Sinossi
This book gives a thorough introduction to both regular and singular perturbation methods for algebraic and differential equations.
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Contenuti
Preface to the classics edition; Preface; Part I. Introduction to Perturbation Theory. 1. Root finding; 2. Regular perturbations; 3. Direct error estimation; Part II. Oscillatory Phenomena. 4. Periodic solutions and Lindstedt series; 5. Multiple Scales; 6. Averaging; Part III. Transition Layers. 7. Initial layers; 8. Boundary layers; 9. Methods of the WKB type; Appendix A. Taylor's theorem; Appendix B. The implicit function theorem; Appendix C. Second order differential equations; Appendix D. Systems of differential equations; Appendix E. Fourier series; Appendix F. Lipschitz constants and vector norms; Appendix G. Logical quantifiers and uniformity; Symbol index; Index.
Product Description
Book by Murdock James A
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Perturbations: Theory and Methods (Classics in Applied Mathematics, Series Number 27)
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Society for Industrial and Applied Mathematics, 1987
ISBN 10: 0898714435
ISBN 13: 9780898714432
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Perturbations : Theory and Methods
Editore:
Society for Industrial and Applied Mathematics, 1999
ISBN 10: 0898714435
ISBN 13: 9780898714432
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Perturbations: Theory and Methods: 27 (Classics in Applied Mathematics, Series Number 27)
Editore:
Society for Industrial and Applied Mathematics, 1987
ISBN 10: 0898714435
ISBN 13: 9780898714432
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Perturbations: Theory and Methods: Vol 27
Editore:
Society for Industrial & Applied, 1999
ISBN 10: 0898714435
ISBN 13: 9780898714432
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Perturbations: Theory and Methods
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Society for Industrial & Applied Mathematics,U.S., 1987
ISBN 10: 0898714435
ISBN 13: 9780898714432
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Perturbations: Theory and Methods: 27 (Classics in Applied Mathematics, Series Number 27)
Editore:
Society for Industrial and Applied Mathematics, 1987
ISBN 10: 0898714435
ISBN 13: 9780898714432
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Perturbations
Editore:
Society for Industrial and Applied Mathematics,U.S., US, 1999
ISBN 10: 0898714435
ISBN 13: 9780898714432
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Paperback. Condizione: New. Provides 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 knowledge of the geometry of the solutions is used to aid in the selection of an effective perturbation method.Dr. Murdock's approach differs from other introductory texts because he attempts to present perturbation theory as a natural part of a larger whole, the mathematical theory of differential equations. He explores the meaning of the results and their connections to other ways of studying the same problems. Codice articolo LU-9780898714432
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