OVERVIEW

This is an introductory laboratory. By the end of this laboratory section, you should be able to start Mathematica on your own or on an Athena system. You should also be able to do a few calculations, use Mathematica's help browser, and save your work.

TASKS

Starting Up

• On your own computer If you are reading this before the laboratory section (and I hope you are!) and you want to get a student copy of Mathematica on your own system (which I recommend!) look at http://itinfo.mit.edu/article.php?id=6842. This year the student license is $30, but I think you will find that you will use this in many of your other classes and would be a good investment. The process involves making an order, and then following instructions on the order-follow-up email; it may take a few days, so get a head-start if possible.

  Once you have Mathematica installed, launch it as you would any other application of your particular flavor of operating system.

• On an Athena computer On an Athena machine, open a shell. Add the Mathematica locker by typing add math at the prompt. Start Mathematica by typing math at the prompt.

Simple Calculations

Try and do the following calculations.

1. Add two integers
2. Multiply and integer and $\pi$
3. Calculate $4 \pi - 4 \times 3.14159265$
4. Define a symbol $Energy$ for the product $h \nu$ . Investigate what happens to $Energy$ if you also define $h$ and then $\nu$ .
5. Find the derivative $d R /dx$ where
   $$R = \sqrt{\frac{1}{1+{\sqrt{\frac{1}{1+{\sqrt{\frac{1}{1+{x}}}}}}}}}$$
   It may be easier to build up $R$ in steps by using definitions.
6. Find the Mathematica Help Browser page that describes the function Rationalize. Find a rational approximation (i.e., of the form $\frac{\text{Integer}_N}{\text{Integer}_M}$ which differs from $\pi$ by less than $10^{-12}$ ,

Save your Work

Save your work as a mathematica notebook: 3016_Lastname_Lab01.nb.

REPORT

This homework will not be graded, but do send you saved mathematica file to 3.016@pruffle.mit.edu at the end of the laboratory period.