MTH 417, Ordinary Differential Equations, Fall 2018

Lectures

Tuesday 10:50-11:50

Friday 12:00-13:00

Tutorials

Monday 8:30-9:30

Weekly homework problems will be uploaded here.

Course contents

Linear ODEs of first and second order.

Linear systems of ODEs, planar linear systems, phase portraits for planar systems, higher-dimensional linear systems, stability theory, nonautonomous linear systems

Nonlinear systems of ODEs, existence and uniqueness theorem, continuous dependence of solutions, linearization, stability theory, gradient and Hamiltonian systems, closed orbits and limit sets, the Poincare map, Poincare-Bendixson theorem

References

1. E. A. Coddington, An introduction to ordinary differential equations

2. M. W. Hirsch, S. Smale, R. L. Devaney, Differential equations, dynamical systems, and an introduction to chaos

3. A.K. Nandakumaran, P. S. Datti, R. K. George, Ordinary differential equations

4. L. Perko, Differential equations and dynamical systems

5. G. F. Simmons, Differential equations with applications and historical notes   

Evaluation

End-sem 30%

Mid-sem 30%

Quizzes 40%