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June 22, 2020
June 22, 2020
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Engineering Application Projects for Teaching Engineering Mathematics and Numerical Methods
One ABET student outcome focuses on the ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics. Engineering mathematics and numerical methods are two upper-level courses offered to mechanical engineering students. These courses are designed to provide students mathematical tools for other mechanical engineering core courses, and equips students with modelling skills to formulate engineering problems into mathematical forms for solutions.
While prerequisite courses in “calculus” and “differential equations” have fairly standard contents, engineering mathematics course may vary considerably in topics. One objective of this course is to provide students the necessary engineering mathematical knowledge for other core courses in mechanical engineering curriculum. For example, vector calculus for Fluid Mechanics, boundary value problems for Heat and Mass Transfer, convolution integral for Vibration Analysis, etc.
Numerical methods are extremely powerful problem-solving tools. They are capable of handling large systems of equations, nonlinearities, and complicated geometries that are often impossible to solve analytically. This course introduces various numerical methods widely applied in engineering modelling and analysis, including the least-square regression, interpolation, numerical integration and differentiation, finite difference method (FDM), finite element method (FEM), etc.
This paper documents some engineering application projects assigned in these two courses. The covered materials include those from the engineering vibration analysis, heat transfer, material engineering, etc. These projects have been designed with an attempt to build a bridge between some real-life mechanical engineering problems and the mathematical theorems learned in class (Laplace transform and transfer function, regression modelling, FDM and FEM, for example). Each project has been presented in details in this paper and the student feedback to these projects are mainly positive.
Zhang, S., & Togbe, A. S. (2020, June), Engineering Application Projects for Teaching Engineering Mathematics and Numerical Methods Paper presented at 2020 ASEE Virtual Annual Conference Content Access, Virtual On line . 10.18260/1-2--34546
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