The Journal of Online Mathematics and Its Applications, Volume 7 (2007)
Experiments with Matrices and Vectors in Calculus and Linear Algebra, Sulewski, Kobylski, and Wattenberg
You will need three items to work with this material.
The first thing many people want to do is substitute their own image for the Black Knight image used in this article. This is really easy. The Black Knight image is a .gif file, named basepicture.gif, and is 135 pixels by 135 pixels. Your image should be roughly the same size but it does not need to be square. It should be a gif and it should have the same name, basePicture.gif. Substitute your image file for the one in the imageAnimationsOSSLET directory. You can try your new image out by double-clicking either OSSLET.html or imageAnimations.swf.
When the OSSLET is loaded it reads in an .xml file that describes the demonstrations, examples, and questions. This is an ordinary text file named imageAnimations.xml. The syntax should be fairly obvious. Open this file in your favorite text editor and look at it as we discuss it. You may want to make a back-up copy, so that you can go back to the original if necessary.
< imageAnimations> and </imageAnimations>. These lines should be left as is.
< matrix a11 = "cos(6 * pi * t)"
a12 = "-sin(6 * pi * t)"
a21 = "sin(6 * pi * t)"
a22 = "cos(6 * pi * t)" />
A block like this describes a matrix. The syntax should be self-expanatory.
< vector b1 = "2.5 * sin(6 * pi * t)"
b2 = "2.5 * cos(6 * pi * t)" />
A line like this describes a vector. The syntax should be self-expanatory.< initial> and < /initial >. This pair of tags describe the vector and matrix (enclosed within the pair) that are shown when the OSSLET is first loaded. This vector and matrix control the display in the lower right. As soon as the user clicks any button other than Play, Pause, or Stop these entries are set to the identity matrix and the zero vector. If you want to present just a list of problems, these should be set to the identity matrix and the zero vector.< problem name = "Question 1"> and < /problem>. Each pair of these tags encloses a matrix and vector that describe a problem. These are not displayed by the OSSLET but they do control what the user sees in the lower left when the Play button is clicked. Notice the phrase name = "Question 1". A phrase like this specifies what should be displayed on the button in the upper right. The problems should be in the order you want them to appear. You can include up to ten. Note that some of these "problems" can be examples. When the OSSLET is first loaded, the first problem is selected. The user selects subsequent problems by clicking the buttons in the upper right.
Often the first "problem" tags and the "initial" tags are used together to set up a demonstration or example in which you want the student to see how something is accomplished. Then subsequent problem tags are real problems in which the student does not see the answers.