This is a sub-site of IDEA (Internet Differential Equations Activities). The qualitative aspects of El Niño - Southern Oscillation, called ENSO, are here modeled in terms of simple differential equations. The model is explored with a series of exercises. These exercises deal with equilibriums and stability, and a Java-applet graphical DE solver 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.
With a series of seven straightforward exercises, the authors build up to an important illustration of chaos in a complex natural system. This considerable accomplishment is achieved through a brief but thorough introduction to the ENSO phenomenon and, then, by a well-chosen reduction of ENSO into a system of three linear differential equations. A hyperlinked glossary provides definitions and clarifies concepts.
A hyperlink to a repeated bibliographical reference to a paper in Science magazine does not work.
Potential Effectiveness as a Teaching Tool
As the authors say at the end of this learning material the current model is valuable in that it allows us rather easily to understand the basic ingredients to a complicated physical system. 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 important 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.
All the exercises lack a certain specificity that would have made them more effective with students. For example, in #3, what aspects of the solution do the authors want described? And in #4, to which equations are the authors referring? Adding such minor details would do wonders for student understanding.
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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