A New Look At Upper Level Mathematics Needs In Engineering Courses At Uab

A four semester-hour course is being designed to follow Calculus II, with the intention of replacing Calculus III and Differential Equations in the engineering curricula at the University of Alabama at Birmingham. As part of the planning process, instructors of all courses with Calculus III or Differential Equations as direct or indirect prerequisites were interviewed to (1) determine their views of the current preparation of students, (2) identify the mathematics skills that were expected of students in their courses, and (3) discuss the possibility of introducing mathematics topics using engineering problems and incorporating both problem-based and active learning techniques. Faculty were very satisfied with the capabilities of the better students to carry out symbolic manipulations of common problems, particularly if the student had recently completed upper-level mathematics courses. However, most students were very poor at applying the mathematics in their engineering courses. There was strong support for a change from teaching mathematical methods in relative isolation to teaching mathematical methods in context. The process that will be adopted involves starting with an engineering problem, including a brief discussion of cause and effect, variables, units, boundary conditions and governing principles. This preamble will be followed by teaching the mathematical tools needed to solve the problem and applying these tools to similar engineering problems. Identifying the requisite mathematical skills required a balance among designing a coherent course, meeting the many needs of the engineering programs, and being able to adequately address the topics in a four semester-hour course using active and problem-based learning. Engineering faculty enthusiastically accepted the trade off of teaching some advanced mathematical methods within their courses in exchange for receiving students with a sound, broad-based foundation and an ability to use mathematics to solve engineering problems. Areas that were deemed critical by most engineering programs were First-Order ODEs; Second-Order Linear ODEs; Vector Differential Calculus: Grad, Div, Curl; Vector Integral Calculus, and an introduction to Partial Differential Equations. The initial offering of this course will be Fall 2008.