Nonlinear dynamic systems; phase plane and nonlinear phenomena; stability; invariance theory; asymptotic methods; geometric methods.

Basic definitions; review of basic theory of ordinary differential equations; phase plane analysis and nonlinear phenomena

Stability definitions and Lyapunov's direct (second) method; total stability; LaSalle's theorem

Stability of linear time-varying systems and Lyapunov's indirect method; periodic systems

Asymptotic methods, including averaging and singular perturbations.

Introduction to geometric methods and elementary bifurcation theory

• H. K. Khalil, Nonlinear Systems, 2nd Ed., Prentice-Hall, 1996.
• M. Vidyasagar, Nonlinear Systems Analysis, 2nd Ed., Prentice-Hall, 1993 (Recommended).

MATH 341 or consent of instructor.

1 unit.