Perturbations: theory and methods
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Philadelphia, Pa.
Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104)
1999
|
| Schriftenreihe: | Classics in applied mathematics
27 |
| Schlagworte: | |
| Online-Zugang: | TUM01 UBW01 UBY01 UER01 Volltext |
| Beschreibung: | Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader Includes bibliographical references and indexes Preface to the Classics edition -- Preface -- Part I. Introduction to perturbation theory. Chapter 1. Root finding -- Chapter 2. Regular perturbations -- Chapter 3. Direct error estimation -- Part II. Oscillatory phenomena. Chapter 4. Periodic solutions and Lindstedt series -- Chapter 5. Multiple scales -- Chapter 6. Averaging -- Part III. Transition layers. Chapter 7. Initial layers -- Chapter 8. Boundary layers -- Chapter 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 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. 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 |
| Beschreibung: | 1 Online-Ressource (xx, 509 Seiten) |
| ISBN: | 0898714435 9780898714432 |
| DOI: | 10.1137/1.9781611971095 |
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| 500 | |a Includes bibliographical references and indexes | ||
| 500 | |a Preface to the Classics edition -- Preface -- Part I. Introduction to perturbation theory. Chapter 1. Root finding -- Chapter 2. Regular perturbations -- Chapter 3. Direct error estimation -- Part II. Oscillatory phenomena. Chapter 4. Periodic solutions and Lindstedt series -- Chapter 5. Multiple scales -- Chapter 6. Averaging -- Part III. Transition layers. Chapter 7. Initial layers -- Chapter 8. Boundary layers -- Chapter 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 | ||
| 500 | |a 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. 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 | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Murdock, James A. |
| author_GND | (DE-588)172268427 |
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| discipline | Mathematik |
| doi_str_mv | 10.1137/1.9781611971095 |
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| spelling | Murdock, James A. (DE-588)172268427 aut Perturbations theory and methods James A. Murdock Philadelphia, Pa. Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104) 1999 1 Online-Ressource (xx, 509 Seiten) txt rdacontent c rdamedia cr rdacarrier Classics in applied mathematics 27 Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader Includes bibliographical references and indexes Preface to the Classics edition -- Preface -- Part I. Introduction to perturbation theory. Chapter 1. Root finding -- Chapter 2. Regular perturbations -- Chapter 3. Direct error estimation -- Part II. Oscillatory phenomena. Chapter 4. Periodic solutions and Lindstedt series -- Chapter 5. Multiple scales -- Chapter 6. Averaging -- Part III. Transition layers. Chapter 7. Initial layers -- Chapter 8. Boundary layers -- Chapter 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 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. 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 Perturbation (Mathematics) Störungstheorie (DE-588)4128420-3 gnd rswk-swf Störungstheorie (DE-588)4128420-3 s DE-604 Society for Industrial and Applied Mathematics Sonstige oth Erscheint auch als Druck-Ausgabe, Paperback 0898714435 (DE-604)BV013070731 Erscheint auch als Druck-Ausgabe, Paperback 9780898714432 Classics in applied mathematics 27 (DE-604)BV040633091 27 https://doi.org/10.1137/1.9781611971095 Verlag Volltext |
| spellingShingle | Murdock, James A. Perturbations theory and methods Classics in applied mathematics Perturbation (Mathematics) Störungstheorie (DE-588)4128420-3 gnd |
| subject_GND | (DE-588)4128420-3 |
| title | Perturbations theory and methods |
| title_auth | Perturbations theory and methods |
| title_exact_search | Perturbations theory and methods |
| title_full | Perturbations theory and methods James A. Murdock |
| title_fullStr | Perturbations theory and methods James A. Murdock |
| title_full_unstemmed | Perturbations theory and methods James A. Murdock |
| title_short | Perturbations |
| title_sort | perturbations theory and methods |
| title_sub | theory and methods |
| topic | Perturbation (Mathematics) Störungstheorie (DE-588)4128420-3 gnd |
| topic_facet | Perturbation (Mathematics) Störungstheorie |
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