MA5390 Ordinary Differential Equations
Introduces the techniques for solving ordinary differential equations
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.
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.
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.