Details of ID4207 (Spring 2015)

Level: 8 Type: Theory Credits: 3.0

Course CodeCourse NameInstructor(s)
ID4207 Ordinary Differential Equations Saugata Bandyopadhyay

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 $ R^2$.

  • 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. E. A. Coddington and N. Levinson Theory of ordinary differential equations. McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955.

  2. M. W. Hirsch, S. Smale and R. L. Devaney Differential equations, dynamical systems, and an introduction to chaos, Second edition. Pure and Applied Mathematics (Amsterdam), 60. Elsevier/Academic Press, Amsterdam, 2004.

  3. P. Hsieh and Y. Sibuya Basic theory of ordinary differential equations, Universitext. Springer-Verlag, New York, 1999.

  4. L. Perko Differential equations and dynamical systems, Third edition. Texts in Applied Mathematics, 7. Springer-Verlag, New York, 2001.

Course Credit Options

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