Tensors and their applications PDF
Preview Tensors and their applications
This page intentionally left blank Copyright © 2006, New Age International (P) Ltd., Publishers Published by New Age International (P) Ltd., Publishers All rights reserved. No part of this ebook may be reproduced in any form, by photostat, microfilm, xerography, or any other means, or incorporated into any information retrieval system, electronic or mechanical, without the written permission of the publisher. All inquiries should be emailed to [email protected] ISBN (13) : 978-81-224-2700-4 PUBLISHING FOR ONE WORLD NEW AGE INTERNATIONAL (P) LIMITED, PUBLISHERS 4835/24, Ansari Road, Daryaganj, New Delhi - 110002 Visit us at www.newagepublishers.com To My parents This page intentionally left blank FOREWORD It gives me great pleasure to write the foreword to Dr. Nazrul Islam’s book entitled “Tensors and Their Applications. I know the author as a research scholar who has worked with me for several years. This book is a humble step of efforts made by him to prove him to be a dedicated and striving teacher who has worked relentlessly in this field. This book fills the gap as methodology has been explained in a simple manner to enable students to understand easily. This book will prove to be a complete book for the students in this field. Ram Nivas Professor, Department of Mathematics and Astronomy, Lucknow University, Lucknow This page intentionally left blank PREFACE ‘Tensors’ were introduced by Professor Gregorio Ricci of University of Padua (Italy) in 1887 primarily as extension of vectors. A quantity having magnitude only is called Scalar and a quantity with magnitude and direction both, called Vector. But certain quantities are associated with two or more directions, such a quantity is called Tensor. The stress at a point of an elastic solid is an example of a Tensor which depends on two directions one normal to the area and other that of the force on it. Tensors have their applications to Riemannian Geometry, Mechanics, Elasticity, Theory of Relativity, Electromagnetic Theory and many other disciplines of Science and Engineering. This book has been presented in such a clear and easy way that the students will have no difficulty in understanding it. The definitions, proofs of theorems, notes have been given in details. The subject is taught at graduate/postgraduate level in almost all universities. In the end, I wish to thank the publisher and the printer for their full co-operation in bringing out the book in the present nice form. Suggestions for further improvement of the book will be gratefully acknowledged. Dr. Nazrul Islam
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