### MA5390 Ordinary Differential Equations

#### Course Details

Existence-Uniqueness for systems:

Picardâ€™s theorem, Non-local existence theorem. (6 lectures)

Second Order Equations:

General solution of homogeneous equations, Non-homogeneous equations, Wronskian, Method of variation of parameters, Sturm comparison theorem, Sturm separation theorem, Boundary value problems, Green's functions, Sturm-Liouville problems. (15 lectures)

Series Solution of Second Order Linear Equations:

ordinary points, regular singular points, Legendre polynomials and properties, Bessel functions and properties. (15 lectures)

Systems of Differential Equations:

Algebraic properties of solutions of linear systems, The eigenvalueeigenvector method of finding solutions, Complex eigenvalues, Equal eigenvalues, Fundamental matrix solutions, Matrix exponential. (4 lectures)

#### Course References:

Text Books:

1. E.A. Coddington, An Introduction to Ordinary Differential Equations, PHI Learning 1999.

2. Tyn Myint U, Ordinary Differential Equations, Elesvier North- Holland, 1978.

Reference Books:

1. M. Braun, Differential Equations and Their Applications, 3rd Ed., Springer-Verlag, 1983.

2. G.F. Simmons, Differential Equations with Applications and Historical Notes, 2nd Ed.,McGrawHill, 1991.

3. P.J. Collins, Differential and Integral Equations, Oxford University Press, 2006.

4. W.E.Boyce and R.C. Di-Prima, Elementary Differential Equations and Boundary Value Problems,
John Wiely & Sons, 2001.

5. R.P. Agarwal and D. O'Regan, An Introduction to Ordinary Differential Equations, Springer- Verlag,
2008.