Introduction

Many physical processes are modelled by differential equations which involve delays. This course will provide an introduction to delay differential equations (DDEs) suitable for graduate students or upper level honours students with the correct background.

This course will concentrate on the key tools needed to understand the behaviour of these equations, and also some of numerical techniques used to approximate solutions. Throughout we will emphasise the similarities and differences between DDEs and ordinary differential equations.

Topics covered will include: DDEs as infinite dimensional dynamical systems, breaking points and smoothing of DDE solutions, continuous Runge-Kutta methods for ODEs and DDEs, linear stability of steady states, bifurcation theory. A selection of more advanced topics will also be covered. The choice of topics will depend on time and the preferences of the participants, but may include state-dependent delays, distributed delays, numerical continuation and bifurcation techniques.

Audience/Prerequisites

The course is intended for upper level undergraduate or graduate students with an interest in delay differential equations and their numerical solution. While it is mainly aimed at graduate students or upper level honours undergraduate students in mathematics, there are no explicit prerequisites other than having a suitable level of mathematical maturity. In particular, it is not required to have previous knowledge of delay differential equations -- these are not included in standard curricula so I will not assume any previous knowledge.

It would be very useful, but not essential, to have some knowledge of dynamical systems and numerical analysis.

For students interested in the material, but not in a position to register for math597, there may be other avenues to participate in the course and gain credit. Please contact me if you are in this situation.

References

There in no required text book for this course. However some material from the following texts may be useful:

Registration

Be aware that there are two Math597 courses in the Fall semester. This course is Section 2 (while Section 1 is Convex Optimization).

PhD students should register in Math761 Section 2, while Masters students and undergraduates should register in Math597 Section 2.

The registration process is complicated. You need to complete a form that I can give you, in order to get permission to register. Once you have permission, you can register on minerva. Tuesday 18th September is the add/drop deadline to either register or drop the course.

The course is open to undergraduate honours applied mathematics or honours mathematics students. Strictly speaking, to register in math597 you should have completed at least 30 credits in required or complementary courses from the Honours in Applied Mathematics program, and have the permission of the Department of Mathematics and Statistics. If you are interested in following the course but do not satisfy those conditions please contact me.

Further Information