An introduction to calculus

Calculus is the study of the effect on functions of small changes in their variables. One can study either the effect of one small change (differential calculus) or the accumulation of many small changes (integral calculus). One amazing result, the Fundamental Theorem of Calculus, shows how these two areas of calculus are related.

We can easily demonstrate all of the main ideas of calculus if we restrict ourselves to the set of all functions of the following form:

$$f:[0,\infty)\rightarrow [0,\infty),\;\;f(x) = kx^p$$

where k > 0 and p is a non-negative integer.

In what follows we will assume that the functions in question have the set of non-negative real numbers as their domain.