Would You Like Some Calculus With Your Physics?

It’s a nice demonstration of the oddity of the blogosphere that a libertarian political blog has become my go-to-source for thoughtful blogging about physics education. Thoreau had two good posts yesterday at Unqualified Offerings, one on the problems created by breaking down incorrect intuition, and another on the lack of calculus in calculus-based physics texts:

The ostensibly calculus-based introductory physics book by Knight is not really a calculus-based book. Sure, integrals and derivatives pop up here and there, but the vast majority of the problems can be solved without them, and calculus is hardly emphasized at all in most of the text and examples. The few problems that do use calculus are generally the hard ones near the end of the problem set, and with very little in the text to prepare them for these problems it’s hard to assign them.

[…]This has been in the back of my mind for a while, but I was able to cope with it because, well, it’s just freshman stuff. But next year I’m supposed to teach the upper division classical mechanics course, and I’m realizing that my students will not have had a truly calculus-based freshman mechanics course, so all of the stuff that I’d like to do must instead be put off until I first redo mechanics (in abbreviated form, of course) with calculus. This does not make me happy.

I’ve noticed much the same thing. In fact, one of my biggest reservations about the Matter and Interactions curriculum is that it has, if anything, even less calculus than the previous intro text we were using.

That may be a little unfair, actually– it has calculus, but in many ways, it’s stealth calculus. The whole text is built around a very computational approach to physics, with lots of time spent on solution methods involving the iterative updating of physical properties over small steps in position or time. These are essentially numerical integrations of the equations of motion, and the book does explicitly say that in several places. But there are essentially no problems involving applied calculus, and all the summary formulae are presented in update form, so I fear that the take-home message is that physics is really algebra-based.

Thoreau’s comment about preparation for upper-level classes is a worry, as well. I’m going to be teaching quantum optics again in the fall (assuming I can cajole enough students into signing up, anyway), and one issue I’ll have to contend with is that a good number of the students will never have seen Maxwell’s equations in differential form. Which makes it a little difficult to get to the wave equation, and set up the necessary background information about the classical model of light as an EM wave.

This is a tough problem, though. There are a lot of problems with trying to make the introductory courses more mathematical, starting with the preparation of our students, many of whom don’t have all that solid a grip on algebra. We list calculus as a co-requisite for intro physics, but the computer system used to handle course registration does not check or enforce prerequisites in any useful way, so we get students in the class who aren’t comfortable with derivatives, let alone differential equations.

On some level, I sort of feel like we should make our students suck it up and deal with the math– after all, the second course in the physics major when I was an undergrad was E&M out of Purcell’s book, and it doesn’t get more mathematical than that. On the other hand, though, I got basically nothing out of that class, and had to re-learn E&M more or less from scratch my junior year. And I was crazy enough to go on to grad school– for the typical wannabe engineer, Purcell would be a slow agonizing death by vector calculus.

Anyway, if anyone knows a foolproof solution for these issues, leave a comment or send me an email, because I’d love to know what to do.