### MA5390 Ordinary Differential Equations

#### Course Details

Existence-Uniqueness: Review of exact solutions of first order, The method of successive approximations, Lipschitz condition, Convergence of successive approximations, Existence and Uniqueness of solutions of initial value problem, Non-local existence of solutions, Existence and uniqueness of solutions to systems, Existence and uniqueness of solutions to linear systems, Equations of order n.

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.

Series Solution of Second Order Linear Equations: ordinary points, regular singular points, Legendre polynomials and properties, Bessel functions and properties.

Systems of Differential Equations: Algebraic properties of solutions of linear systems, The eigenvalue-eigenvector method of finding solutions, Complex eigenvalues, Equal eigenvalues, Fundamental matrix solutions, Matrix exponential, Nonhomogeneous equations, Variation of parameters.

#### Course References:

Text Books:

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

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

3. R.P. Agarwal and R.C.Gupta, Essentials of Ordinary Differential Equations, McGraw-Hill, 1993.

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

References:

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

2. G.F. Simmons and S.G. Krantz, Differential Equations: Theory, technique and practice, Tata McGraw-Hill, 2007.

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

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