Details of ID4207 (Spring 2013)
| Level: 4 | Type: Theory | Credits: 3.0 |
| Course Code | Course Name | Instructor(s) |
|---|---|---|
| ID4207 | Ordinary Differential Equations | Priyanka Shukla |
| Syllabus |
|---|
| Fundamental Theory: Existence of solutions under continuity, existence and uniqueness under Lipschitz condition, non-uniqueness and Knesers theorem. Extension of solutions. Dependence of solutions with respect to initial data and parameter. The flow of an ordinary differential equation.
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. Poincar-Bendixson Theory: Limit sets, local sections. Poincar-Bendixson Theorem and its applications. Boundary-Value Problems of Linear Differential Equations of the Second-Order: Zeros of solutions, Sturm-Liouville Problems, Eigenvalue problems, Eigenfunction expansions. |
| References |
|---|
| 1. Coddington E. A. and Levinson N. Theory of ordinary differential equations. McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955.
2. Hirsch M. W., Smale S and Devaney R. L. Differential equations, dynamical systems, and an introduction to chaos. Second edition. Pure and Applied Mathematics (Amsterdam), 60. Elsevier/Academic Press, Amsterdam, 2004. 3. Hsieh P and Sibuya Y. Basic theory of ordinary differential equations. Universitext. Springer-Verlag, New York, 1999. 4. Perko L. Differential equations and dynamical systems. Third edition. Texts in Applied Mathematics, 7. Springer-Verlag, New York, 2001. |
Course Credit Options
| Sl. No. | Programme | Semester No | Course Choice |
|---|---|---|---|
| 1 | IP | 2 | Elective |
| 2 | IP | 4 | Elective |
| 3 | MS | 8 | Elective |
| 4 | RS | 1 | Elective |