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 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-ordinates
7 Method of multiple scales
8 Improved convergence
Bibliography
Index
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