Homework # 5:  Visualization with Mathematica

Below are a few simple exercises that will help you understand some of the problems you may have encountered while working on Module 5.  You may use the Documentation Center to assist you with these problems.

Please format your solutions appropriately.  Use text format, not input format, when you are typing text.  Write coherent sentences and paragraphs;  part of your grade will depend on how clearly you present your ideas.

You must work on these exercises by yourself, not in pairs;  if you get stuck and cannot find the solution in the Documentation Center, you may consult the labbie or the instructor during their office hours.

Visualization Functions

1.  Explain in your own words what each the following visualization functions can be used to do.  In each case give an example to show the function in action:
	i.	Plot
	ii.	Plot3D
	iii.	ContourPlot3D
	iv.	ParametricPlot
	v.	ParametricPlot3D
	vi.	ListPlot

2.  Explain in your own word the difference between Plot and ListPlot.  In particular, explain when you should use Plot and when you should use ListPlot.

3.  Suppose that you have a list of ten numbers {(Subscript[y, 1]),...,(Subscript[y, 10])}  that correspond to the values of a function at the parameters 1/10, 2/10,...,10/10.

a.  Explain how to use ListPlot to display these y-values with the correct x-coordinates.

b.  Give an example to verify that your answer to part a is correct.

Spheres, Cylinders, and Cone

1.  Write down implicit equations for the following three surfaces:

i.	the sphere,
	ii.	the right circular cylinder,
	iii.	the right circular cone.

(Hint:  You can find these equations in the Documentation Center or in a standard Calculus text.)

2.  Apply ContourPlot3D to visualize:

i.	the sphere,
	ii.	the right circular cylinder,
	iii.	the right circular cone.

3.  Write down parametric equations for the following three surfaces:

i.	the sphere,
	ii.	the right circular cylinder,
	iii.	the right circular cone.

(Hint:  You can find these equations in the Documentation Center or in a standard Calculus text.)

4.  Apply ParametricPlot3D to visualize:

i.	the sphere,
	ii.	the right circular cylinder,
	iii.	the right circular cone.

Manipulate

1.  Create a blue sphere sitting inside a partially transparent cuboid as in Module 5.  Now use Manipulate to control the opacity of the cuboid.

2.  Create a piecewise linear curve with 5 vertices, where each vertex is attached to a different locator.  Now use locators to model the first initial of one of your names.