Sauce: I'm an EE.
(This assumes chip design work (ASIC's etc), but general hardware design (uC work) the same principle applies, and then you don't need the calculus and physics knowledge really).
Sauce: I'm an EE too... :D
That's also true about software. Once you get past the usual "comment your code carefully and make sure you're not redundant in it", 99% of the stuff that is useful in practice is stuff you derive from practice.
Software is full of thin ice where you can walk out on it, jump around, then, mistakenly thinking it's frozen over, drive your truck on, only to have it fall through. It looks easy. But there's a reason 90% of the Rails apps I've looked at had no tests.
[0] - http://ocw.mit.edu/courses/electrical-engineering-and-comput...
I've seen some physicists put together mind blowing electrical systems.