Introduction

Post-calculus classical applied math is scattered through courses in differential equations, boundary value problems, vector calculus, matrix algebra, complex variables, and numerical methods. Most of this material can be found in texts entitled Advanced Engineering Mathematics. The mathematics in such texts is truly classical, having been available in its present format for many years, if not centuries. The apprenticeship for working in the field of classical applied mathematics is long and arduous because the apprentice must master material from so many different disciplines.

Twenty-first century software allows this apprenticeship to be both shorter and more effective. Modern computer algebra systems can be the tool of first-recourse for teaching, learning, and doing such applicable mathematics. Software tools such as Maple, Mathematica, MuPAD, and Macsyma implement nearly all the manipulations of the undergraduate program in applied and engineering mathematics. The time has come to use these twenty-first century tools for teaching eighteenth and nineteenth century mathematics.

A complete post-calculus applied math curriculum in which a computer algebra system is the primary working tool appears in [1]. In this text the software is not just an add-on to a traditional by-hands pedagogy. Instead, the software is used as an active partner in the student's participation in applied mathematics.

We give two examples taken from [1], examples that show how use of a computer algebra system enhances pedagogy.