Although the major part of this book is concerned with mathematics of direct value in describing situations arising in physical science and engineering, this opening chapter, although directed to the same end, is of a less obviously ‘applied’ nature. It is concerned with those techniques of mathematics, principally in the field of calculus, which are the nuts and bolts of the more particularly orientated methods presented in later chapters.

Two particular factors have to be taken into account in its presentation; firstly the various levels of previous knowledge which different readers will possess, and secondly the fact that the subjects to be treated in this chapter form a less coherent whole than do those in any other.

The first of these has been approached at the ‘highest common factor’ level, namely, knowledge has been presumed only of those topics which will normally be familiar to a student who, in his previous studies, has taken mathematics in conjunction with other science subjects, rather than as his main or only subject. As a result, although several parts of this chapter will almost certainly be unfamiliar to him, the reader with more than this presumed level of knowledge may in some sections find it sufficient to make sure he can solve the corresponding exercises, marked by the symbol ▸, and then pass on to the next section.

As a result of the rather diverse nature of the topics considered, the degree of difficulty of the material does not vary ‘monotonically’ throughout the chapter.