圖書信息
出版社: 世界圖書出版公司; 第1版 (2006年11月1日)
叢書名: 經典英文數學教材系列
平裝: 160頁
正文語種: 簡體中文
ISBN: 7506282240
條形碼: 9787506282246
尺寸: 22.2 x 14.6 x 0.8 cm
重量: 222 g
作者簡介
作者：(英國)欣奇
內容簡介
《擾動法》是一部經典教材，劍橋大學出版社初版於1991年，之後曾4次重印，由此證明《擾動法》很受讀者歡迎。全書共有8章，主要內容包括：代數方程，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。
《擾動法》適用於套用數學及相關專業的高年級本科生和低年級研究生。
目錄
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
