You may find that using mathematical software such as *Mathematica* (or
Maple, MathCAD, Matlab, etc.) can help you to visualize parametrized curves,
graphs of functions of two variables, contour diagrams, and more. Once you get
past the syntax, it's not hard to use these tools. *Mathematica* may be
available for use on some of the Harvard computers. A student version is
available at reduced cost. More information is available at www.wolfram.com.

*Mathematica* uses “notebooks” to organize things. You can either
open a previous notebook (the file will be named something like “filename.nb”)
or you can build your own. We have several notebooks written that you will find
useful in learning how to use *Mathematica*. All you have to do is __right-click__
on one of their names (below), save the file to your computer desktop, then open
the file with *Mathematica*. (You will, of course, need to have *Mathematica*
installed to open the files.) Each lab is (relatively) self-explanatory. You
should also be aware that the Help menu of *Mathematica* is quite good and
should enable you to work your way out of any confusion about syntax, etc.

One of the nice features of *Mathematica* is that it's very easy to
export the pictures you produce into word processing applications (such as
Microsoft Word). There you can augment the pictures with text to produce (and
print) good-looking documents. If you're up on Adobe Acrobat, you can also
create Acrobat (PDF) documents that can be posted on the web.

**Hands-On Start to Mathematica**(Flash presentation from Wolfram.com)*Mathematica*Lab 1 (exercises in basic syntax and drawing parametrized curves)*Mathematica*Lab 2 (exercises in graphing functions of several variables, contours, etc.)*Mathematica*Lab 3 (further topics)

If you have trouble using *Mathematica* or want to learn more about how
to use some other relevant software, send e-mail to Robert@math.rwinters.com.
I'll do what I can to help you out.

Robert Winters