I'm interested in the differentials-based approach advocated by Dray and Manogue at [Bridging the Vector Calculus Gap](http://www.physics.orst.edu/bridge/).  This is for multivariable calculus, but they do [discuss the one-variable version](http://www.physics.orst.edu/bridge/papers/CMJdifferentials.pdf) (pdf).  As they mention, people have *reviewed* calculus (especially for science courses) in these terms, but has anybody lately *taught* it this way?

(Also, the theory behind this approach is a little unclear beyond the first derivative, which is what led me to [this question](https://mathoverflow.net/questions/60474/is-there-a-convenient-differential-calculus-for-cojets).)