扰动法
2006-11
世界图书出版公司
欣奇
160
无
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。
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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非常经典，可惜没有对应的中文，所以要多花点时间看，但是值得推荐。