Advanced Engineering Math Through Symbolic Software

Robert Lopez
Math department at Rose-Hulman.
(r.lopez@rose-hulman.edu)  or
lopez@nextwork.rose-hulman.edu

The course typically called "Advanced Engineering Mathematics."
supported by numerous texts of the same name, samples material from at
least six standard mathematics courses.  In particular, chapters of any
of these texts have titles like Ordinary Differential Equations,
Boundary Value Problems, Complex Variables, Linear Algebra, Numerical
Analysis, Vector Calculus, Optimization, etc.

We are beginning to see appear Advanced Engineering Math texts that
reference the use of symbolic software packages like Maple and
Mathematica.  However, to date, these texts still follow a traditional
methodology and view the symbolic software package as a useful
calculator to be invoked in the solution of some of the problems.

Given the power of these software packages, it is time to begin seeing
texts written from the perspective that the symbolic software is the
tool of ordinary recourse for teaching and learning, as well as doing,
engineering analysis.  This talk will consist of examples taken from
the speaker's courses at Rose-Hulman Institute of Technology where the
standard learning environment is a computer-equipped classroom.  These
examples will illustrate why it is necessary that texts, and courses,
begin to reflect a pedagogy predicated on a universal and ubiquitous
access to appropriate software facilities during class, during exams,
and during all forms of instructional activities.