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.
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.
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