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9780898714432 Academic Inspection Copy

Perturbations

Theory and Methods
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An introduction to both regular and singular perturbation methods for algebraic and differential equations. It 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 proved.
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.
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