Asymptotic Analysis and Perturbation Theory

This self-contained text makes the difficult subject of asymptotics easy to comprehend. It immediately introduces asymptotic notation and then applies this tool to familiar problems, including limits, inverse functions, and integrals. Along the way, the book explores the properties of some important...

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Bibliographic Details
Main Author Paulsen, William
Format eBook Book
LanguageEnglish
Published United Kingdom Chapman & Hall 2013
Chapman and Hall/CRC
CRC Press, Taylor & Francis Group
CRC Press LLC
CRC Press
Edition1
Subjects
Asymptotic theory
Differential equations
Differential equations > Asymptotic theory > Textbooks
Mathematics
Perturbation (Mathematics)
Perturbation (Mathematics) > Textbooks
Textbooks
Continued Fraction
Bernoulli Polynomials
Euler Maclaurin Formula
Maclaurin Series
Richardson Extrapolation
Shanks Transformation
Asymptotic Series
Leading Behavior
Continued Fraction Representation
Regular Singular Point
Dominant Balance
Strained Coordinate
Irregular Singular Point
Generalized Richardson Extrapolation
Exact Solution
Airy Functions
Difference Equation
Arbitrary Constants
Recursion Formula
Full Asymptotic Expansion
Frobenius Series
Homogeneous Equation
Stieltjes Function
Inhomogeneous Equation
Borel Sum
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Cover

Table of Contents:
  • Front Cover -- Contents -- List of Figures -- List of Tables -- Preface -- Acknowledgments -- About the Author -- Symbol Description -- Chapter 1. Introduction to Asymptotics -- Chapter 2. Asymptotics of Integrals -- Chapter 3. Speeding Up Convergence -- Chapter 4. Differential Equations -- Chapter 5. Asymptotic Series Solutions for Differential Equation -- Chapter 6. Difference Equations -- Chapter 7. Perturbation Theory -- Chapter 8 WKBJ Theory -- Chapter 9. Multiple-Scale Analysis -- Guide to the Special Functions -- Answers to Odd-NumberedProblems -- Bibliography -- Back Cover