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

## James G. Simmonds and James E. Mann, Jr.: A First Look at Perturbation Theory

Published $1986$, 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
A Roots of $T_\epsilon \left({z}\right)$ and $T_0 \left({z}\right)$
B Proof that $R_{N+1} = O \left({\beta^{N+1}}\right)$
C Approximate Evaluation of Integrals