擾動法

內容概要

本書是一部經(jīng)典教材，劍橋大學出版社初版于1991年，之后曾４次重印，由此證明本書很受讀者歡迎。全書共有8章，主要內容包括：代數(shù)方程，漸近逼近，積分，偏微分方程中的正則置換，匹配漸近展開式，應變座標方法，多重尺度法，改進收劍法。　　本書適用于應用數(shù)學及相關專業(yè)的高年級本科生和低年級研究生。

書籍目錄

Preface1 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 roots2 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 plane3 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 body4 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 cylinder5 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-ordinates7 Method of multiple scales8 Improved convergenceBibliographyIndex

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