Ordinary Differential Equations

Basics concepts: Phase space, existence and uniquness theorems, dependence on initial conditions, flows.

Linear system: The fundamental matrix, stability of equilibrium points. Sturm-Liouvile theory .

Nonlinear system and their stability: The Poincare-Bendixon theorem, perturbed linear systems, Lyapunov methods.

Books

• Coddington, E. A. and Levinson, N., Theory of Ordinary Differential Equations, Tata McGraw-Hill 1972.

• Birkhoff, G. and Rota, G.-C., Ordinary Differential Equations, wiley, 1989.

• Hartman, P., Ordinary Differential Equations, Birkhaeuser, 1982.