## Details of MA4202 (Spring 2020)

Level: 4 |
Type: Theory |
Credits: 4.0 |

Course Code | Course Name | Instructor(s) |
---|---|---|

MA4202 |
Ordinary Differential Equations |
Rajib Dutta |

Syllabus |
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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. |

References |
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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 | 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 |