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Asymptotic approximations of integrals /
Asymptotic Approximations of Integrals.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Boston :
Academic Press,
�1989.
|
| Colección: | Computer science and scientific computing.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Asymptotic Approximations of Integrals; Copyright Page; Dedication; Table of Contents; Preface; Chapter I. Fundamental Concepts of Asymptotics; 1. What Is Asymptotics?; 2. Asymptotic Expansions; 3. Generalized Asymptotic Expansions; 4. Integration by Parts; 5. Watson's Lemma; 6. The Euler-Maclaurin Summation Formula; Exercises; Supplementary Notes; Chapter II. Classical Procedures; 1. Laplace's Method; 2. Logarithmic Singularities; 3. The Principle of Stationary Phase; 4. Method of Steepest Descents; 5. Perron's Method; 6. Darboux's Method; 7. A Formula of Hayman; Exercises.
- Supplementary NotesChapter III. Mellin Transform Techniques; 1. Introduction; 2. Properties of Mellin Transforms; 3. Examples; 4. Work of Handelsman and Lew; 5. Remarks and Examples; 6. Explicit Error Terms; 7. A Double Integral; Exercises; Supplementary Notes; SHORT TABLE OF MELLIN TRANSFORMS; Chapter IV. The Summability Method; 1. Introduction; 2. A Fourier Integral; 3. Hankel Transform; 4. Hankel Transform (continued); 5. Oscillatory Kernels: General Case; 6. Some Quadrature Formulas; 7. Mellin-Barnes Type Integrals; Exercises; Supplementary Notes.
- 4. Hilbert Transforms5. Laplace and Fourier Transforms Near the Origin; 6. Fractional Integrals; 7. The Method of Regularization; Exercises; Supplementary Notes; Chapter VII. Uniform AsymptoticExpansions; 1. Introduction; 2. Saddle Point near a Pole; 3. Saddle Point near an Endpoint; 4. Two Coalescing Saddle Points; 5. Laguerre Polynomials I; 6. Many Coalescing Saddle Points; 7. Laguerre Polynomials II; 8. LegendreFunction; Exercises; Supplementary Notes; Chapter VIII. Double Integrals; 1. Introduction; 2. Classification of Critical Points; 3. Local Extrema; 4. Saddle Points.
- 5. A Degenerate Case6. Boundary Stationary Points; 7. Critical Points of the Second Kind; 8. Critical Points of the Third Kind; 9. A Curve of Stationary Points; 10. Laplace's Approximation; 11. Boundary Extrema; Exercises; Supplementary Notes; Chapter IX. Higher DimensionalIntegrals; 1. Introduction; 2. Stationary Points; 3. Points of Tangential Contact; 4. Degenerate Stationary Point; 5. Laplace's Approximation inRn; 6. Multiple Fourier Transforms; Exercises; Supplementary Notes; Bibliography; Symbol Index; Author Index; Subject Index.