Asymptotic Analysis and Perturbation Theory
- Introduction to Asymptotics
- Basic De finitions
- Defi nition of ~ and <<
- Hierarchy of Functions
- Big O and Little o Notation
- Asymptotics of Integrals
- Integrating Taylor Series
- Repeated Integration by Parts
- Optimal asymptotic approximation
- Laplace’s Method
- Review of Complex Numbers
- Method of Stationary Phase
- Method of Steepest Descents
- Speeding Up Convergence
- Shanks Transformation
- Generalized Shanks Transformation
- Differential Equations
- Asymptotic Series Solutions for Di Differential Equations
- Di fference Equations
- Perturbation Theory
- WKBJ Theory
- Multiple-Scale Analysis
- Appendix{Guide to the Special Functions