Details of MA4202 (Spring 2020)

Level: 4 Type: Theory Credits: 4.0

Course CodeCourse NameInstructor(s)
MA4202 Ordinary Differential Equations Rajib Dutta

Fundamental Theory: Existence of solutions under continuity, existence and uniqueness under Lipschitz condition, non-uniqueness and Kneser's theorem, extension of solutions, dependence of solutions with respect to initial data and parameter, flow of an ordinary differential equation.

Boundary-Value Problems of Linear Differential Equations of the Second Order: Zeros of solutions, Sturm-Liouville problems, eigenvalue problems, eigenfunction expansions.

Linear System: Exponentials of operators, fundamental theorem for linear systems,
linear systems in R2.

Stability Theory: Stable, unstable and asymptotically stable points; Liapunov functions; Stable manifolds.

Poincare-Bendixson Theory: Limit sets, local sections, Poincar_e-Bendixson theorem and its applications.

1. Barreira. L. and Valls, C., Ordinary Differential Equations: Qualitative Theory, American Mathematical Society .
2. Birkhoff. G. and Rota. G.C., Ordinary Differential Equations, Wiley.
3. Coddington, E.A. and Levinson, N., Theory of Ordinary Differential Equations, McGraw-Hill.
4. Hirsch, M.W., Smale, S. and Devaney, R.L., Differential Equations, Dynamical Sys-tems, and an Introduction to Chaos, Elsevier/Academic Press, Amsterdam.
5. Hsieh, P. and Sibuya, Y., Basic Theory of Ordinary Differential Equations, Springer-Verlag.
6. Perko, L., Differential Equations and Dynamical Systems, Springer-Verlag.
7. Simmons. G.F., Differentials Equations with Applications and Historical Notes, Tata McGraw-Hill.
8. Teschl. G., Ordinary Differential Equations and Dynamical Systems, American Math-ematical Society.

Course Credit Options

Sl. No.ProgrammeSemester NoCourse Choice
1 IP 2 Core
2 IP 4 Core
3 IP 6 Not Allowed
4 MR 2 Not Allowed
5 MR 4 Not Allowed
6 MS 8 Core
7 RS 1 Not Allowed
8 RS 2 Not Allowed