ISBN/ASIN: N/A | 1967 | English | djvu | 126/126 pages | 1.71 Mb
Publisher: Van Nostrand Reinhold | Author: Barry Spain | Edition: Second
This revised second edition provides a systematic account of vector
algebra and calculus from the fundamental definitions. Improvements
include a rigorous proof of Taylor's theorem for a vector function, a
vectorial definition of directional derivative, more material on Green s
identity and several extra examples. The book is intended for first year
students reading an honours course in mathematics and for students of
mathematics, the physical sciences and engineering at universities and
The theory is developed with emphasis on the vector as an entity in itself rather than on its definition as a number triple. It includes a chapter on line integrals, surface integrals and volume integrals, as many students require these concepts in vector theory before they have taken a formal course on integration.
The theory is presented independently of any co-ordinate system. In particular, the gradient is defined in terms of the directional derivative whilst the divergence and curl are defined by means of limits of integrals.