Advanced Calculus
This is a text-book for students of engineering and science who are taking a first course in advanced calculus. It is based on a lecture course given at the University of Dundee and the University of Western Australia. A knowledge of elementary calculus of real-valued functions of one variable and of some properties of vectors is assumed. Emphasis is placed on the many worked examples and exercises that enable the student to fully understand what he or she is doing rather than taking a merely mechanical approach to the subject. This text is aimed at engineers and scientists who are primarily concerned with the applications of the material, and to mathematicians who are interested in the material for its own sake.