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

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