I need to take one more graduate math class to finish up my master’s in mechanical engineering. Which one am I going to benefit the most from? Here are my options:
Vector Calculus. Topics covered: Calculus of functions of several variables and of vector fields in orthogonal coordinate systems. Optimization problems, implicit function theorem, Green’s theorem, Stokes’ theorem, divergence theorems, and applications to engineering and the physical sciences.
Advanced Math for Engineering and Physics. Topics covered: Divergence theorem, Stokes’ Theorem, complex variables, contour integration, calculus of residues and applications, conformal mapping, and potential theory.
Personally, I’m leaning toward vector calculus, despite the school recommending the second class for engineering grad students. It seems like it would be more applicable to my major. Also, it at least sounds like it will be a little easier, since I’ve already been exposed to some vector calculus in an undergrad multivariate calc class. And no I’m not just looking for the easy way out, but I would like to prevent a nightmarish workload like the one I’ve had this semester.
Any suggestions? What’s the relative difficulty of the topics mentioned?
They both cover similar areas in multivariable calculus, so you think in terms of which course has topics that most impact your engineering applications.
Their rationale for pushing the second course may be addressed above, and/or the level of rigor in the second may be better for non-mathematics people. The vector course may be more rigorous, and more narrow than what they generally find useful.
As an ME-in-training myself, I think I’d recommend the second course, if only because it might be more oriented towards engineering problems. When my professor covered Stokes’ and Green’s Theorems in an undergraduate-level vector calculus class, I had no idea that the H he was talking about. It wasn’t until a professor utilized the theorems in fluid mechanics to derive some equations that I finally grasped them.
IIRC, Stokes/Greens/YadaYada is about computing something called “Flux” by integrating vector flow through a surface…or something like that. The math gets heavy, but the notation is very pretty.
One thing you need to find out is the target audience for each class. If the first is more proof-oriented and the second focuses more on calculations, then that should be a factor in your decision.
Seems sort of weird to have a vector calc class be the last math course you take towards a masters in Engineering. Most people take it their sophmore year in under-grad, and I’d think it would be a pre-requisite to even starting an higher level Engineering degree.
I did take an undergrad vector calculus class, which is why I was thinking it might be a bit simpler since I’ve been exposed to a lot of it already.
Can you take a class on Numerical Analysis?
Hit enter too soon.
I have found that the 2 semesters of numerical analysis I took during my masters program in EE were probably the most beneficial classes I ever took. I have also taken an advanced mathematical physics course and a lot of courses that were heavy with vector / tensor calculus, and I do use them in my career, but I found I can learn enough of this stuff for my career pretty easily just by opening a book.
The numerical analysis was more practical as it helps you understand how math is done by computers. For me it was also less intuitive (YMMV), so I don’t think I could have really mastered it on my own. Numerical integration, curve fitting, root finding, interpolation and extrapolation, all with an emphasis on rates of convergence, error analysis, etc… Great stuff. I will say that in my current position at a company with >50 engineers of various stripes (>15 of whom have a Ph.D), there is only one other person who understands this topic like I do (a Ph.D material scientist who specialized in semiconductor physics). Having this knowledge has really set me apart in my career and been a great benefit. Just my 2 cents.