This notebook has been written in Mathematica by
Mark J. McCready
Professor and Chair of Chemical Engineering
University of Notre Dame
Notre Dame IN 46556
It is copyrighted to the extent allowed by whatever laws pertain to the World Wide Web and the Internet.
I would hope that as a professional courtesy that this notice remain visible to other users.
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More recent versions of this notebook should be available at the web site:
Please solve these problems using Mathematica. The examples above should be sufficient to solve them, or look at the "Help Browser" or send email to someone who can help.
1. Take the dot product of two orthogonal (3 element) vectors that you make up. Make sure you get the right answer. Now give the answer for the cross product. (Did you use the right hand or the left hand rule to get this answer? I'll bet you did not know that your answer is not really a vector, it is a pseudo-vector)
2. + = ?
3. Plot the sine and cosine functions to show their periodicity (ie. change this) and relative phase.
4. Integrate and then figure out how to take the derivative of both the sine and cosine.
5. Are the sine and cosine orthogonal functions? Show this with Mathematica.
6. Which differential equation from your past or future will be solved by sine and or cosine functions?