Elementary calculus may be taught as a theory of real functions on the real line. It is then natural to introduce symbols for composition and for the identity function. But there is a general hesitation to do this. The reason is that most applications of calculus actually deal with real functions on a one‐dimensional manifold, and with their differentials. This paper shows how the scalars and differentials of tensor analysis may be presented at this level. The resulting theory is not only simple to understand, but is necessary in order to make any sense out of elementary calculus.