University of Wyoming
Rocky Mountain Mathematics Consortium
Summer Conference

Dynamic Equations on Time Scales and Their Applications

July  8--19, 2002
University of Wyoming
Laramie, Wyoming



 

Allan Peterson
Department of Mathematics
University of Nebraska-Lincoln

Lincoln, NE 68588-0323
apeterso@math.unl.edu

Martin Bohner
Department of Mathematical Sciences

Florida Institute of Technology
Melbourne, FL
bohner@umr.edu

Two presentations (each 75 minutes) will be given each morning by the lecturers. Informal discussions, problem solving sessions, and contributed talks will be scheduled for the afternoon. There will be no afternoon talks either Friday, July 12 or Friday, July 19.

The study of dynamic equations on time scales, which has recently received a lot of attention, was introduced by Stefan Hilger in his Ph.D. thesis in 1988 (supervised by Bernd Aulbach) in order to unify continuous and discrete analysis. A time scale is just a closed subset of the real numbers. When the time scale is the set of real numbers the dynamic equation is a differential equation and when the time scale is the set of integers the dynamic equation is a difference equation. These lectures will be an introduction to the study of dynamic equations on time scales. We will only assume that the participants have had a first course in differential equations and a first course in linear algebra. We will systematically go through the book of Bohner and Peterson which is listed below. During the second week of the lectures we will discuss some of the latest developments in this area of research and discuss open problems. Anyone interested in differential equations or difference equations will be interested in attending these lectures.

There are numerous applications of dynamic equations on time scales in biology, engineering, economics, physics, social sciences and nerual networks. For example, a dynamic equation where the time scale consists of disjoint closed intervals can model insect populations that are continuous while in season, die out in (say) winter, while their eggs are incubating or dormant, and then hatch in a new season, giving rise to a nonoverlapping population. Another example of this type is an electric RLC circuit where the capacitor is periodically discharged. Several time scales are very important for numerically approximating solutions of differential equations. The so called q-difference equations are important in the asymptotic behavior of solutions. Many examples will be given during these lectures.

PREREQUISITES

TEXTS

Martin Bohner and Allan Peterson, Dynamic Equations on Time Scales: An Introduction With Applications, Birkhauser, Boston, 2001. The book normally costs about $55 and you will get a 20% discount if you purchase this book at the conference. Please indicate your desire to purchase the book when registering for the conference.

COURSE OUTLINE

ROOM AND BOARD STIPENDS

A limited number of stipends to cover the cost of room and board are available. These will be issued on a competitive basis and will be divided among both faculty and graduate students. Participants who wish to pay their own room and board will be accepted as long as space is available. Double rooms and board are $375 per person, and a single room and board is $450. Participants who do not wish to apply for funding should indicate this in writing. In addition, both e-mail and regular addresses should be included.

FACULTY APPLICATIONS

Each faculty applicant seeking funding should submit a vita and a letter describing his or her professional aspirations and what he or she hopes to accomplish by participation in this conference. A letter of recommendation from the applicant's department chairperson should accompany the application. Faculty not seeking funding should fill out the conference registration form .

GRADUATE STUDENT APPLICATIONS

Graduate students should apply following the instructions on the conference registration form. A letter of recommendation from a major professor or department chairperson is also required and can be e-mailed or sent directly to the address below.

DEADLINES

The deadline for application is April 1, 2002. Applications received after this date will be considered as long as space and funds are available. Applications processed after May 28, 2002 may be assessed a $50.00 late fee. For further information please contact:


        Bryan Shader
        Mathematics Department

        University of Wyoming

        P.O. Box 3036

        Laramie, WY  82071

        bshader@uwyo.edu