As another (recent) Caltech grad, I'll take a stab this. The Caltech intro calc class is very heavily proof-based. We started with easy problems that had noth

As another (recent) Caltech grad, I'll take a stab this. The Caltech intro calc class is very heavily proof-based. We started with easy problems that had nothing to do with calculus like proving that 1/sqrt(3) is irrational, went into epsilon-delta proofs for limits, and continued on to showing that the Dirichlet function is discontinuous everywhere. I don't think we evaluated a single integral in that class. A strange feature of the class was that the weeks where we studied derivatives were a lot harder than the weeks when we studied integrals. Although derivatives are a lot easier to evaluate than integrals, it's a lot harder to prove that they exist. Most of our problems were proving the existence of derivatives and integrals, not evaluating them, so it was a weird inversion in what is normally considered difficult in calculus. If you want a sample of the problems, here's one of the problem sets from this year's class: http://www.math.caltech.edu/%7E2011-12/1term/ma001a1/homework/11Ma1a1Hw3.pdf http://www.math.caltech.edu/%7E2011-12/1term/ma001a1/homewor...