扰动法 目录

Preface1 Algebraic equations1.1 Iteration and expansionlterative methodExpansion method1.2 Singular perturbations and rescalingIterative methodExpansion methodRescaling in the expansion method1.3 Non-integral powersFinding the ezpansion sequencelterative method1.4 Logarithms1.5 Convergence1.6 Eigenvalue problemsSecond order perturbationsMultiple rootsDegenerate roots2 Asymptotic approximations2.1 Convergence and asymptoticness2.2 Definitions2.3 Uniqueness and manipulations2.4 Why asymptotic?Numerical use of diverging series2.5 Parametric expansions2.6 Stokes phenomenon in the complex plane3 Integrals3.1 Watson's lemmaApplication and explanation3.2 Integration by parts3.3 Steepest descentsGlobal considerationsLocal considerationsExample: Stirling's formulaExample: Airy function3.4 Non-local contributionsExample IExample 2Splitting a range of integrationLogarithms3.5 An integral equation: the electrical capacity of a long slender body4 Regular perturbation problems in partial differential equations4.1 Potential outside a near sphere4.2 Deformation of a slowly rotating self-gravitating liquid mass4.3 Nearly'uniform inertial flow past a cylinder5 Matched asymptotic expansion5.1 A linear problem5.1.1 The exact solution5.1.2 The outer approximation5.1.3 The inner approximation (or boundary layer solution)5.1.4 Matching5.1.5 Van Dyke's matching rule5.1.6 Choice of stretching5.1.7 Where is the boundary layer?5.1.8 Composite approximations5.2 Logarithms5.2.1 The problem and initial observations5.2.2 Approximation for r fixed as e\05.2.3 Approximation for p = er fixed as e \05,2.4 Matching by intermediate variable5.2.5 Further terms5.2.6 Failure of Van Dyke's matching rule

扰动法 内容简介

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。

扰动法 节选

《扰动法》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《扰动法》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。《扰动法》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。