cp ~bfarr/Surf_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 `Surf_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.

The simplest way of describing a surface in Cartesian coordinates is as the graph of a function over a domain, e.g. a set of points in the plane. The domain can have any shape, but a rectangular one is the easiest to deal with.

Another common, but more difficult way of describing a surface is as the graph of an equation , where is a constant. In this case, we say the surface is defined implicitly.

- Plot the graphs of the following functions over the given
domains. Use the
`plot3d`command.- , for and .
- , for and .
- over the interior of the ellipse .

- Use the
`implicitplot3d`command to plot the graphs of the following equations. You should come up with plot ranges that show the surfaces clearly.- The cylinder .
- . Can you explain why the surface only exists for ?

- Consider the equation

In the book, it says that such an equation can be reduced by rotation and translation to one of the two forms

or

Use the implicitplot3d command to graph the surface corresponding to the equation given above. You should be able to identify the graph as one of the types of graphs, i.e. paraboloid, hyperboloid, or ellipsoid, shown in the text. Can you use your graph to determine which of the two forms shown above the equation can be transformed into? Do**not**try to do the transformation - you don't need to to answer the question.

2001-11-12