Name: ___________________

Math 122 Lab 8: Mathematica

Introduction

Mathematicians and users of mathematics rely more and more on computer software to provide assistance with calculations and graphs. One of the most powerful Computer Algebra Systems is Mathematica. It is not the most user-friendly software, so the introduction given in this assignment may be extremely valuable to you later.

What to Turn In

Do not turn in this cover sheet. Repeat all commands and answer the questions in the attached Mathematica introduction. Then, in the same file, use Mathematica to work problems 1-8 below and turn in your Mathematica “notebook.” I prefer that you submit your file electronically, but you may turn in hardcopy if necessary. You should save to the Y: drive. To do so, click on File, choose Save As and change the directory to Y: and the folder “Mathmatica”. Save the file under your name(s). I’ll grade it in this folder and you can retrieve it.

Problems

After typing in the all of the commands in the attached Mathematica introduction (this is part of your grade!), use what you have learned to answer the following questions. Produce your graphs and type in explanations in the same Mathematica file that you have been creating.

1. Graph the vector-valued function <cost,cost,sint>.
2. Redraw the graph in problem 1 using the ViewPoint (0,40,0). Explain why the graph now looks like a circle.
3. Given the result of problem 2, explain why the curve in problem 1 is not a circle.
4. Graph the vector-valued function <cost,cost,sint>.
5. Find a viewpoint from which this looks like a circle.
6. Compute the magnitude of the function in problem 4.
7. Explain why the graph in problem is in the plane y = x.
8. Use your answers to problems 6 and 7 to determine whether the graph in problem 4 is actually a circle or not.