cp ~bfarr/Surfaces_start.mws ~

You can copy the worksheet now, but you should read through the lab
before you load it into Maple. Once you have read to the exercises,
start up Maple, load
the worksheet `Surfaces_start.mws`, and go through it
carefully. Then you can start working on the exercises.

One of the most valuable services provided by computer software such as Maple is that it allows us to produce intricate graphs with a minimum of effort on our part. This becomes especially apparent when it comes to functions of two variables, because there are many more computations required to produce one graph, yet Maple performs all these computations with only a little guidance from the user.

Two common ways of representing the graph of a function of two variables are the surface plot and the contour plot. The first is simply a representation of the graph in three-dimensional space. The second draws the level curves for several values of in the plane. We will explore how to produce these kinds of graphs in Maple, and how to use the graphs to study the functions.

- Generate a surface plot and contour plot for the
following function on the given domain.

for and . - What does the contour plot look like in the regions where the surface plot has a steep incline? What does it look like where the surface plot is almost flat?
- What can you say about the surface plot in a region where the contour plot looks like a series of nested circles?

- Generate a surface plot and contour plot for the
following function on the given domain.
- Consider the following function

which represents the deviation, in inches, of last year's rainfall from the average annual rainfall in a certain area.- Graph the surface corresponding to the function .
- What are (approximately) the maximum and minimum values of the rainfall deviation and where do they occur? (Hint - values from plots are accurate enough.)
- Use a contour plot to find the region in this domain in which the deviation was between inches inches.

2002-08-23