Excerpt from Vector Calculus: With Applications to Physics
This volume embodies the lectures given on the subject to graduate students over a period of four repetitions. The point of view is the result of many years of consideration of the whole field. The author has examined the various methods that go under the name of Vector, and finds that for all purposes of the physicist and for most of those of the geometer, the use of quaternions is by far the simplest in theory and in practice. The various points of view are mentioned in the introduction, and it is hoped that the essential differences are brought out. The tables of comparative notation scattered through the text will assist in following the other methods.
The place of vector work according to the author is in the general field of associative algebra, and every method so far proposed can be easily shown to be an imperfect form of associative algebra. From this standpoint the various discussions as to the fundamental principles may be understood. As far as the mere notations go, there is not much difference save in the actual characters employed. These have assumed a somewhat national character. It is unfortunate that so many exist.
The attempt in this book has been to give a text to the mathematical student on the one hand, in which every physical term beyond mere elementary terms is carefully defined. On the other hand for the physical student there will be found a large collection of examples and exercises which will show him the utility of the mathematical methods.
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