# Book:James G. Simmonds/A First Look at Perturbation Theory/Second Edition

## James G. Simmonds and James E. Mann, Jr.: A First Look at Perturbation Theory (2nd Edition)

Published $\text {1998}$, Dover Publications, Inc.

ISBN 0-486-67551-3

### Contents

Preface
$1$ Introduction and Overview
$2$ Roots of Polynomials
$3$ Singular Perturbations in Ordinary Differential Equations
$4$. Periodic Solutions of the Simplest Nonlinear Differential Equations. Poincaré's Method
$5$. Introduction to the Two-scale Method
$6$. The WKB Approximation
$7$. Transition Point Problems and Langer's Method of Uniform Approximation
$8$. Introduction to Boundary Layer Theory
$9$. Cables and Cells: Ancient and Modern Problems
Bibliography
$\text A$ Roots of $\map {T_\epsilon} z$ and $\map {T_0} z$
$\text B$ Proof that $R_{N + 1} = \map O {\beta^{N + 1} }$
$\text C$ Approximate Evaluation of Integrals

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