I'm interested in the differentials-based approach advocated by Dray and Manogue at Bridging the Vector Calculus Gap. This is for multivariable calculus, but they do discuss the one-variable version (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.)
