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Advanced Mathematical Methods for Scientists and Engineers I

Asymptotic Methods and Perturbation Theory

  • Textbook
  • © 1999

Overview

Authors:
  1. Carl M. Bender

    1. Department of Physics, Washington University, St. Louis, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Steven A. Orszag

    1. Department of Mathematics, Yale University, New Haven, USA

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    You can also search for this author in PubMed   Google Scholar

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Fundamentals

    1. Front Matter

      Pages 1-2
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    2. Ordinary Differential Equations

      • Carl M. Bender, Steven A. Orszag
      Pages 3-35

    3. Difference Equations

      • Carl M. Bender, Steven A. Orszag
      Pages 36-57

  3. Local Analysis

    1. Front Matter

      Pages 59-60
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    2. Approximate Solution of Linear Differential Equations

      • Carl M. Bender, Steven A. Orszag
      Pages 61-145

    3. Approximate Solution of Nonlinear Differential Equations

      • Carl M. Bender, Steven A. Orszag
      Pages 146-204

    4. Approximate Solution of Difference Equations

      • Carl M. Bender, Steven A. Orszag
      Pages 205-246

    5. Asymptotic Expansion of Integrals

      • Carl M. Bender, Steven A. Orszag
      Pages 247-316

  4. Perturbation Methods

    1. Front Matter

      Pages 317-318
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    2. Perturbation Series

      • Carl M. Bender, Steven A. Orszag
      Pages 319-367

    3. Summation of Series

      • Carl M. Bender, Steven A. Orszag
      Pages 368-416

  5. Global Analysis

    1. Front Matter

      Pages 417-417
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    2. Boundary-Layer Theory

      • Carl M. Bender, Steven A. Orszag
      Pages 419-483

    3. WKB Theory

      • Carl M. Bender, Steven A. Orszag
      Pages 484-543

    4. Multiple-Scale Analysis

      • Carl M. Bender, Steven A. Orszag
      Pages 544-576

  6. Back Matter

    Pages 577-593
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Keywords

About this book

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) 

Authors and Affiliations

  • Department of Physics, Washington University, St. Louis, USA

    Carl M. Bender

  • Department of Mathematics, Yale University, New Haven, USA

    Steven A. Orszag

Bibliographic Information

  • Book Title: Advanced Mathematical Methods for Scientists and Engineers I

  • Book Subtitle: Asymptotic Methods and Perturbation Theory

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

  • DOI: https://doi.org/10.1007/978-1-4757-3069-2

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1999

  • Hardcover ISBN: 978-0-387-98931-0Published: 29 October 1999

  • Softcover ISBN: 978-1-4419-3187-0Published: 01 December 2010

  • eBook ISBN: 978-1-4757-3069-2Published: 09 March 2013

  • Edition Number: 1

  • Number of Pages: XIV, 593

  • Additional Information: Originally published by McGraw Hill, 1978

  • Topics: Analysis, Mathematical and Computational Engineering, Mathematical Methods in Physics, Numerical and Computational Physics, Simulation

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