**MTH ****306: Ordinary Differential Equations**** ****(4)**

**Pre-requisites**: MTH 303 Real Analysis I

First-Order Linear equations: exact equations, orthogonal trajectories, homogeneous equations, integrating factors, reduction of order

Second-order linear equations: equations with constant coefficients, method of undetermined coefficients, variation of parameters, power series solutions, special functions, applications

Higher-order linear equations

Some basic concepts of Fourier series

Quick review of elementary linear algebra, Picard’s existence and uniqueness theorem, Sturm comparison theorem

Systems of first-order equations, homogeneous linear systems with constant coefficients

Non-linear equations: critical points and stability, Liapunov’s direct method, Poincare-Bendixson theory

*Suggested Books*:

- George F. Simmons & Steven Krantz,
*Differential equations*, Paperback edition, Tata-McGraw Hill 2009 - G. Birkhoff & G. C. Rota,
*Ordinary differential equations*, Paperback edition, John Wiley &Sons, 1989 - E. Coddington & N. Levinson,
*Theory of ordinary differential equations*, Paperback edition, Tata-McGrawa Hill, 2008 - W. Hurewicz,
*Lectures on ordinary differential equations*, Dover, New York, 1999

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