Dr Michael Chen, The University of Adelaide
Differential equation models of real world problems are often very complex. Perturbation methods and asymptotic techniques can be used to systematically derive simpler versions of these models by exploiting the presence of small (or large) parameters; the idea being that the new model is mathematically tractable and still describes the behaviour of the original. This is useful, for example, in problems which involve slender geometries, or for situations where both small and large time scales are important.
This course is a broad introduction to asymptotic techniques and their application. Topics covered include: asymptotic evaluation of integrals; perturbation methods; boundary-layer theory; asymptotic matching; multi-scale analysis and asymptotics beyond all orders. Case studies will be used to demonstrate the utility of these techniques for problems from fluid mechanics, biology and industry.
Introduction to asymptotics
Regular perturbation methods
Boundary layer theory and matching
Evaluation of integrals
(Assessment subject to change)
Lecture notes will be provided during the course.
(Optional) Some books in this area include:
Pre-course quiz will be available shortly
Dr Michael Chen
The University of Adelaide
Mike Chen is a lecturer in applied mathematics at the University of Adelaide. His research uses a combination of computational and asymptotic techniques to look at problems drawn from biology and industry. He has previously held positions at the University of Tasmania, University of Adelaide and University of Oxford.