Teaching Page

Math 556: Industrial Mathematics (Outline)

Supplements to the Lectures: (.pdf files) The mathematical content, typsetting, and numerics, for some of the .pdf files below were expertly put together by Laura Dunwoody starting from my original notes for Math 556. Laura was an undergraduate research assistant in the IAM in the summer of 2007. I thank her for her contribution.

As I mentioned in class, you are to turn in 6 problem sets during the course worth a total of 60% of your grade. I will give a problem set roughly each week. However, you need turn in only 6 of them. If you are choosing to turn a particular assignment in, then you will have two weeks to do so. Collaboration is permitted, but you must turn in your own work. At the end of April, a final term paper of approximately 20 pages is due worth 40% of your grade. This term paper is to summarize the contents of a particular paper from a possible list that I will post in February, or perhaps a paper on a topic that you have found (in this case, please show me the paper in advance so that I can have a look and give my approval.)

Notes on Forced Nonlinear Oscillators Click here For other older notes click here

Application I: Stick-Slip Oscillations Click here

Notes on Hysteresis and Slow Passage Through Bifurcation Points: Saddle-Node Points Click here

Notes on Hysteresis and Slow Passage Through Bifurcation Points: Hopf-Bifurcation Points Click here

Hopf Bifurcation Notes Click here

Application II: Slow Passage Papers Click here

Notes on Floquet Theory I Click here

Notes on Floquet Theory II Click here

Notes on Delay Equations Click here For notes on perturbation methods applied to delay equations click here

Notes on Bifurcation Theory: Critical Patch Size in Ecology Click here: For notes on heat equation and Sturm Liouville: REVIEW from undergrad PDE (see pages 6--10) of Click here

Notes on MEMS Devices Click here

Notes on Steady-State Combustion Click here

Notes on Lubrication Theory Click here

Notes on Hopf Bifurcation Click here