扰动法(英文版)

书籍目录

Preface

1 Algebraic equations

  1.1 Iteration and expansion

    lterative method

    Expansion method

  1.2 Singular perturbations and rescaling

    Iterative method

    Expansion method

    Rescaling in the expansion method

  1.3 Non-integral powers

    Finding the ezpansion sequence

    lterative method

  1.4 Logarithms

  1.5 Convergence

  1.6 Eigenvalue problems

    Second order perturbations

    Multiple roots

    Degenerate roots

2 Asymptotic approximations

  2.1 Convergence and asymptoticness

  2.2 Definitions

  2.3 Uniqueness and manipulations

  2.4 Why asymptotic?

    Numerical use of diverging series

  2.5 Parametric expansions

  2.6 Stokes phenomenon in the complex plane

3 Integrals

  3.1 Watson's lemma

    Application and explanation

  3.2 Integration by parts

  3.3 Steepest descents

    Global considerations

    Local considerations

    Example: Stirling's formula

    Example: Airy function

  3.4 Non-local contributions

    Example I

    Example 2

    Splitting a range of integration

    Logarithms

  3.5 An integral equation: the electrical capacity of a long slender body

4 Regular perturbation problems in partial differential equations

  4.1 Potential outside a near sphere

  4.2 Deformation of a slowly rotating self-gravitating liquid mass

  4.3 Nearly'uniform inertial flow past a cylinder

5 Matched asymptotic expansion

  5.1 A linear problem

    5.1.1 The exact solution

    5.1.2 The outer approximation

    5.1.3 The inner approximation (or boundary layer solution)

    5.1.4 Matching

    5.1.5 Van Dyke's matching rule

    5.1.6 Choice of stretching

    5.1.7 Where is the boundary layer?

    5.1.8 Composite approximations

  5.2 Logarithms

    5.2.1 The problem and initial observations

    5.2.2 Approximation for r fixed as e\0

    5.2.3 Approximation for p = er fixed as e \0

    5,2.4 Matching by intermediate variable

    5.2.5 Further terms

    5.2.6 Failure of Van Dyke's matching rule

　　……

6 Method of strained co-ordinates

7 Method of multiple scales

8 Improved convergence

Bibliography

Index

作者简介

本书是一部经典教材，剑桥大学出版社初版于1991年，之后曾４次重印，由此证明本书很受读者欢迎。全书共有8章，主要内容包括：代数方程，渐近逼近，积分，偏微分方程中的正则置换，匹配渐近展开式，应变座标方法，多重尺度法，改进收剑法。

　　本书适用于应用数学及相关专业的高年级本科生和低年级研究生。

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