Perturbations: Theory and Methods

This is a course in perturbation theory for the solution of algebraic and differential equations, especially ordinary differential equations. It covers all of the methods commonly used in both regular and singular perturbations: Taylor series, Lindstedt series, strained parameters, multiple scales, averaging, matching and WKB methods. The text pays great attention to understanding the meaning of the results, as it is extremely easy to make mistakes and draw invalid conclusions from a perturbation analysis.