Using projects in mathematics and engineering mathematics courses designed to stimulate learning

During the fall of 2008, an engineering mathematics course was developed at the University of Alabama at Birmingham to incorporate lessons in multivariable calculus and differential equations. The goal was to focus on topics with direct applicability in ensuing engineering courses, adding logical components, like units and dimensional analysis, tying mathematics and engineering together. The course added more of an engineering appeal to the traditional multivariable calculus and differential equations material with the use of engineering-based homework problems, test questions, and projects. The projects typically tackle problems in mechanics, electrical systems, population dynamics, optimizations, etc. designed to address the major focal areas of the course. This paper includes projects that tackle first-order ordinary differential equations (ODEs), second order ODEs, and multivariable calculus.