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Teaching Differential Equations in a Diverse Classroom

Abstract

A course on ordinary differential equations is included in the core of almost all undergraduate engineering programs. Therefore, it is common practice to tailor such a traditional course towards an audience of engineering students. What becomes interesting, however, is teaching differential equations when only one section of this course is offered each semester and it is populated by students majoring in engineering, mathematics, chemistry, geology or even sociology.

This paper discusses the methodology adopted to teach ordinary differential equations to undergraduate students at Lake Superior State University (LSSU). Since 2005 fall semester, the 3-credit course has been team-taught by two instructors; one from the School of Mathematics and Computer Science and one from the School of Engineering and Technology. The course covers traditional topics such as first-order equations, second-order linear equations with constant coefficients, Laplace transforms, and systems of first-order equations. The emphasis is on the real-life modeling applications of differential equations.

The small size and highly diverse population of the classroom provide opportunities for students to work on modeling applications of differential equations within an interdisciplinary team. The final projects incorporated into the course cover topics ranging from earth sciences to vehicle systems, electrical circuits to robotics. Given the fact that the course material has an emphasis on linear ordinary differential equations, the final projects are utilized to introduce more advanced topics such as model nonlinearities, parameter uncertainties and numerical methods for solving differential equations. The paper will exemplify the student work and discuss the effectiveness of our methodology.

Introduction

Teaching mathematics in a classroom filled with students from various science and engineering majors poses challenges to the instructor. It seems that even though the students appreciate the importance of studying mathematics for their professional careers, they don’t show the same levels of interest. Many students view the mathematics courses as part of their degree requirements only and perform with low levels of motivation in the classroom. The instructor’s challenge then becomes to build the bridge from the abstract mathematical concepts to practical applications of the theory. The key to success is to find the right balance between the understanding of mathematics and its applications in one’s own field of study1. A course on ordinary differential equations works quite well to implement this building the bridge philosophy as many real-life applications yield differential equations as mathematical models.

Examples of teaching a mathematics course with an emphasis on applications have been reported in literature numerous times2-7. One common approach is to employ the project based learning (PBL) methods2. The students are assigned challenging real-life problems which are typically open-ended and unstructured. This approach seems to work well in classrooms populated by the

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Padir, T., & Muller, K. O., & Coullard, C. (2008, June), Teaching Differential Equations In A Diverse Classroom Paper presented at 2008 Annual Conference & Exposition, Pittsburgh, Pennsylvania. 10.18260/1-2--3922