Faculty of Science

Objectives

To introduce students to qualitative methods for analyzing nonlinear ordinary differential equations.

Contents

Linear systems with periodic coefficients (Floquet theory, Mathieu equation); Perturbation methods (direct methods, Poincaré-Lindstedt method, singular perturbations); Stability (Poincaré stability, Liapunov stability); Plane autonomous systems and determination of stability (perturbation methods, Liapunov methods, Poincaré-Bendixson theorem, averaging methods); Elementary bifurcations and chaos.