Mathematics Of Modern Engineering - Vol I

MATHEMATICS OF MODERN ENGINEERING VOLUME I BY ROBERT E. DOHERTY M. A., MS., LL. D. President, Carnegie Institute, of Technology AND ERNEST G. KELLER M. S., PhD. University of Chicago Consulting Mathctnatiiian, Curtm-Wri hl Corporation One of a Series written in the interest of the General Electric Advanced Engineering Program NEW YORK JOHN WILEY SONS, INC. LONDON CHAPMAN HALL, LIMITED COPYRIGHT, 1936 BY THE GENERAL ELECTRIC COMPANY All Rights Reserved This book or any part thereof must not be reproduced in any form without the written permission of the publisher. SEVENTH PRINTING, OCTOBER, 1949 PREFACE The purpose of this text is to facilitate the study and use of mathe matics with especial reference to its applications in engineering. The justification of another text in this general field, however, is not its purpose merely, which is broadly the same as that of any book on the same subject, but the point of view from which it is written. The latter has been tempered, first, by the joint participation of a mathe matician who has worked in engineering and of an engineer who has worked with mathematics and secondly, by the atmosphere of the engineering office and the classroom. On its educational side, the text represents a gradual development of material and form during a class room experience of ten years and, on the engineering side, embodies a scope and method suggested by engineering work extending over a much longer period. It is thus neither a text on mathematics nor one on engineering, nor yet merely a handbook on engineering mathe matics. Rather, it is, first, a guide in bridging the gap in engineering between physics and mathematics by the scientific method and secondly, apresentation, suitable for engineers, of those aspects of mathematics which the experience of a large manufacturing organiza tion in dealing with electrical and mechanical problems has indicated to be of value to engineers. Such a book may appear choppy and lacking in unity from the mathematicians point of view. However, the unity of the text lies in its method of approach in the mathematical formulation of engineer ing problems. The problems themselves and the mathematical devices used in solving them afford a great variety, and it is this variety that may, in a superficial review, present the appearance of choppiness. We believe that there is a broad educational field for a text which outlines the application of mathematics from the point of view referred to, and which is of proved usefulness in class work. The text was originally developed for the Advanced Course in Engineering of the General Electric Company. Although prepared for that course, which comprises a selected group of engineering graduates just out of college, nevertheless the book should be useful as well in college in both undergraduate and graduate engineering work. This volume covers ground which those students who are interested in the higher VI PREFACE levels of engineering service should study as undergraduates. The material of the second volume fits more appropriately in graduate work. The only knowledge presupposed for understanding Volume I is the calculus. On account of the special nature and purpose of the text it has seemed desirable to include a Foreword for Instructors which may be helpful to them in presenting the point of view to the student. Assistance from engineers of the General Electric Company isacknowledged. They have suggested problem material from actual engineering work, and offered valuable criticisms. We are especially indebted to Dr. A. R. Stevenson and Messrs. P. L. Alger, E. E. Johnson, and Alan Howard of the General Electric Company. Finally, we wish to express our thanks to Professor B. R. Teare, Jr., formerly of Yale University, and of the General Electric Company, now at Carnegie Institute of Technology, not only for his valuable suggestions but also for his assistance in the selection and presentation of material...