Asymptotic analysis and perturbation theory

 Content: Introduction to Asymptotics  Basic Definitions Limits via Asymptotics  Asymptotic Series  Inverse Functions  Dominant Balance   Asymptotics of Integrals  Integrating Taylor Series  Repeated Integration by Parts  Laplace's Method Review of Complex Numbers Method of Stationary Phase  Method of Steepest Descents  Speeding Up Convergence  Shanks Transformation  Richardson Extrapolation  Euler Summation  Borel Summation  Continued Fractions  Pade Approximants  Differential Equations  Classification of Differential Equations First Order Equations Taylor Series Solutions  Frobenius Method   Asymptotic Series Solutions for Differential Equations  Behavior for Irregular Singular Points  Full Asymptotic Expansion  Local Analysis of Inhomogeneous Equations  Local Analysis for Nonlinear Equations  Difference Equations  Classification of Difference Equations First Order Linear Equations Analysis of Linear Difference Equations The Euler-Maclaurin Formula Taylor-Like and Frobenius-Like Series Expansions  Perturbation Theory  Introduction to Perturbation Theory  Regular Perturbation for Differential Equations  Singular Perturbation for Differential Equations  Asymptotic Matching  WKBJ Theory  The Exponential Approximation  Region of Validity  Turning Points  Multiple-Scale Analysis  Strained Coordinates Method (Poincare-Lindstedt)  The Multiple-Scale Procedure  Two-Variable Expansion Method   Appendix: Guide to the Special Functions  Answers to Odd-Numbered Problems  Bibliography  Index