Overview

While the principal concepts of the calculus were developed in the seventeenth century, a sound mathematical formulation of the subject would have to wait until the nineteenth. Critics of the early formulations pointed to the rather casual way in which infinitesimal and infinite quantities were defined. Lagrange attempted to replace the need for derivatives in the differential calculus with a requirement that the difference between the values of a function at two values of its argument be expressed as a power series. The theory of power series would eventually play an important role in the solution of differential equations and in the machine calculation of special functions.

Background

In the seventeenth century, mathematicians had arrived at the notion of a function as a well-defined combination of mathematical operations that allows for one quantity to be obtained from another quantity. Thus f...