| Credit Hours: |
3-0-3 |
| Prerequisites: |
Sufficient background in undergraduate mathematics; at least calculus through differential equations and linear algebra. Knowledge of computer packages such as MATLAB are strongly recommended, graduate standing. |
| Catalog Description: |
Investigation of nonlinear systems using analytical and numerical techniques. |
| Textbooks: |
Dominic W. Jordan, Peter Smith, and P. Smith; Nonlinear Ordinary Differential Equations, 3rd Edition, Oxford University Press, 1999. |
| Instructors: |
Aldo Ferri |
| Topics: |
- Introduction; properties of nonlinear systems
- Phase portraits for second order systems; characterization of singular points and local stability; first and second methods of Lyapunov
- Limit cycles; Poincaré Index; Poincaré-Bendixon Theorem
- Time-integration techniques for nonlinear initial value problems
- Averaging techniques
- Perturbation methods
- Harmonic balance and sinusoidal describing functions
- Subharmonic and superharmonic response to sinusoidal excitation
- Parametric excitation; Mathieu/Hill equations; Floquet theory.
- Partial differential equations; Perturbation methods, Galerkin methods.
|
| Grading Scheme (%): |
Homework |
20 |
Midterm |
30 |
Final |
50 |
|
