This applet draws a two-dimensional vector field F(x,y) = f(x,y) i + g(x,y) j supplied by the user. The user is then able to click anywhere in the applet window to have it plot the flow line (or space curve) corresponding to the given vector field F with the chosen (clicked) initial point.
Type of Material:
A Java-enabled browser.
Identify Major Learning Goals:
This material is designed to illustrate the concept of a vector field and its associated flow lines as used in vector analysis, differential equations, physics, and chemistry..
Target Student Population:
College-level students studying topics in Differential Equations, Multivariate Calculus, Physics, or Physical Chemistry.
Prerequisite Knowledge or Skills:
The standard calculus sequence should suffice.
Vector Field is a part of a larger site Interactive Math Programs that is designed to accompany a textbook on Differential Equations. The applet is simple but informative. The simple interface allows the user to easily input two functions f(x,y) and g(x,y) , then the vector field f(x,y)i + g(x,y)j is sketched. The user can then select an initial point, using the mouse, and the flow line through that point is sketched in red. There are instructions on how to use the applet as well as explanations of the underlying mathematics. This applet provides a simple and effective illustration of a vector field. The graphical display is very clear and looks like a standard DE textbook illustration. Window settings for the graph can be entered independently
The site containing the applet would benefit from some introductory text (outside of the help window) on vector fields.
Potential Effectiveness as a Teaching Tool
The applet does one thing, and does it well. As a support and demonstration tool, instructors can use the site to illustrate textbook examples and homework assignments. Students could benefit from visiting the site and spending 20-30 minutes checking their homework or working through a planned worksheet.
A screen capture of the applet in use together with a textbook example, placed on the same page as the applet, would be a plus.
Ease of Use for Both Students and Faculty
This is a very straightforward applet to use. The average user should be able to run it immediately. The automatic help and error windows facilitate this simplicity. Moreover, the expression syntax is very similar to the syntax used by most graphing calculators and common computer algebra systems.
A simple way to print different plots might be useful. Help directions could be a little more systematic and use more careful and common language.
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