations of Integrals contains the "distributional method," which is 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.
This book can be used either as a text for graduate students in mathematics, physics, and engineering or as a reference for research workers in these fields. Engineers and scientists will find it easy to apply the techniques and results presented.
Preface; Chapter I: Fundamental Concepts of Asymptotics; Chapter II: Classical Procedures; Chapter III: Mellin Transform Techniques; Chapter IV: The Summability Method; Chapter V: Elementary Theory of Distributions; Chapter VI: The Distributional Approach; Chapter VII: Uniform Asymptotic Expansions; Chapter VIII: Double Integrals; Chapter IX: Higher Dimensional Integrals; Bibliography; Symbol Index; Author Index; Subject Index.
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