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