This is a sub-site of IDEA (Internet Differential Equations Activities). This learning material is a lab-type exploration of how a neuron responds to external stimulus. The physical system is modeled using the Morris-Lecar differential equations, which are similar to the Hodgkin-Huxley equations. For phase plane analysis, a Java-applet graphing utility is provided.
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 a computer-based activity for applied differential equations.
Target Student Population:
Students studying applications of differential equations.
Prerequisite Knowledge or Skills:
Basic course of ordinary differential equations and some knowledge of dynamical systems.
This site contains a series of exercises that let the user analyze the behavior of a mathematical model based on a system of differential equations (Morris-Lecar equations). In their Nobel prize winning research, Hodgkin and Huxley established that a neuron can be modeled via an equivalent electrical circuit and ultimately by a system of four differential equations. The system considered in this site is similar to the Hodgkin-Huxley equations and shows how a neuron responds to external stimulus.
Performing the lab steps and exercises a user develops an understanding of the behavior of this dynamical system. The site also contains a brief yet thorough introduction that helps a user understand the nature of the problem studied.
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.
Potential Effectiveness as a Teaching Tool
The main Differential Equation component of the site is presented as arising out of a very interesting biological problem. Then the DE is used as a tool to analyze the problem and assess the model. Two levels of this analysis are offered in this project that broadens targeted student population and gives an opportunity to assign the project on different levels.
As with other activities in the IDEA group, this one is not aimed at teaching the techniques of solving differential equations. Rather, its goal is to show that analysis of a simple differential equation model can provide significant insights into a physical system. This goal is accomplished very well.
This material is a very good source for an interdisciplinary project in Differential Equations.
Because no assessment of results is available on-site, this site is probably not effective for self-study. Most students will need the guidance of a teacher.
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.
Ease of Use for Both Students and Faculty
The site has easy navigational structure and is straightforward to use. The Java-applet graphing tools work flawlessly.
Glossary links only work if opened in a separate window.
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