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.

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.

Last updated: 31 May 2023