Title: CAS: Tool of First Recourse in Classical Applied Mathematics

Author: Robert J. Lopez* (r.lopez@rose-hulman.edu)

Affiliation: Dept. of Mathematics, Rose-Hulman Institute of Technology, USA

Abstract: Post-calculus classical applied and engineering math includes material found in courses on ordinary and partial differential equations, vector calculus, matrix algebra, complex variables, and numerical analysis. Modern computer algebra systems implement nearly all the calculations found in these disciplines, and should be used as the tool of first recourse for teaching, learning, and doing applied math. The nine units in Advanced Engineering Mathematics, Addison-Wesley's new text by Robert Lopez, develop a complete applied math curriculum based on a CAS. The text is written in traditional mathematical notation and language - no computer code appears in the text. However, it is paralleled by 273 Maple worksheets that contain the exposition and calculations described in the text. The text retains the order and structure made possible by reliance on software tools for executing calculations. The proposed talk will use examples to illustrate the new pedagogy made possible by this active use of a CAS in teaching and learning applicable mathematics. Hence, we will demonstrate introductions to the Laplace transform and the wave equation on a string, computation of convolutions, construction of Bezier curves, derivation of the gradient in polar coordinates, and the Joukowski map of complex variables