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This book provides an up-to-date account of the asymptotic approximation of integrals. Included are logarithmic singularities, Mellin transform techniques for multiple integrals, summability methods, distributional approach, uniform asymptotic expansions via a rational transformation, and double integrals with a curve of stationary points. Classical methods are included for completeness. All results are proved and error bounds are given whenever possible. The reader is assumed to know advanced calculus and complex variable theory. Courses of study could be designed to use the book, but it probably will find most use as a reference work. Contents: 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.
π SIMILAR VOLUMES
The NAG (Numerical Analysis Group of six British Universities) Library now contains, at Mark 12, 688 routines. This book is designed to fill part of the documentation gap of that Library. Described are the most commonly used numerical methods, emphasizing those of the NAG Library, but other methods