Text: Kostelich and Armbruster, Introductory Differential
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.
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.
There will be two in-class exams. Each will count 20% of your final
grade. Tentative exam dates are 9-17 and 10-8.
- 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
- 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