MA 2431 Mathematical Modeling with ODEs B term 2006

Text: Paul Waltman, A Second Course in Elementary Differential Equations
Professor: W. Farr, 105A Stratton, X5496, E-mail - bfarr.
Office Hours: MWF 11-1, TR 9-11, or by appointment.
Web page: http://www.math.wpi.edu/Course_Materials/MA2431B06/

Course Goals

The primary goal of this course is to provide students with the knowledge and skills needed to derive and analyze ODE models of physical, chemical, or biological systems. This requires some additional background on ODE's as well as some material on deriving models and making them non-dimensionless.

We will find that this process can become rather involved, even for relatively simple models, so a secondary goal for this course is for you to become familiar with some computer tools. The main one of these is the CAS Maple, which is useful for solving for steady states, plotting vector fields, and solving (analytically and numerically) differential equations.

Anther secondary goal is for you to work in teams on extended problems and communicate your results orally and in writing. Analyzing a model on your own provides a valuable experience that is a lot different from following what I do in class!

Course Structure

Topics to be covered

Week 1
Introduction to Modeling, Systems of ODE's
Secs. 1.1, 1.2, 1.3, 1.4
Week 2
Constant Coefficient Linear Systems
Secs. 1.5, 1.6, 1.7, 1.8
Week 3
Non-homogeneous systems, periodic systems
Secs. 1.9, 1.10, 1.12, 2.1, 2.2
Week 4
Phase plane
Secs. 2.3, 2.4, 2.5, 2.7
Week 5
Non-dimensionalization
Class Notes
Week 6
Examples

Week 7
Project presentations

William W. Farr
2006-10-25