Math tools for engineering: A new approach to teaching calculus iii and differential equations

Abstract

During the fall of 2008 at the University of Alabama at Birmingham, a new course (EGR/MA 265 - Mathematical Tools for Engineering Problem Solving) was offered in a joint effort by the School of Engineering and the Department of Mathematics combining differential equations and calculus III into a four-hour semester-long course to aid in the transition of students from pure mathematics into engineering. This course was offered as an alternate track to the traditional calculus III and differential equations courses. Due to the time constraints within any one semester, a careful review of topics was made after interviewing every professor within the five departments of the School of Engineering who taught courses requiring calculus III or differential equations as a pre- or co-requisite. Initially, major areas to emerge were first-order linear ordinary differential equations; second-order linear ordinary differential equations with constant coefficients; multivariable functions, partial differentiation, and multiple integrals. The professors of the new course decided that they may be able to include integral theorems and an introduction to partial differential equations. In addition to the traditional material that these courses would typically provide, many application-based homework assignments and projects were given to provide engineering context. Each project assignment was given the same weight as a test but the projects were far more exploratory. Students were provided static notes in PDF format as well as dynamic notes in notebook player file format provided via the use of Mathematica Player by Wolfram to illustrate visually many of the concepts taught. Anonymous student comments via Individual Development and Educational Assessment (IDEA) surveys - an internal course evaluation tool - indicated that student perception of the course was generally positive. © American Society for Engineering Education, 2009.