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 Ratings
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| Reviewed: |
May 13, 2004 by Mathematics |
| Overview: |
This java applet solves and graphically displays the solutions to ordinary differential equations. The user can select from an extensive list of standard "Left Hand Side" (homogeneous differential equations) and "Right Hand Side" (drive functions); the user can also graphically input a drive function. The user graphically selects a fixed point of the solution and can change the values of parameters that occur in the differential equation and/or drive function. The solution is updated and displayed in real time as all changes are made. The applet also displays the solution in analytical form for some of the simpler differential equations. |
| Learning Goals: |
Visualization of solutions of ordinary differential equations, primarily; also, this applet facilitates experimentation with the effects of equation parameters, initial conditions, and different drive functions on solutions. |
| Target Student Population: |
Students taking a course in ordinary differential equations and especially students in applied/engineering courses. |
| Prerequisite Knowledge or Skills: |
Students should be familiar with solution curves and drive (forcing) functions in the study of ordinary differential equations. |
| Type of Material: |
Simulation. |
| Recommended Uses: |
Classroom demonstrations and student resource. |
| Technical Requirements: |
Should run in any Java-enabled browser. |
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| Strengths: |
This is an easy-to-use graphing application for solution curves of many of the more standard ordinary differential equations and drive functions. It allows the user considerable flexibility in choosing initial points and inputting parameter values. The instructions for use of the application are adequate, and links are provided for in-depth information on some differential equation types (Bessel?s, Legendre?s, Hermite?s, etc.) Particularly impressive is the instantaneous redrawing of graphs as changes are made, either through graphical input or through changing parameter values. |
| Concerns: |
This is not a content site in the educational sense, and the rating in this category reflects this fact. |
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Potential Effectiveness as a Teaching Tool |
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| Strengths: |
This site is an excellent resource for students and teachers involved in the study of ordinary differential equations. It would be especially useful in applied courses where the effects of various drive functions on solution curves are under investigation. That the viewing window can be enlarged to full-screen size will be particularly beneficial in classroom demonstrations. |
| Concerns: |
Except for a few links to other sites, no specific educational content is provided on-site. It would be nice to have some hints for various operations, like how to use the sliding initial conditions in an analysis of stability. |
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Ease of Use for Both Students and Faculty |
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| Strengths: |
This applet has a highly intuitive interface. The instructions for use of the applet are adequate and well written, and the technique for changing parameter values is truly unique and ingenious. |
| Concerns: |
The graphs do not provide a scale for either axis nor is there any way to change the size or location of the viewing window. The drive function capability does not appear to work for Bessel?s equations.
The limitation to certain left and right sides can be a problem when one has a particular equation in mind and has to figure out how to make the applet work for this DE. Also,
the adjustment of numerical parameters through sliding the mouse can be annoying if one wants to enter specific values. |
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| Other Issues and Comments: |
This site author is obviously an accomplished Java programmer who has effectively applied his considerable skills to some mathematical applications. Browsers are encouraged to check out his other Java programs, links to which are provided on this site. |
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