Perturbations: Theory and Methods

Erscheinungsjahr 1987
ISBN: 978-0-89871-443-2
Verlag: Society for Industrial & Applied Mathematics,U.S.

Buch, Englisch, 529 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 714 g

Reihe: Classics in Applied Mathematics

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.

Autoren/Hrsg.

Murdock, James A.

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematische Analysis

Inhaltsverzeichnis

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.