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Advanced Mathematical Methods for Scientists and Engineers I

Asymptotic Methods and Perturbation Theory

Authors: Bender, Carl M., Orszag, Steven A.

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  • ISBN 978-0-387-98931-0
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Softcover $99.00
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  • ISBN 978-1-4419-3187-0
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About this Textbook

The triumphant vindication of bold theories-are these not the pride and justification of our life's work? -Sherlock Holmes, The Valley of Fear Sir Arthur Conan Doyle The main purpose of our book is to present and explain mathematical methods for obtaining approximate analytical solutions to differential and difference equations that cannot be solved exactly. Our objective is to help young and also establiShed scientists and engineers to build the skills necessary to analyze equations that they encounter in their work. Our presentation is aimed at developing the insights and techniques that are most useful for attacking new problems. We do not emphasize special methods and tricks which work only for the classical transcendental functions; we do not dwell on equations whose exact solutions are known. The mathematical methods discussed in this book are known collectively as­ asymptotic and perturbative analysis. These are the most useful and powerful methods for finding approximate solutions to equations, but they are difficult to justify rigorously. Thus, we concentrate on the most fruitful aspect of applied analysis; namely, obtaining the answer. We stress care but not rigor. To explain our approach, we compare our goals with those of a freshman calculus course. A beginning calculus course is considered successful if the students have learned how to solve problems using calculus.

Reviews

"This book is a reprint of the original published by McGraw-Hill \ref [MR0538168 (80d:00030)]. The only changes are the addition of the Roman numeral I to the title and the provision of a subtitle, "Asymptotic methods and perturbation theory". This latter improvement is much needed, as the original title suggested that this was a teaching book for undergraduate scientists and engineers. It is not, but is an excellent introduction to asymptotic and perturbation methods for master's degree students or beginning research students. Certain parts of it could be used for a course in asymptotics for final year undergraduates in applied mathematics or mathematical physics.

This is a book that has stood the test of time and I cannot but endorse the remarks of the original reviewer. It is written in a fresh and lively style and the many graphs and tables, comparing the results of exact and approximate methods, were in advance of its time. I have owned a copy of the original for over twenty years, using it on a regular basis, and, after the original had gone out of print, lending it to my research students. Springer-Verlag has done a great service to users of, and researchers in, asymptotics and perturbation theory by reprinting this classic."  (A.D. Wood, Mathematical Reviews) 


Table of contents (11 chapters)

  • Ordinary Differential Equations

    Bender, Carl M. (et al.)

    Pages 3-35

  • Difference Equations

    Bender, Carl M. (et al.)

    Pages 36-57

  • Approximate Solution of Linear Differential Equations

    Bender, Carl M. (et al.)

    Pages 61-145

  • Approximate Solution of Nonlinear Differential Equations

    Bender, Carl M. (et al.)

    Pages 146-204

  • Approximate Solution of Difference Equations

    Bender, Carl M. (et al.)

    Pages 205-246

Buy this book

eBook $74.99
price for USA (gross)
  • ISBN 978-1-4757-3069-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.00
price for USA
  • ISBN 978-0-387-98931-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $99.00
price for USA
  • ISBN 978-1-4419-3187-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Advanced Mathematical Methods for Scientists and Engineers I
Book Subtitle
Asymptotic Methods and Perturbation Theory
Authors
Copyright
1999
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4757-3069-2
DOI
10.1007/978-1-4757-3069-2
Hardcover ISBN
978-0-387-98931-0
Softcover ISBN
978-1-4419-3187-0
Edition Number
1
Number of Pages
XIV, 593
Additional Information
Originally published by McGraw Hill, 1978
Topics