Scaling, self-similarity and intermediate asymptotics
Math 488 Sec. G1
Spring 2001

Basic Information

Course outline

This is a "topics" course in applied mathematics. We aim for a working knowledge of similarity and asymptotic methods that will be useful for the future research of students in the class.

We will attempt to digest G. I. Barenblatt's book "Scaling, self-similarity and intermediate asymptotics" (Cambridge Texts in Applied Mathematics 14, 1996).

There will be only occasional homework. Students will make final presentations, hopefully on papers from the similarity literature.

Prerequisites: classical ordinary and partial differential equations. For example, Math 444 should provide plenty of background. But you also need a love of calculus and applications!

We plan to cover the following topics:

And I'll try to arrange some guest lectures from workers in the field.

Application areas we will encounter include: heat flow, nuclear explosions, fluid flow, filtration, shock waves, flame fronts, and fracture of solids. No prior knowledge of those areas is needed. We will just dive in and see what we can learn.

If you have any questions or concerns, please contact me by e-mail at laugesen@illinois.edu.

- Richard Laugesen