Programs Math and ME double major, math course selection

[anonymity]

I am a mechanical engineering and math double major at a state-university, and as far as math goes am mostly focusing on math that can be applied to the fields of engineering (specifically mechanical and nuclear).

I am going to be finished with all of the undergrad differential equations sequences my school offers after the coming school year is completed (end of my sophomore year). My school offers graduate level applied math and differential equations courses, as well as undergrad level computational math/modeling courses. I plan on taking all of the computational/modeling/numerical analysis courses (fairly small math dept.), and maybe a grad level course or two, but my real question has to do with real and complex analysis.

Is this something that is worth taking, for someone like me, with my (rough) plans in mind?

Everything that I have *READ* basically says that analysis is entirely pure mathematics, and has no applications. I don't really believe that this is fully true (for starters, because I know for a fact that theoretical physicists use proof-based math all the time), and was wondering if you guys could help me decide whether or not these courses (intro to proof based real and complex analysis) would be a waste of my time (our math program basically let's you pick whatever courses you want to take,they require a few basics, like linear algebra and an intro proof course, but it's pretty lenient). I will also talk to my adviser, but would like to hear what you guys have to say.

Thanks =D

edit/ps:

I added an edit, but it was just a few sentences of my bias inclination, so i took it out. =0

 

[edgepflow]

I feel that there are very few math or physics courses that do not benefit engineering students in some way. Having said that, I would assign the applied math, numercical & modeling courses a higher priority than ones based on proofs.