Also on the curling-up-and-huddling-in-bed list for today: "Visual Complex Analysis" by Tristan Needham. Lots of neat stuff about complex numbers and why they're important - with tons of diagrams. Maybe (if I'm feeling brave) a few pages from Roger Penrose's "The Road to Reality" which is a great book for the serious layperson. (But as one reader writes in a review, "not for the faint of heart!")
My last math adventure was trying to derive the integral of (sin2 x) using complex numbers and Euler's formula. It actually worked! (Yay.) Today if I get really bold I might try to work out some values of (ex) with just pen and paper, using the series expansion of the exponent function.
I find I get more out of math - and trust it more - if I can see all the steps, preferably by reducing it to pen-and-paper computations. They don't usually teach you this in school, but you can approximate all the important functions - circular functions, exponents and logarithms, etc. - by doing them as series expansions. (Of course, unlike Jahnke and Emde, we can always fall back on our electronic calculators.) This didn't click for me the first time I was learning about convergent and divergent series; I sat there thinking, "C'mon, series are BORING!"
But now I think almost everything in math depends on series in one way or another. In fact, the very first mathematical operation we learn is a series function ... counting!
BTW, I have the dubious distinction of having tried unsuccessfully to pass more semesters of Calculus than probably anybody you know. It's one of those things I find fascinating but I'm terrible at ... at least in a classroom setting. I'm hoping if I spend more time just playing with it, I'll get comfortable enough that I'll finally be able to pass 3rd semester next time I take it. Wish me luck.