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Synopsis
Excerpt from Elementary Vector Analysis With Application to Geometry and Physics
My object in writing this book was to provide a simple exposition of elementary Vector Analysis, and to show how it may be employed with advantage in Geometry and Mechanics. It was thought unnecessary, in the present volume, to enter upon the more advanced parts of the subject, built upon the ideas of gradient, curl and divergence. Vector algebra and the differentiation of vectors with respect to one scalar variable furnish a powerful instrument even for the higher parts of dynamics.
The work does not claim to be a complete text-book in either Geometry or Mechanics, though a good deal of ground is covered in both subjects. The use of vector analysis in the former is abundantly illustrated by the treatment of the straight line, the plane, the sphere and the twisted curve, which are dealt with as fully as in most elementary books, and a good deal more concisely. In Mechanics I have explained and proved all the important elementary principles. The equations of equilibrium for a rigid body are deduced from the equations of motion. This is contrary to the ordinary practice and, of course, is not recommended for young beginners. But for a student who is able to read this volume, it is certainly desirable to show that the principles of statics are only particular cases of the dynamical ones, and that the long line of argument followed by text-books in Statics, to prove the theorems about moments, parallel forces, couples and the equilibrium of bodies, is really unnecessary. All these theorems are immediately deducible from the equations of motion of a rigid body, as shown in Chapter VIII.
Another departure from the ordinary practice has been made in connection with the theory of centroids.
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- PublisherForgotten Books
- Publication date2018
- ISBN 10 1330407520
- ISBN 13 9781330407523
- BindingPaperback
- LanguageEnglish
- Number of pages214
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Elementary Vector Analysis: With Application to Geometry and Physics
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Paperback. Condition: New. Print on Demand. This book provides a clear and concise introduction to the principles of vector analysis, a powerful tool for tackling problems in geometry and mechanics. The author traces the evolution of vector analysis from its roots in the work of mathematicians like Hamilton and Grassmann, highlighting its development as a system designed to simplify complex calculations in physics and applied mathematics. The book delves into the fundamental concepts of vector addition, subtraction, and multiplication, illustrating their application to geometry through the study of straight lines, planes, spheres, and twisted curves. The author also explores the crucial role of vectors in mechanics, presenting a detailed analysis of the equations of motion for rigid bodies and a thorough explanation of centroids, including the concept of center of mass. The book's unique approach showcases how the principles of statics can be derived from the fundamental equations of dynamics, simplifying traditional methods of analysis and offering a more unified understanding of these interconnected fields. Ultimately, the book demonstrates the elegance and efficiency of vector analysis as a tool for comprehending the physical world. 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 # 9781330407523_0
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Elementary Vector Analysis
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Elementary Vector Analysis
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Elementary Vector Analysis with Application to Geometry and Physics (Classic Reprint)
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Paperback. Condition: Brand New. 214 pages. 9.00x6.00x0.49 inches. This item is printed on demand. Seller Inventory # zk1330407520
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