I had just finished a Calculus II class on antiderivatives using the natural logarithm, and as I was erasing the board (filled with indefinite integrals, u-substitutions, and things like "ln|sec(t)|"), one of my precalculus students came into class to ask me something. I shifted gears to answer his question, and realized that while I considered most of the stuff on the board pretty easy, to a precalculus student, it must look incredibly complicated, and perhaps like sheer gibberish. And of course it seems transparent to me; I've been doing calculus since 1988, so it's been over 20 years now. (Amazingly, things like this have stopped making me feel old.)
It's much like the conversation I had with another colleague once: We were talking about low-level, introductory courses at the university (Big State Tech U), and meant any of the various calculus sequences.* But we observed that for the general population, "calculus" is used as a metaphor for anything unbelievably advanced and difficult. (Sort of like "brain surgery" and "rocket science", although if you are a brain surgeons or rocket scientist, you mastered calculus long ago.) Most mathematicians (and a number of other scientists) see calculus at the starting point for our fields, while most of the general population sees it as the pinnacle of learning.
*Of course, that conversation was at Big State Tech U. Now I do teach at a school that teaches a wide variety of courses lower than calculus, including lots of algebra, a general education math course, courses for elementary teachers, and even remedial courses. Not that I don't still consider calculus the first real college level math class.
