Department of Mathematics

INDIAN INSTITUTE OF SCIENCE

MA 241: Ordinary Differential Equations

Credits: 3:1

Prerequisite courses: MA 221

(Additional )Prerequisite courses for Undergraduates: UM 204

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:

1. Hartman, Ordinary Differential Equations, P. Birkhaeuser, 1982.
2. Coddington, E. A. and Levinson, N., Theory of Ordinary Differential Equations, Tata McGraw-Hill, 1972.
3. Perko, L., Differential Equations and Dynamical Systems, Springer-Verlag, 1991.

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