MA 3431Modeling with ODEs A term 1997

Text: Kostelich and Armbruster, Introductory Differential Equations

Professor: W. Farr, 109B Stratton, X5496, E-mail - bfarr.
Office Hours: 9-11 MTThF , or by appointment.

Course Goals

The primary goal of this course is to provide students with the knowledge and skills needed to analyze ODE models of physical, chemical, or biological systems. By the end of this course you will be able to find the steady states of a model described by a system of ODEs and compute their stability.

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 first of these is the CAS Maple, which is useful for solving for steady states, plotting vector fields, and solving (analytically and numerically) differential equations. To investigate asymptotic behavior, we will use the xrk simulation program.

Other secondary goals are for you to work in teams on extended problems and communicate your results. As part of the communication, we will be making use of the WWW for distributing class materials. You will also be strongly encouraged to use the web for communicating with each other, as well as with me.

Course Structure

Topics to be covered

Week 1
ODE review
Chaps. 1-5
Week 2
Linear systems
Secs. 6.1, 6.2, 6.3, 7.1, 7.2, 7.3
Week 3
Phase plane
Secs. 7.4, 7.5, 7.6
Week 4
Nonlinear systems
Secs. 8.1, 8.2, 8.3, 8.4
Week 5
Linearization, bifurcation
Secs. 8.5, 8.6, 8.7, 8.8
Week 6
More on biological and chemical models

Week 7
More on bifurcation

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William W. Farr
Tue Sep 9 15:24:51 EDT 1997