A course and text are being developed for upper level undergraduates who are interested in the use of sophisticated mathematics to solve problems arising in industry. The goal of the course is to demonstrate the usefulness of mathematics in contemporary industrial problems, with students modeling and solving real-life problems. The mathematics foundation will be the theory of ordinary and partial differential equations. Particular attention will be given to the formulation of open ended questions arising in the industrial problems. Computational and analytical approaches will both be important in the mathematical analysis necessary to address physically motivated issues.