Here are the topics for the Applied Mathematics qualifying exam:
Dynamical Systems
- Stability of Equilibria
- Omega-limit sets
- Floquet Theory
- Lyapunov Functions
- Bifurcation Theory
- Poincaré-Bendixson
- Index Theory
- Hamiltonian Systems
Applied Mathematics
- Dimensional Analysis
- Buckingham pi-theorem
- Random walks and continuum limits
- Regular and Singular Perturbation Theory
- Boundary layer theory
- Calculus of Variations
- Hyperbolic Conservation Laws
- Modeling with PDE
Sources
- James D. Meiss, Differential Dynamical Systems
- C. C. Lin, L. A. Segel, Mathematics Applied to Deterministic Problems in the Natural Sciences
- J. David Logan, Applied Mathematics