Notes to Instructor
We intend this module to be an introduction to the use of mathematical models in population dynamics. Several other JOMA modules cover natural growth or exponential models (Exploration: Exponential Functions and Derivatives, Exponential Functions), logistic growth (Logistic Growth Model), coalition growth models (World Population Growth) and briefly introduce Predator-Prey models (Predator Prey). This module allows students to consider some of these models from a biological perspective. (A follow-up module on Predator-Prey models is planned.) The module includes harvesting and various functional responses of the population growth rate. Our purposes are to incorporate biologically significant phenomena into the mathematics and to connect the terminology between the disciplines.
Technical Issues: In order to use this module, you will need a maplet-capable version of MAPLE (version 8.0 or higher), and a minimum screen resolution of 800x600. Maplets are not available in earlier versions of MAPLE. Maplets allow the programmer to create graphical interfaces instead of worksheets, thereby allowing the user access to the power of MAPLE without having to learn MAPLE syntax. The differential equation solver in the maplet is a Runge-Kutta 4 numerical method, and in certain instances errors can accumulate and distort the results.
Prerequisites: We assume basic knowledge of differential equations and their use in mathematical models. It would be appropriate to assign this module in a sophomore-level differential equations course or an introductory mathematical biology course.