Advanced Mathematical Methods for Scientists and Engineers I

Asymptotic Methods and Perturbation Theory

  • Carl M. Bender
  • Steven A. Orszag

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Fundamentals

    1. Front Matter
      Pages 1-2
    2. Carl M. Bender, Steven A. Orszag
      Pages 3-35
    3. Carl M. Bender, Steven A. Orszag
      Pages 36-57
  3. Local Analysis

    1. Front Matter
      Pages 59-60
    2. Carl M. Bender, Steven A. Orszag
      Pages 61-145
    3. Carl M. Bender, Steven A. Orszag
      Pages 146-204
    4. Carl M. Bender, Steven A. Orszag
      Pages 205-246
    5. Carl M. Bender, Steven A. Orszag
      Pages 247-316
  4. Perturbation Methods

    1. Front Matter
      Pages 317-318
    2. Carl M. Bender, Steven A. Orszag
      Pages 319-367
    3. Carl M. Bender, Steven A. Orszag
      Pages 368-416
  5. Global Analysis

    1. Front Matter
      Pages 417-417
    2. Carl M. Bender, Steven A. Orszag
      Pages 419-483
    3. Carl M. Bender, Steven A. Orszag
      Pages 484-543
    4. Carl M. Bender, Steven A. Orszag
      Pages 544-576
  6. Back Matter
    Pages 577-593

About this book

Introduction

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.

Keywords

calculus difference equation differential equation numerical methods ordinary differential equation

Authors and affiliations

  • Carl M. Bender
    • 1
  • Steven A. Orszag
    • 2
  1. 1.Department of PhysicsWashington UniversitySt. LouisUSA
  2. 2.Department of MathematicsYale UniversityNew HavenUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-3069-2
  • Copyright Information Springer-Verlag New York 1999
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-3187-0
  • Online ISBN 978-1-4757-3069-2
  • About this book