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

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2019 ASEE Annual Conference & Exposition


Tampa, Florida

Publication Date

June 15, 2019

Start Date

June 15, 2019

End Date

October 19, 2019

Conference Session

Mathematics Division Technical Session 2

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Paper Authors


Scott W. Campbell University of South Florida

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Dr. Scott Campbell has been on the faculty of the Department of Chemical & Biomedical Engineering at the University of South Florida since 1986. He currently serves as the department undergraduate advisor. Scott was a co-PI on an NSF STEP grant for the reform of the Engineering Calculus sequence at USF. This grant required him to build relationships with engineering faculty of other departments and also faculty from the College of Arts and Sciences. Over the course of this grant, he advised over 500 individual calculus students on their course projects. He was given an Outstanding Advising Award by USF and has been the recipient of numerous teaching awards at the department, college, university (Jerome Krivanek Distinguished Teaching Award) and state (TIP award) levels. Scott is also a co-PI for a Helios-funded Middle School Residency Program for Science and Math (for which he teaches the capstone course) and is on the leadership committee for an NSF IUSE grant to transform STEM Education at USF. His research is in the areas of solution thermodynamics and environmental monitoring and modeling.

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Carlos A. Smith PhD University of South Florida

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Carlos A. Smith is a Professor Emeritus in the Department of Chemical & Biomedical Engineering at the University of South Florida. His interests are in Process Control, Process Engineering, and Engineering Education. He is co-author of three editions of "Principles and Practice of Automatic Process Control," John Wiley, and two editions of "A First Course ion Differential Equations, Modeling and Simulation," CRC.

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Silvia M. Calderon Universidad de Los Andes, Venezuela

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Professor, School of Chemical Engineering, University of Los Andes, Venezuela. Senior Research Fellow, University of Oulu, Finland.
Ph.D in Chemical Engineering, University of South Florida, USA. M.Sc. in Applied Engineering Mathematics, University of Los Andes Venezuela.

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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.

Campbell, S. W., & Smith, C. A., & Calderon, S. M. (2019, June), A Course in Differential Equations, Modeling, and Simulation for Engineering Students Paper presented at 2019 ASEE Annual Conference & Exposition , Tampa, Florida. 10.18260/1-2--31953

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