Perturbations – Theory and Methods
Theory and Methods

This book gives a thorough introduction to both regular and singular perturbation methods for algebraic and differential equations.

James A. Murdock (Author)

9780898714432

Paperback / softback, published 31 August 1999

530 pages
33.3 x 29.6 x 2.7 cm, 0.74 kg

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.

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.

Subject Areas: Miscellaneous items [WZ]