This book is intended for students of physical science, applied science and engineering, who, for the understanding and practice of their principal subjects, need a working knowledge of applicable mathematics.

Since it is not possible in a single text to cater for all degrees of mathematical facility, nor for all tastes in abstraction, a broad middle course has been adopted, set at the level of what, at the risk of being misunderstood, I describe as the ‘average student’. It is hoped, however, that what is presented will also be of value to those who fall on either side of this central band, either as a less than rigorous introduction to the subject for the one group, or as an explanatory and illustrative text for the other.

The ground covered is roughly those areas of applied mathematics usually met by students of the physical sciences in their first and second years at university or technical college. Naturally much of it also forms parts of courses for mathematics students.

In any book of modest size it is impossible to cover all topics fully, and any one of the areas mentioned in this book can be, and has been, the subject of larger and more thorough works. My aim has been to take a ‘horizontal slice’ through the subject centred on the level of an average second-year student.

The preliminary knowledge assumed is that generally acquired by any student prior to entering university or college.