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Indian Institute of Science Education and Research Bhopal

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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