A Course in Differential Equations, Modeling, and Simulation for Engineering Students

Engineering students generally take a course in differential equations during their sophomore year, after completing a calculus sequence. Almost exclusively, this course is offered by a mathematics department and is highly weighted to the mathematical side of the subject, with little coverage of applications. With the belief that engineering students are better motivated to learn mathematics when they can see its applications, the authors (engineering faculty) have developed a course in which differential equations are introduced and developed in the context of mathematical modeling of physical systems. Both analytical and numerical solution techniques are covered, with commercial software used to implement the latter. Applications are drawn from several engineering disciplines and include electrical circuits, mechanical (spring-mass) systems and thermal systems. Students taking the course represent all seven engineering disciplines at the authors’ institution and the course has been formally recognized by the College of Engineering as a substitute for the standard Differential Equations course. In this paper, we describe the course by providing a list of topics for the course, how they are structured, and how the three main components (modeling, analytical solutions and numerical solutions) are integrated with one another. Because some students at our institution take this course and others take a standard differential equations course, the opportunity to compare the two groups of students exists. We provide several comparisons including results of testing the abilities of both groups to solve differential equations in later semesters, performance in related courses, graduation rates and persistence, and results from student assessment of instruction. Results are discussed in terms of both short and longer-term impacts to the students.