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Full Product Details

Author:   Norman Bleistein ,  Richard A. Handelsman
Publisher:   Dover Publications Inc.
Imprint:   Dover Publications Inc.
Edition:   New edition
Dimensions:   Width: 13.60cm , Height: 2.10cm , Length: 21.50cm
Weight:   0.468kg
ISBN:  

9780486650821

ISBN 10:   0486650820
Pages:   464
Publication Date:   28 March 2003
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

CHAPTER 1. Fundamental Concepts 1.1. Introduction 1.2 Order Relations 1.3. Asympototic Power Series Expansions 1.4. Asymptotic Sequences and Asymptotic Expansions of Poincare Type 1.5. Auxiliary Asymptotic Sequences 1.6. Complex Variables and Stokes Phenomenon 1.7 Operations with Asymptotic Expansions of Poincare Type 1.8. Exercises References CHAPTER 2. Asymptotic Expansions of Integrals: Preliminary Discussion 2.1. Introduction 2.2. The Gamma and Incomplete Gamma Functions 2.3. Integrals Arising in Probability Theory 2.4. Laplace Transform 2.5. Generalized Laplace Transform 2.6. Wave Propagation in Dispersive Media 2.7. The Kirchhoff Method in Acoustical Scattering 2.8. Fourier Series 2.9. Exercises References CHAPTER 3. Integration by Parts 3.1. General Results 3.2. A Class of Integral Transforms 3.3. Identification and Isolation of Critical Points 3.4. An Extension of the Integration by Paris Procedure 3.5. Exercises References CHAPTER 4. h-transforms with Kernels of Monotonic Argument 4.1. Laplace Transforms and Watson's Lemma 4.2. Results on Mellin Transforms 4.3. Analytic Continuation of Mellin Transforms 4.4. Asymptotic Expansions for Real ? 4.5. Asymptotic Expansions for Real ?: Continuation 4.6. Asymptotic Expansions for Small Real ? 4.7. Asymptotic Expansions for Complex ? 4.8. Electrostatics 4.9. Heat Conduction in a Nonlinearly Radiating Solid 4.10. Fractional Integrals and Integral Equations of Abel Type 4.11. Renewal Processes 4.12. Exercises References CHAPTER 5. h-Transforms with Kernals of Nonmonotonic Argument 5.1. Laplace's Method 5.2. Kernels of Exponential Type 5.3. Kernels of Exponential Type: Continuation 5.4. Kernels of Algebraic Type 5.5. Expansions for Small ? 5.6. Exercises References CHAPTER 6. h-Transforms with Oscillatory Kernels 6.1. Fourier Integrals and the Method of Stationary Phase 6.2. Further Results on Mellin Transforms 6.3. Kernels of Oscillatory Type 6.4. Oscillatory Kernels: Continuation 6.5. Exercises References CHAPTER 7. The Method of Steepest Descents 7.1. Preliminary Results 7.2. The Method of Steepest Descents 7.3. The Airy Function for Complex Agrument 7.4. The Gamma Function for Complex Argument 7.5. The Klein-Gordon Equation 7.6. The Central Limit Theorem for Identically Distributed Random Variables 7.7. Exercises References CHAPTER 8. Asymptotic Expansions of Multiple Integrals 8.1. Introduction 8.2. Asymptotic Expansions of Double Integrals of Laplace Type 8.3. Higher-Dimensional Integrals of Laplace Type 8.4. Multiple Integrals of Fourier Type 8.5. Parametric Expansions 8.6. Exercises References CHAPTER 9. Uniform Asymptotic Expansions 9.1. Introduction 9.2. Asymptotic Expansion of Integrals with Two Nearby Saddle Points 9.3. Underlying Principles 9.4. Saddle Point near on Amplitude Critical Point 9.5. A Class of Integrals That Arise in the Analysis of Precursors 9.6. Double Integrals of Fourier Type 9.7. Exercises References Appendix General References Index

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