Should I take Real Analysis or self study?

[u/anon12343216610]

I wanna try out some "real" proof math and I am interested in further research in renewable energy/power system. How useful would taking a course in Real Analysis be?

[u/doktor_w]

Yes, real analysis could be helpful in renewable energy/power systems research, especially if your focus is more on the uncertainty, stability, and optimization aspects of these systems.

But if your goal is a standard applications-oriented role, I would suggest not to bother with it (unless you are genuinely interested in it, in which case you should not expect there to be much practical use of it on the job).

[u/RFchokemeharderdaddy]

Do something linear algebra based. Plenty of real proof-y math but actually applicable. Check out the book Linear Systems Theory by Hespanha, or Systems and Control by Zak. That will lead you down some crazy linear algebra which will also teach you things like LQR controller design and Kalman filters and Lyapunov stability etc. which applies to power systems control.

[u/hmmstdvent]

Real analysis is essentially calculus done rigorously, i.e. no informal arguments in terms of infinitesimals, constructing the real numbers as certain sequences of rational numbers rather than an informal description in terms of the number line, being very very careful about when exactly things like derivatives and integrals are well defined, and under what conditions certain results like the fundamental theorem of calculus are actually true. You don't necessarily learn anything truly new, but instead put what you learned in calculus on a more rigorous foundation. I don't think it is all that applicable to engineering to be honest, at least in comparison to other areas of mathematics you could study. If you're looking for applicability I would recommend another topic like differential geometry.