ProofWiki:Books/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, 2nd Edition 1998, Dover Publications, Inc..

ISBN 0-486-67551-3

Subject Matter

• Numerical Analysis
• Perturbation Theory

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