Synopsis
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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Paperback. Condition: New. Print on Demand. This book delves into the fascinating realm of vector calculus, a branch of mathematics that deals with quantities possessing both magnitude and direction, like velocity or force. Emerging from early attempts to expand the concept of numbers beyond mere measurement, vector calculus has evolved into a powerful tool with applications in various scientific disciplines. The author expertly navigates through the historical development of vector calculus, comparing and contrasting different approaches such as quaternions, dyadics, and the works of mathematicians like Grassmann. The book emphasizes the practical applications of vector calculus in physics and geometry, providing a comprehensive collection of examples and exercises to solidify understanding. By focusing on the intrinsic properties of vectors rather than relying on specific coordinate systems, the author unveils the elegance and universality of vector operations. Concepts like gradient, divergence, and curl are explored, revealing their significance in describing physical phenomena such as fluid flow, electromagnetic fields, and gravitational forces. The book's insights into vector calculus equip readers with a deeper understanding of the fundamental principles governing our physical world and its mathematical representation. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Seller Inventory # 9781330325575_0
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