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# Applied Asymptotic Analysis

### About this Title

**Peter D. Miller**, *University of Michigan, Ann Arbor, MI*

Publication: Graduate Studies in Mathematics

Publication Year:
2006; Volume 75

ISBNs: 978-0-8218-4078-8 (print); 978-1-4704-1154-1 (online)

DOI: https://doi.org/10.1090/gsm/075

MathSciNet review: MR2238098

MSC: Primary 34-01; Secondary 34Exx, 35A35, 35Q53, 35Q55, 41A60

### Table of Contents

**Download chapters as PDF**

**Front/Back Matter**

**Part 1. Fundamentals **

- Chapter 0. Themes of asymptotic analysis
- Chapter 1. The nature of asymptotic approximations

**Part 2. Asymptotic analysis of exponential integrals **

- Chapter 2. Fundamental techniques for integrals
- Chapter 3. Laplace’s method for asymptotic expansions of integrals
- Chapter 4. The method of steepest descents for asymptotic expansions of integrals
- Chapter 5. The method of stationary phase for asymptotic analysis of oscillatory integrals

**Part 3. Asymptotic analysis of differential equations **

- Chapter 6. Asymptotic behavior of solutions of linear second-order differential equations in the complex plane
- Chapter 7. Introduction to asymptotics of solutions of ordinary differential equations with respect to parameters
- Chapter 8. Asymptotics of linear boundary-value problems
- Chapter 9. Asymptotics of oscillatory phenomena
- Chapter 10. Weakly nonlinear waves
- Appendix: Fundamental inequalities