ORDINARY DIFFERENTIAL EQUATIONS
Basic concepts: Phase spaces, Existence and uniquness theorems, Dependence on Initial conditions and associated flows. Linear systems: Fundamental matrix, Stability of equilibrium points. Sturm- Liouville theory. Nonlinear systems and their stability: Poincare-Bendixon theorem, Purturbed linear systems, Lyaounov methods.
Books
- Hartman, P., Ordinary Differential Equations, Birkhaeuser, 1982.
- Coddington, E. A. and Levinson, N., Theory of Ordinary Differential Equations, Tata McGraw-Hill, 1972.
- Perko, L., Differential Equations and Dynamical Systems, Springer-Verlag, 1991.
- Simmons, G. F., Differential Equations with Applications and Historical Notes, McGraw Hill, 1991.