This is a subsite associated with the parent site called IDEA (Internet Differential Equation Activities). The activity on this page explores the effects of drag and thrust in modeling the motion of a hydroplane racing boat using the basic force balancing equation. Interactive Java applet graphing utilities provide visualizations of the results.
Type of Material:
Simulation and tutorial.
A part of a take-home project in 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.
Whenever mathematics applies itself to something of popular interest, like racing, kudos are in order. Such applications are likely to pique the interest of most students. This application to hydroplane racing is certainly not an exception. Students should enjoy using the Java applet graphing tools to experiment with and make predictions about this dynamical system. The computational complexities have been avoided here; students will not learn how to solve differential equations. But, equally as important, students will learn how phase plane analysis can provide important and sometimes surprising insights.
The glossary links do not work. Also, the link to hydroplane racing at the bottom of the page does not work.
Potential Effectiveness as a Teaching Tool
Three exercises explore the effects on the model of various assumptions about the hydroplanes thrust. This site should be effective in piquing students interest and in drawing students into the qualitative analysis of phase portraits in dynamical systems.
The site would be most effective if it were part of a more elaborate take-home project with appropriate additional input and direction from the instructor.
Because no assessment of results is available on-site, this site is probably not effective for self-study. Also, the problems would have been more effective had they been stated more explicitly. For example, in problem #2 users are asked to explain the phenomenon wherein the thrust T increases at a constant rate. What aspects of the model do the authors have in mind? It is specifics such as these that instructors will have to provide their students for the site to be an effective teaching tool.
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.
Changing the values of parameters in the Java-applet graphing tools is a bit awkward and non-intuitive, but in these applications that is not a significant issue.
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