Standard syllabus
Asymptotic & perturbation methods · Graduate · Math
Topics
Perturbation series
- Regular perturbation theory for algebraic equations
- Poincaré–Lindstedt method for periodic solutions
- Method of multiple scales for weakly nonlinear oscillators
- Averaging methods (Kruskal–Prudnikov / standard forms, introduction)
- Renormalization group methods (introduction)
Boundary layers and matched asymptotics
- Singular perturbations and inner/outer expansions
- Method of matched asymptotic expansions
- WKB theory for linear ODEs with large parameters
- Turning points and connection formulas (overview)
- Boundary-layer theory for PDEs (introduction)
Integral asymptotics
- Laplace's method and Watson's lemma
- Method of stationary phase
- Steepest descent and saddle-point methods (introduction)
- Asymptotics of special functions
- Summation of divergent series: Borel summability (introduction)
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