Multiple Scale and Singular Perturbation Methods (Applied Mathematical Sciences)

Rating:
Summary: A Classic Text in Perturbation Methods
Review: A classic in singular perturbation techiques, this book should be on the shelf of every applied mathematician. It's focus is mainly upon multiscale methods, although a brief review of regular perturbation techniques is present. The author's carefully develop the theory of multiscale methods and provide numerous applications to real world engineering and scientific problems. While I would not recommend this as a first book on perturbation theory due to it's complexity and at times dense notation, anyone who is serious about singular perturbations should buy this book.

Rating:
Summary: Tedious Perturbations
Review: This is an expanded version of an earlier text by the second author (Cole). The latter was clearly written, to the point, and a useful resource. The same cannot be said of this book. It obscures the ideas underlying perturbation methods with excessive detail on problems of marginal interest. It also, oddly, fails to adequately explain a fundamental method such as multiple scales. Their explanation of how and why scales are selected misses the point completely. This is odd as the authors made contributions to the early development of this method and, as pointed out by the other reviewer, this is the main focus of the book. I would not recommend this book, even as a second or third text on the subject.

Rating:
Summary: Not recommended as a textbook
Review: We used this as the textbook for a graduate course I took last fall semester (Fall, 2003) on multiple scales and singular perturbation methods. What a mistake. It is impossible to learn the subject from this book. In the course we started with regular expansions, which is part of Chapter 1. The style of presentation is: here is a complicated problem and so let's assume this expansion. This is made worse by the use of hard to read notation (superscripts on top of superscripts, the overuse of * and + in the super-superscript position, etc). Moreover there is little explanation as to why choices are made and this made doing homework very difficult. It was fortunate we were able to find other books that did explain how to use perturbation methods otherwise many of us would have dropped the course. I can not recommend this book.