Basics concepts:Introduction and examples through physical models, First and
second order equations, general and particular solutions, linear and nonlinear
systems, linear independence, solution techniques.
Existence and Uniqueness Theorems :Peano’s and Picard’s theorems, Grownwall’s
inequality, Dependence on initial conditions and associated flows.
Linear system:The fundamental matrix, stability of equilibrium points, Phase-
plane analysis, Sturm-Liouvile theory .
Nonlinear system and their stability:Lyapunov’s method, Non-linear Perturbation
of linear systems, Periodic solutions and Poincare- Bendixson theorem.

Suggested books and references:

Hartman, Ordinary Differential Equations, P. 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.