Dr. Thomas LoFaro
Dr. Kevin Cooper
Dr. Ray Huffaker
Pure and Applied Mathematics
Washington State University
Pullman, WA 99164
lofaro@tom.math.wsu.edu
Applications of
Differential Equations from Environmental and Life Sciences
The objective of this project is to develop a collection of computer
exercises illustrating the use of differential equations and modern
phase plane techniques to applications in the agricultural,
environmental, and life sciences. These will comprise a set of four
exploratory exercises utilizing available dynamical systems software.
The exercises will guide the student in developing the mathematical
models, analyzing these models using modern mathematical and
computational techniques, and finally interpreting the resulting
dynamical behavior in terms of the original applied problem.
Because of the origins of the field of differential equations, and its
close links with physics and engineering, this subject has hitherto had
a strong physical flavor. With a few exceptions, applications that are
seen in textbooks have come from the physical sciences, or have not
corresponded to natural phenomena at all. We propose to redress the
balance in favor of agricultural and biological exercises. This allows
students from disciplines in which the use of differential equations
has been limited to come to an understanding of how the subject can be
valuable in their fields.
We will utilize these exercises in our Intermediate and/or Advanced
Differential Equations as well as Natural Resource Economics courses in
the School of Agriculture to illustrate both mathematical concepts and
the utility of dynamical systems as a means of analyzing and
understanding applied problems. The university has several wellequipped
computer laboratories for the implementation of this project.
Although there are many outstanding examples of the use of dynamical
systems throughout the sciences, we plan to focus on these particular
fields because, as a major land grant university, one of the primary
missions Washington State University is the education of young men and
women going into these areas. We strongly believe that a project such
as this helps accomplish this goal.
Last modified: 17 July, 1997
Thomas L. Marchioro
uces_info@krellinst.org