Details of MA4202 (Spring 2025)
| Level: 4 | Type: Theory | Credits: 4.0 |
| Course Code | Course Name | Instructor(s) |
|---|---|---|
| MA4202 | Ordinary Differential Equations | Saugata Bandyopadhyay |
| Syllabus |
|---|
| 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. |
| Prerequisite |
|---|
| Analysis II (MA2201) |
| References |
|---|
| 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. | Programme | Semester No | Course Choice |
|---|---|---|---|
| 1 | IP | 2 | Not Allowed |
| 2 | IP | 4 | Not Allowed |
| 3 | IP | 6 | Not Allowed |
| 4 | MP | 2 | Core |
| 5 | MP | 4 | Not Allowed |
| 6 | MR | 2 | Not Allowed |
| 7 | MR | 4 | Not Allowed |
| 8 | MS | 10 | Elective |
| 9 | MS | 4 | Not Allowed |
| 10 | MS | 6 | Not Allowed |
| 11 | MS | 8 | Core |
| 12 | RS | 1 | Elective |
| 13 | RS | 2 | Elective |