TY  - BOOK
AU  - Peter D. Miller 
TI  - Applied asymptotic analysis
T2  - Graduate Studies in Mathematics
SN  - 9780821840788
AV  - QA431 
PY  - 2006///]
CY  - Rhode Island
PB  - American Mathematical Society
KW  - Mathematics
N1  - 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

N2  - This book is a survey of asymptotic methods set in the current applied research context of wave propagation. It stresses rigorous analysis in addition to formal manipulations. Asymptotic expansions developed in the text are justified rigorously, and students are shown how to obtain solid error estimates for asymptotic formulae. The book relates examples and exercises to subjects of current research interest, such as the problem of locating the zeros of Taylor polynomials of entire nonvanishing functions and the problem of counting integer lattice points in subsets of the plane with various geometrical properties of the boundary.

The book is intended for a beginning graduate course on asymptotic analysis in applied mathematics and is aimed at students of pure and applied mathematics as well as science and engineering. The basic prerequisite is a background in differential equations, linear algebra, advanced calculus, and complex variables at the level of introductory undergraduate courses on these subjects. --- summary provided by publisher
ER  -