This is a subsite associated with the parent site called IDEA (Internet Differential Equation Activities). The activity on this page is an introduction to exponential and logistic growth models applied to various ecological systems. Nine problems explore such concepts as asymptotic behavior, carrying capacity, harvesting, equilibriums, and stability. Java applet graphing utilities are conveniently placed throughout to provide visualization of solutions.
Type of Material:
Simulation and tutorial
A source of lab assignments or similar activities with applications of differential equations
Identify Major Learning Goals:
This site provides students and teachers with computer-based activities for differential equations in a wide variety of disciplines.
Target Student Population:
Students studying Applied Differential Equations.
Prerequisite Knowledge or Skills:
Basic course of Ordinary Differential Equations.
A main strength of this sites content lies in its collection of laboratory projects/exercises that connect the theory of Differential Equations to various problems in biology and ecology. There are nine problems on the site associated with different growth models that are actually practice exercises that students can attempt on their own. The important concepts of Differential Equations such as asymptotic behavior, equilibrium, and stability are related to biological concepts of population growth, harvesting, etc.
The Java-applet tools and graphing utilities provide immediate visualization and computational components that reinforces the basic ideas of the site. A hyperlinked glossary provides definitions and clarifies concepts.
The wording of some of the problems is unnecessarily vague. Problem #3 speaks of initial conditions between 0 and 1 without identifying the variables involved. Problem #4 asks for a conclusion in which two things are shown to be qualitatively identical without specifying the criteria for this judgment. In several problems, the reader is asked to explain conclusions in terms of the model. By model, does the author mean the equation or does he mean the ecological system as modeled by the equation? All of these concerns would be fairly insignificant to anyone experienced in modeling with differential equations. But to a student in an introductory DE course, they could be quite confusing.
Potential Effectiveness as a Teaching Tool
Connecting mathematics to its scientific applications is very important to assure that students are able to use mathematics in context. Efforts such as this site in particular and IDEA project in general are a step in the right direction. The Differential Equation component of the site is presented as arising out of concrete biological and ecological problems. Then the DE is used as a tool to analyze the problem and assess the model. This reinforces the basic precept that the only effective way to learn mathematics is by doing mathematics. The Java-applet graphing and computational tools are well chosen to reinforce and supplement the topics covered.
The hyper-referenced glossary is very helpful.
This material is a very good source for interdisciplinary projects in Differential Equations.
One of the reviewers had problems using the supplied downloadable file of the site with the downloadable optional DynaSys software that can be used with this set of activities.
Because no assessment of results is available on-site, this site is probably not effective for self-study. Strong instructor input will undoubtedly be required, in other words, for the site to be effective.
Ease of Use for Both Students and Faculty
The site has a very easy navigation structure and is very straightforward to use. The Java-applet tools are also easy to use, and they seem to work flawlessly.
Changing the values of parameters in the Java-applet graphing tools is a bit awkward and non-intuitive.
The two links to the biological content sites at the bottom of the page do not seem to be working.
The dependent variable in the graph in Problem 3 should be y, not x.
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