The site contains a Java Applet and two links to the description and source code. The applet is a simulation that is designed to demonstrate various properties of predefined vector fields. The applet shows particle movements in the field and has a pop-up menu allowing the user to choose among four different demonstration modes: Velocity, Force, Curl Detectors, and Equipotential. Outside of the field and particle movement selection the user can control the number of particles and color coding of the background (floor colors).
Type of Material:
Simulation.
Recommended Uses:
In class demonstration or self-guided activity.
Technical Requirements:
A Java-enabled browser.
Identify Major Learning Goals:
To illustrate the concept of a vector field, gradient, divergence, curl, etc., as used in vector analysis, differential equations, physics, and chemistry.
Target Student Population:
College-level students studying topics in Advanced Calculus, Differential Equations, Physics, or Physical Chemistry.
Prerequisite Knowledge or Skills:
Complete Calculus sequence
Content Quality
Rating:
Strengths:
This applet provides a simple and effective illustration of a vector field. The graphical display is very clear and similar to what one might find in professional-quality software.
The user can select from a number of vector fields and see how particles move. Although the user can only choose pre-defined functions, the selection is quite extensive. In addition to that every function has a very comprehensive description that can be invoked by pressing on Function Info button.
The applet can be used to illustrate the concepts of such vector field properties as divergence and curl. If the vector field is a gradient field the user will see the particles moving on a surface determined by the potential function associated with the field. Showing the particles rolling downhill on the surface gives a very nice visual to the gradient. If the field is a force field, they may roll uphill too if they have enough momentum.
One useful aspect of the applet is the fact that the user can do line and surface integrals selecting appropriate modes of the applet. This is done by clicking and dragging out a rectangular area. The display window will show then the circulation around that area or, respectively, the flux through the bounds of that area.
Concerns:
The applet would definitely benefit if the user had an opportunity to enter a user-defined function representing vector fields.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
The Applet gives the user a very nice way to visualize vector fields. In spite of a very simple user interface it is still a very versatile tool that can be used to understand the basic concepts of vector fields. As a support and demonstration tool, instructors can use the site to illustrate textbook examples and homework assignments. As a part of self-guided activity the site can be used as a helpful textbook companion. Providing the basic definitions and function descriptions in the Function Info section is a big plus. There is also a 3-D version of the Applet,
which can also be accessed from the same website.
Concerns:
None
Ease of Use for Both Students and Faculty
Rating:
Strengths:
This is a very straightforward applet to use. The average user should be able to run it immediately. The directions section is very helpful. By clicking and dragging of the mouse cursor the user can change the view angle and/or adjust the orientation or size of the 3-d view. It is also very handy to be able to control the number of particles and field strength.
Concerns:
None
Creative Commons:
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