Ignatios Vakalis

The entire module is of hypertext nature and includes interactive code for both Maple and Mathematica. The interactivity (ability to open a Maple/Mathematica window with a click of a button and execute a session of commands) offered in this module allows greater experimentation (with a CAS) and ease of use.

Two versions of the "electrostatic potential" problem are explored:

• 1-D Finite Length Wire: A charged wire resides on the y-axis on the interval [-1, 1]. The problem of formulating and solving a model for calculating the potential at a given point is presented. A discrete model is developed and Maple/Mathematica are used to obtain its solution. A continuous model is also derived expressing the potential as an 1-D integral. Fortran/C implementations of the Trapezoidal and Simpson's rules are used as one way of solving the continuous model. Maple/Mathematica explorations lead to symbolic and numeric solutions of the model as well as to the derivation of the "error term" involved in the development of the two elementary quadrature rules.
• Infinite Length Wire: An extension of the previous case to an infinite length wire is explored. A discussion of the limitations of the Trapezoidal and Simpson's rule for this case is provided, and the power offered by a CAS is employed in an attempt to find an exact or an approximate value of the potential at a given point. A numerical integration routine, adopted from NETLIB is provided, thus giving the user the chance to explore its power and sophistication.