The aim of these volumes is that they shall together form a complete course in Calculus from its beginnings up to the point where it joins with the subject usually known as analysis. The whole conception is based on considerable dissatisfaction with much that seems rough-and-ready in the basic ideas with which pupils reach the universities, so that almost anything seems acceptable for ‘proof’ which is superficially plausible. Of course the early work cannot be treated with the rigour appropriate to more mature judgement; but I have tried here, however unsuccessfully, to present the subject in such a way that the more exact treatment, when it comes, can follow by natural development, without being forced to return to a fresh beginning which is often felt to be both unnecessary and even pointless. (How many students lose the thread of analysis just because they do not see any reason for the first few lectures and therefore do not give them serious attention?)

The first volume deals with the basic ideas of differentiation and integration. Graphical methods are used freely, but, it is hoped, in such a way that the essential logical development is never far away. The examples at this stage are mainly very simple, and beginners should have no difficulty in acquiring a fluent technique. Integration appears from the start as area and summation, the method of calculation by inverse differentiation being deduced.