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Theory and Methods

Part of Classics in Applied Mathematics

  • Date Published: August 1999
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial null Mathematics for availability.
  • format: Paperback
  • isbn: 9780898714432


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About the Authors
  • 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.

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    Product details

    • Date Published: August 1999
    • format: Paperback
    • isbn: 9780898714432
    • length: 529 pages
    • dimensions: 228 x 155 x 28 mm
    • weight: 0.714kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial null Mathematics for availability.
  • Table of Contents

    Preface to the classics edition
    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

  • Author

    James A. Murdock

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