Teaching Advanced Engineering Mathematics to Graduate Students: Lessons Learned

Advanced engineering mathematics, sometimes known as advanced engineering analysis, is a required course in many graduate engineering programs as it provides coverage of topics of mathematics required to succeed in the graduate study of any engineering discipline. The author has been teaching a core engineering mathematics class to incoming first year graduate students in mechanical engineering since 2002. Advances in mathematical soft ware and tools make teaching the class challenging as traditional methods of teaching engineering mathematics may not be appropriate when use of mathematics software is prevalent. In addition, teaching engineering students how to apply mathematical principles and models in relevant subjects of engineering is a necessity for this kind of class. The class covers a wide range of subjects but the major emphasis is on partial differential equations and their solutions. Other topics include vector calculus, vector integral theorems, numerical solutions of ordinary and partial differential equations, statistics and probability. This paper discusses and summarizes the lessons learned from teaching the class for many years. The experience and lessons learned may be beneficial to other faculty members developing or teaching similar classes to graduate students.