Perturbations: theory and methods
Series: Classics in Applied Mathematics, 27Publication details: Society for Industrial and Applied Mathematics, 1999. Philadelphia:Description: xx, 509p.; pbk; 23cmISBN:- 9780898714432
- 515.35 MUR
Item type | Current library | Collection | Call number | Copy number | Status | Date due | Barcode |
---|---|---|---|---|---|---|---|
Books | IIT Gandhinagar | General | 515.35 MUR (Browse shelf(Opens below)) | 1 | Available | 031894 |
Includes index and references
Perturbations: Theory and Methods gives a thorough introduction to both regular and singular perturbation methods for algebraic and differential equations. Unlike most introductory books on the subject, this one distinguishes between formal and rigorous asymptotic validity, which are commonly confused in books that treat perturbation theory as a bag of heuristic tricks with no foundation. The meaning of "uniformity" is carefully explained in a variety of contexts. All standard methods, such as rescaling, multiple scales, averaging, matching, and the WKB method are covered, and the asymptotic validity (in the rigorous sense) of each method is carefully proved. First published in 1991, this book is still useful today because it is an introduction. It combines perturbation results with those known through other methods. Sometimes a geometrical result (such as the existence of a periodic solution) is rigorously deduced from a perturbation result, and at other times a knowledge of the geometry of the solutions is used to aid in the selection of an effective perturbation method.
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