How I'd Rewrite the Syllabus for the Calculus Circus

Everyone knows that it's not real calculus. This is the class that you get credit for if you scored a 3 on AB calculus.

First off, I'd take out every calculation dealing with limits. I'd talk about continuity in pretty vague terms -- warning students that stupid things can happen if the function is undefined at a point (division by zero) or if the pieces of a piecewise-defined function don't line up.

None of that definition of the derivative, either. We'd talk about the derivative as a slope, sure, but we wouldn't delve into the nitty gritty of it. Certainly no calculations that require tedious algebra. From there, once we hit max/min, we would skip everything about local max / local min and only deal with global max / global min.

And then in the integration chapter, we'd leave out the part where they actually calculate Riemann sums.

Now that is a calculus course that I could successfully teach in one semester to the students who I have.