Advanced Undergraduate Engineering Mathematics

Michael P. Hennessey

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Conference: 2015 ASEE Annual Conference & Exposition
Location: Seattle, Washington
Publication Date: June 14, 2015
Start Date: June 14, 2015
End Date: June 17, 2015
ISBN: 978-0-692-50180-1
ISSN: 2153-5965
Conference Session: Mathematics Division Technical Session 1
Tagged Division: Mathematics
Page Count: 12
Page Numbers: 26.161.1 - 26.161.12
DOI: 10.18260/p.23500
Permanent URL: https://peer.asee.org/23500
Download Count: 10046

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Michael P. Hennessey University of St. Thomas

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Michael P. Hennessey (Mike) joined the full-time faculty as an assistant professor in the fall of 2000. Mike gained 10 years of industrial and academic laboratory experience at 3M, FMC, and the University of Minnesota prior to embarking on an academic career at Rochester Institute of Technology (3 years) and Minnesota State University, Mankato (2 years). He has taught over 20 courses in mechanical engineering at the undergraduate and graduate level, advised 11 MSME graduates, and has written (or co-written) 45 technical papers (published or accepted), in either journals (11), conference proceedings (33), or in magazines (1). He also actively consults with industry and is a member of ASME, SIAM and ASEE.

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Abstract

Advanced Engineering MathematicsAbstractDue to increasing undergraduate enrollments in both electrical and mechanical engineeringwithin the School of Engineering and interest in helping our graduates be better prepared tohandle the applied mathematical rigors of engineering graduate school, especially at topinstitutions, a technical elective course entitled Advanced Engineering Mathematics wasdeveloped and has now been taught a total of three times. Topics were selected to appeal to boththe needs of electrical and mechanical engineering, and for which there are mainstreamtextbooks available. The prerequisites were both Multivariable Calculus and an Introduction toDifferential Equations & Linear Algebra.More specifically, topics covered included vector integral calculus (a review of one’sundergraduate knowledge) and an introduction to Fourier series, integrals, and transformations;partial differential equations; complex analysis, including conformal mapping and potentialtheory. To emphasize applications, numerous examples from solid & fluid mechanics, heattransfer, control theory, electro-static, and electro-magnetic field theory are covered in additionto an overview of some of the instructor’s own industrial/research work that uses advancedengineering mathematics. Much of the above material is classic engineering mathematics thathas been around for many decades and hasn’t really changed that much. However, modernsoftware (e.g. MATLAB in this case) brings the material more to life and offers tremendousadvantages for numeric, graphic, and project work.It is worth noting that vector integral calculus was selected as a topic (vs. another topic like thecalculus of variations), as theoretically students should be experts on this topic already, havingseen it in the Multivariable Calculus course, taught by the Mathematics Department. However,based on discussions with various faculty and observing student competence and their comfortlevel, it was felt that another pass through the material from a slightly different perspective waswarranted, especially since it can’t be guaranteed that all three integral theorems (Green, Gauss,& Stokes) are covered in Multivariable Calculus.Project work gave the students an opportunity to delve more deeply into a specific problem,focus on an application of interest to them, be creative, perform some numerical and graphicalcomputing using MATLAB, and lastly, present their work to the class in our own “conference.”Some example projects completed by students have included: (1) 2D wave equation for arectangular membrane, (2) 2D electrostatics of nonsymmetrical semicircular plates, and (3)plotting out streamlines for potential flow. Beyond the numeric work and static plots, studentswere encouraged to use the movie making capability resident within MATLAB. Seeing studentsplaying movies of partial differential equation solutions on their smart phones and sharing themovie clips with others was particularly satisfying.Some things learned having taught the course 3 times come in the form of: (1) feedback fromstudents and (2) an appreciation of some topical areas that students have trouble with,misconceptions, etc. Feedback from students has been very positive and anecdotally, a relativelyhigh percentage of students taking this course have gone on to graduate school in engineering.

Citation
Format

Hennessey, M. P. (2015, June), Advanced Undergraduate Engineering Mathematics Paper presented at 2015 ASEE Annual Conference & Exposition, Seattle, Washington. 10.18260/p.23500

TY  - CPAPER
AB  -                           Advanced Engineering MathematicsAbstractDue to increasing undergraduate enrollments in both electrical and mechanical engineeringwithin the School of Engineering and interest in helping our graduates be better prepared tohandle the applied mathematical rigors of engineering graduate school, especially at topinstitutions, a technical elective course entitled Advanced Engineering Mathematics wasdeveloped and has now been taught a total of three times. Topics were selected to appeal to boththe needs of electrical and mechanical engineering, and for which there are mainstreamtextbooks available. The prerequisites were both Multivariable Calculus and an Introduction toDifferential Equations &amp; Linear Algebra.More specifically, topics covered included vector integral calculus (a review of one’sundergraduate knowledge) and an introduction to Fourier series, integrals, and transformations;partial differential equations; complex analysis, including conformal mapping and potentialtheory. To emphasize applications, numerous examples from solid &amp; fluid mechanics, heattransfer, control theory, electro-static, and electro-magnetic field theory are covered in additionto an overview of some of the instructor’s own industrial/research work that uses advancedengineering mathematics. Much of the above material is classic engineering mathematics thathas been around for many decades and hasn’t really changed that much. However, modernsoftware (e.g. MATLAB in this case) brings the material more to life and offers tremendousadvantages for numeric, graphic, and project work.It is worth noting that vector integral calculus was selected as a topic (vs. another topic like thecalculus of variations), as theoretically students should be experts on this topic already, havingseen it in the Multivariable Calculus course, taught by the Mathematics Department. However,based on discussions with various faculty and observing student competence and their comfortlevel, it was felt that another pass through the material from a slightly different perspective waswarranted, especially since it can’t be guaranteed that all three integral theorems (Green, Gauss,&amp; Stokes) are covered in Multivariable Calculus.Project work gave the students an opportunity to delve more deeply into a specific problem,focus on an application of interest to them, be creative, perform some numerical and graphicalcomputing using MATLAB, and lastly, present their work to the class in our own “conference.”Some example projects completed by students have included: (1) 2D wave equation for arectangular membrane, (2) 2D electrostatics of nonsymmetrical semicircular plates, and (3)plotting out streamlines for potential flow. Beyond the numeric work and static plots, studentswere encouraged to use the movie making capability resident within MATLAB. Seeing studentsplaying movies of partial differential equation solutions on their smart phones and sharing themovie clips with others was particularly satisfying.Some things learned having taught the course 3 times come in the form of: (1) feedback fromstudents and (2) an appreciation of some topical areas that students have trouble with,misconceptions, etc. Feedback from students has been very positive and anecdotally, a relativelyhigh percentage of students taking this course have gone on to graduate school in engineering.
AU  - Michael P. Hennessey
CY  - Seattle, Washington
DA  - 2015/06/14
PB  - ASEE Conferences
TI  - Advanced Undergraduate Engineering Mathematics
UR  - https://peer.asee.org/23500
DO  - 10.18260/p.23500
ER  -