The justification for adding one more to the many available texts on vector analysis cannot be novelty of content. In this book I have included a few topics that are more frequently encountered as part of the discussion of a specific physical topic – in the main in fluid dynamics or electrodynamics – but this in itself does not justify telling the whole story over again, perhaps least of all in the classical way – in bold-type vectors, excluding suffixes, tensors, n-dimensional space etc. However, after giving a course in the standard shape for many years (to Scottish students in their second year – roughly comparable in level to an English first-year University course) I gradually developed a way of presenting the subject which gave the old tale a new look and seemed to me to make a more coherent whole of it. Once my course had taken this shape the students were left without a suitable text to work from. More and more ad hoc handouts became necessary and finally the skeleton of this book emerged.

In preparation for publication I spent more time on devising the sections of exercises than on the main text which was largely in existence from the start. The exercises were indeed devised rather than compiled and I am well aware that they reveal my idiosyncrasies. I see them as a necessary part of learning a language.