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. Follow the instructions for the attached Mathematica introduction, use the commands to work problems 1-8 below and turn in your Mathematica “notebook.” I prefer that you get your file to me electronically, but you may turn in hardcopy if necessary. You should save to the Y: drive in the folder “Mathmatica” under your name(s).

 

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.

 

  1. Plot the graph of z = sin(x + y) and briefly describe what the graph looks like.
  2. Redraw the graph in problem 1 using the ViewPoint (100,−100,0). Explain why most of the graph has disappeared. Then redraw the graph from the perspective (100,100,0). Briefly describe what you are seeing from this perspective.
  3. Plot the graph of z = (y − 3x)2. Then find a viewpoint from which the graph appears to be a simple parabola. As fully as possible, describe all viewpoints (x,y,z) that will produce a similar picture.
  4. The graph of z = x2 + y2 is a circular paraboloid. Use Plot3D to graph this with both x and y between −2 and 2. Explain why the graph does not appear to be circular at the top.
  5. Use ParametricPlot3D to graph the surface in #1. You will need to figure out parametric equations for the surface first. Which graph looks better?
  6. The graph of  is a hyperboloid of one sheet. Solve this equation for z and use Plot3D to graph the top half of this surface. You will need to play some with the x-range and y-range to get a decent-looking graph.
  7. Use ParametricPlot3D with  to graph the hyperboloid. Find a viewpoint to make this look good.
  8. Use ParametricPlot3D to graph . It can be shown that with these equations which means that this graph is a part of the hyperboloid graphed in #7. Describe as completely as possible how this graph relates to the full graph in #7.