MA5390 Ordinary
Differential Equations Objectives:
Introduces the techniques for solving ordinary differential equations
Course contents:
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. 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, 2^{nd} 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. |