MA5390 Ordinary Differential Equations
Existence-Uniqueness for systems:
Picard’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)
1. E.A. Coddington, An Introduction to Ordinary Differential Equations, PHI Learning 1999.
2. Tyn Myint U, Ordinary Differential Equations, Elesvier North- Holland, 1978.
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,