Advanced Undergraduate Engineering Mathematics

This paper presents the details of a course on advanced engineering mathematics taught several times to undergraduate engineering students at the University of St. Thomas. Additionally, it provides motivation for the selection of different topics and showcases related numerical and graphical work done mostly in MATLAB. Primary course topics covered in this survey course include: (1) vector integral Calculus, (2) an introduction to Fourier series, (3) an introduction to partial differential equations (PDEs), (4) an introduction to complex analysis, and (5) conformal mapping and applications. Also, examples of student project work are shown. Lastly, useful student feedback and lessons learned is shared that others involved in engineering mathematics instruction may find useful or be able to relate to.