Will these math courses be of much use to a ME

[Gauss M.D.]

In ME, we're required to take the usual single- and multivariable calculus, differential equations, linear algebra and a bunch of courses in finite element analysis and such. For some weird reason, Fourier analysis isn't required. I would really like to add some extra math to my degree (which will be a masters in the end) but I'm not sure which courses would be most useful. I'd like to optimize for a specialization in computational mechanics, possibly a phd.

Multi variable calculus II
Complex analysis
Fourier analysis
Statistics and probability II
Optimization II
Signals and systems

It's basically more math, or a bunch of programming courses. I guess it's worth mentioning that the mandatory programming courses don't add up to much at all so it's not like there's a shortage of non-math courses that would be useful.

 

[MechanicalEngr]

IMHO, anything resembling vector analysis is a big plus, you will be confronting tensors head on in that specialization, intro to PDE would be huge plus... also, I wouldn't discount programming, your whole world will revolve around mathematical modeling( with cpu ). I'd take math and programing 50/50.

 

[AlephZero]

Probably the most generally useful in industry would be Stats II and Opt II.

Depending on what your interest are, MV Calc II would be relevant to FE theory, and the other three to dynamics, especially vibration measurement and experimental modal analysis (which can involve plenty of theory, as well as sticking accelerometers on things and hitting them with hammers!)

The other three

 

[Gauss M.D.]

Thanks for the input guys!

Sounds like signals and systems and complex analysis would be the least useful to a ME then? Or will complex analysis show up enough in enough weird, unexpected ways that it might be worthwhile?

 

[Matrix0]

I can assure you that math courses are crucial for any field, especially for someone pursuing a degree in ME and specializing in computational mechanics. While the specific math courses required may vary between programs, it is important to have a strong foundation in calculus, linear algebra, and differential equations. These courses provide the fundamental tools for solving complex problems and are essential for understanding the principles of mechanics and computational methods.

Additionally, courses in Fourier analysis and complex analysis can greatly enhance your understanding of computational mechanics and its applications. Fourier analysis is particularly important for understanding and analyzing signals and systems, which is a key aspect of computational mechanics. Complex analysis also has many applications in ME, such as in fluid mechanics and electromagnetics.

Statistics and probability are also essential for any field, including ME. Understanding the principles of probability and statistics allows for better analysis and interpretation of data, which is crucial in any research or engineering work.

Optimization is another important aspect of computational mechanics, and a course in optimization can greatly enhance your skills in finding efficient solutions to complex problems.

In summary, while programming courses are also important for computational mechanics, it is crucial to have a strong foundation in mathematics. I would recommend taking all of the math courses listed, as they will provide you with a well-rounded understanding of the principles and techniques used in computational mechanics. As for which courses to prioritize, I would suggest discussing with your academic advisor or potential PhD advisor to determine which courses would be most beneficial for your specific research interests and career goals.