As we've seen in class, computing the curvature, , and the
unit normal and tangent vectors is a tedious process, even for the
simplest of curves. Fortunately, Maple procedures can be written to do
these calculations and this lab will introduce you to the ones that we
have written here at WPI as part of the `CalcP` package. As usual,
before you can use any of these commands, you must load the package with the
following command. Since some of the commands use the `linalg`
package, it is probably a good idea to load it as well.

> with(linalg):

Warning: new definition for norm Warning: new definition for trace

> with(CalcP):

The
list below gives the names of the procedures we will be using, as well
as brief descriptions. Maple `help` screens are available for all
of these procedures, so refer to them for further examples. To refresh
your memories, the commands introduced in the previous lab are also
listed.

- VDiff
- Differentiates vector-valued functions.
- VPlot
- Plots vector-valued functions in two and three dimensions.
- VMag
- Computes the magnitude of a vector.
- ParamPlot
- Animates parametric curves in two dimensions.
- ParamPlot3D
- Animates parametric curves in three dimensions.
- Speed
- Computes the speed of a particle moving on a path defined by a vector-valued function .
- unitvect
- Computes the unit vector associated with a vector .
- tanvect
- Computes the unit tangent vector, , for a vector-valued function .
- normalvect
- Computes the unit normal vector, , for a vector-valued function .
- Curvature
- Computes the curvature, , for a
vector-valued function .

Wed Mar 27 11:12:57 EST 1996