Vector Analysis: A Text-Book for the Use of Students of Mathematics and Physics

Excerpt from Vector Analysis: A Text-Book for the Use of Students of Mathematics and Physics

When I undertook to adapt the lectures of Professor Gibbs on Vector Analysis for publication in the Yale Bicentennial Series, Professor Gibbs himself was already so fully engaged upon his work to appear in the same series, Elementary Principles in Statistical Mechanics, that it was understood no material assistance in the composition of this book could be expected from him. For this reason he wished me to feel entirely free to use my own discretion alike in the selection of the topics to be treated and in the mode of treatment. It has been my endeavor to use the freedom thus granted only in so far as was necessary for presenting his method in text-book form.

By far the greater part of the material used in the following pages has been taken from the course of lectures on Vector Analysis delivered annually at the University by Professor Gibbs. Some use, however, has been made of the chapters on Vector Analysis in Mr. Oliver Heaviside's Electromagnetic Theory (Electrician Series, 1893) and in Professor Föppl's lectures on Die Maxwell'sche Theorie der Electricitāt (Teubner, 1894). My previous study of Quaternions has also been of great assistance.

The material thus obtained has been arranged in the way which seems best suited to easy mastery of the subject. Those Arts, which it seemed best to incorporate in the text but which for various reasons may well be omitted at the first reading have been marked with an asterisk (*). Numerous illustrative examples have been drawn from geometry, mechanics, and physics. Indeed, a large part of the text has to do with applications of the method.

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