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

Simmons, Differential Equations with Applications and Historical Notes, 2 nd Ed.,McGraw- Hill, 1991. Agarwal and R.C.Gupta, Essentials of Ordinary Differential Equations, McGraw-Hill, 1993. Braun, Differential Equations and Their Applications, 3rd Ed., Springer-Verlag, 1983. References: 1. Collins, Differential and Integral Equations, Oxford University Press, 2006.

Differential Equations with Applications and Historical Notes, Third Edition.

Simmons and S.G. Krantz, Differential Equations: Theory, technique and practice, Tata McGraw-Hill, 2007. W.E.Boyce and R.C. Di-Prima, Elementary Differential Equations and Boundary Value Problems, John Wiely & Sons, 2001. Agarwal and D. O'Regan, An Introduction to Ordinary Differential Equations, Springer- Verlag, 2008.

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