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Teaching Differential Equations With An Engineering Focus

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2006 Annual Conference & Exposition


Chicago, Illinois

Publication Date

June 18, 2006

Start Date

June 18, 2006

End Date

June 21, 2006



Conference Session

Integrating Math, Science, & Engineering

Tagged Division


Page Count


Page Numbers

11.1205.1 - 11.1205.12



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Paper Authors


Stephen Pennell University of Massachusetts-Lowell

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Stephen Pennell is a Professor in the Department of Mathematical Sciences at the University of Massachusetts Lowell.

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Peter Avitabile University of Massachusetts-Lowell

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Peter Avitabile is an Associate Professor in the Mechanical Engineering Department and the Director of the Modal Analysis and Controls Laboratory at the University of Massachusetts Lowell. He is a Registered Professional Engineer with a BS, MS and Doctorate in Mechanical Engineering and a member of ASEE, ASME, IES and SEM.

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John White University of Massachusetts-Lowell

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John R. White is a Professor in the Chemical Engineering Department at the University of Massachusetts Lowell.

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NOTE: The first page of text has been automatically extracted and included below in lieu of an abstract

Teaching Differential Equations with an Engineering Focus


Students’ lack of motivation is a significant obstacle to their learning basic STEM (Science, Technology, Engineering and Mathematics) material. Students often do not see the relevance of their mathematics courses, for example, to courses in their majors or to their careers until long after the courses have ended. Consequently, their motivation to learn the material in mathematics courses is low, and their retention of this material is poor.

Mathematics faculty members teaching engineering and science majors often introduce applications into their courses in an attempt to improve student motivation. However, the instructors are speaking “mathematics,” not “engineering,” and their emphasis is on the mathematical aspects of the applications. Differential equations courses, for example, have traditionally focused on techniques for generating solution formulas. Even in applications, the differential equation was the object of interest, and the goal was to obtain information about the equation’s solution. From the engineering point of view, however, the system being modeled is the object of interest, and a primary goal is to understand how the system responds to different classes of inputs5.

The Laplace Transform is another topic that is viewed quite differently by mathematicians and engineers. When introduced in a differential equations course, the Laplace Transform is usually regarded as a tool for solving linear, constant-coefficient differential equations. Since there are easier ways to solve this class of equations, students are often left wondering why anyone would use the transform method. When the Laplace Transform is approached from the engineering point of view, however, its utility is more apparent.

The authors of this paper (a mathematician and two engineers) are collaborating on a program whose goal is to develop interdisciplinary, multisemester projects designed to improve students’ learning of basic STEM material. As a result of this collaboration, the mathematician has modified his Engineering Differential Equations course to reflect more of the engineering point of view. This paper describes these course modifications as well as the collaborative program and the teaching modules being developed to implement it.

Differential Equations Course Modifications

The changes in the Engineering Differential Equations course discussed in this paper grew out of a larger program designed to improve student motivation to learn basic STEM material and to improve their retention of this material from one semester to the next. The main idea of this program is to develop projects spanning several courses and several semesters. Two such projects have been developed to date. The first involves a simple RC series circuit (modeled by a first-order linear differential equation), and the second involves a single-degree-of-freedom forced mass-spring-dashpot system (modeled by a second-order linear differential equation).

Pennell, S., & Avitabile, P., & White, J. (2006, June), Teaching Differential Equations With An Engineering Focus Paper presented at 2006 Annual Conference & Exposition, Chicago, Illinois. 10.18260/1-2--527

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