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.

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