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扰动法
图书信息
出版社: 世界图书出版公司; 第1版 (2006年11月1日)
丛书名: 经典英文数学教材系列
平装: 160页
正文语种: 简体中文
ISBN: 7506282240
条形码: 9787506282246
尺寸: 22.2 x 14.6 x 0.8 cm
重量: 222 g
作者简介
作者：(英国)欣奇
内容简介
《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。
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
