Tuesday, August 25, 2009

Calculus Two: The Awesome Way

Before the semester started I was talking to The Topologist about calculus. He's teaching Calc 2 in the engineering sequence this fall. I told him about my way of teaching Calc 2. I start where the other Calc 2 classes do with the techniques of integration (Stewart "Contexts and Concepts" Chapter 5), then instead of continuing on to Chapter 6 (zillions of stupid problems that need integration) and then doing the sequences and series (Chapter 8) at the end of the semester, I do the sequences and series in the middle and then use the "applications of integration" as a review for the last few weeks.

He has decided to take this even further. He is starting with the sequences and series. I ask him, "What about the integral test? What about the part at the end of the chapter where you integrate series term-by-term?" He's just skipping those sections for now and will mention them when he does integration.

As this is Calc 2 in the fall, his class is a mix of freshmen with AP credit and sophomores+ who are off sequence. So far he reports that none of his freshmen are doing that exasperated sigh of, "I don't see why I have to take this class since I learned all of this in high school." The freshmen are having a lot of fun so far with some of the problems that he has assigned. The upperclassmen are not so psyched about the sequences and series. But it's not like they'd be any happier about learning sequences and series in November.

Plus, once the students know about series and series notation and all that, the Riemann sum makes a pretty nice transition to integration. He promises that this is as much as he is going to mix up calculus and he will not introduce de Rham cohomology to motivate the Fundamental Theorem of Calculus.