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Book Review

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Society for Industrial and Applied Science



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This is an introduction to perturbation methods, at the beginning graduate level, suitable for courses focusing on methods rather than justification. Boundary layers and fluid flow are emphasized much more than nonlinear oscillations, but given this constraint, this book may have some advantages over its nearest competitor, Nayfeh’s Introduction to Perturbation Techniques. The author introduces perturbation expansions with a few examples, such as motion with small friction, roots of polynomials, and integration by parts. This leads to a second chapter on order symbols, asymptotic expansions, and uniformity. The next four chapters are each devoted to one of the basic classes of perturbation methods for differential equations, strained coordinates, multiple scales, matching, and WKB. (Strained coordinates are handled mostly by renormalization, that is, computing a nonuniform straightforward expansion and then rendering it uniform by straining.) A final chapter concerns asymptotic evaluation of integrals. The chapters on strained coordinates, multiple scales, and matching each have lengthy sections treating a serious physical application at a depth that is unusual in an introductory book; for strained coordinates and matching, these concern fluid flow, while for multiple scales the application is to lubricated bearings.


This review is published as Review of Pertubation Methods for Engineers and Scientists, by Alan W. Bush, SIAM Review 36, 1994, 136-137. Posted with permission.

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Society for Industrial and Applied Science



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Mathematics Commons