Background

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 .

• Examples