Ordinary Differential Equations
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.
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.