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.
- A group of oceanographers is mapping the ocean floor to assist in
the recovery of a sunken ship. Using sonar, they develop the model

where is the depth and and are the distances in kilometer.- Graph the surface corresponding to the function .
- Plot at least contours of the function and note the values
of at these contours.
- What is the depth of the ship if it is located at the coordinate
?
- Use contours to approximate the slope of the ocean floor in the positive
direction at the ship's location ()?

- Graph the surface corresponding to the function .

2001-09-07