Text: Kostelich and Armbruster, *Introductory Differential
Equations*

Professor: W. Farr, 109B Stratton, X5496, E-mail - bfarr.

Office Hours: 9-11 MTThF , or by appointment.

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.

- Homework

There will be weekly homework assignments that will be collected and graded. Some will be paper and pencil problems from the book, others will require the use of a computer. Homework scores will count as 35% of your final grade. - Exams

There will be two in-class exams. Each will count 20% of your final grade. Tentative exam dates are 9-19 and 10-10. - Major Project

You will work in teams on a major project, analyzing a particular model. A report will be required. This project will be worth 25% of your final grade.

**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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