Teaching: (Fall 2015) Asymptotics and Perturbation Methods
Natural phenomena and engineering
design usually depend on a large number of parameters, and their
scientific enquiry is fraught with the possibility of too many such
parameters. Furthermore, for many cases, these parameters lie in an
extreme regime, which cannot be captured adequately by numerical
solutions. Computational studies, therefore, frequently remain
suggestive but inconclusive.
In this course, we present asymptotic and perturbation methods as an alternative method of inquiry, which complements numerical methods. Asymptotic and perturbation methods help build accurate intuition about the phenomena under consideration, and the analytical nature of the method leads to conclusive result. These methods have recently seen a revival in the scientific literature with enormous success. Key examples from the literature will also be considered.