Matrix Operations for Engineers and Scientists An Essential Guide in
Engineers and scientists need to have an introduction to the basics of linear algebra in a context they understand. Computer algebra systems make the manipulation of matrices and the determination of their properties a simple matter, and in practical appl
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Alan Jeffrey
Matrix Operations for Engineers and Scientists An Essential Guide in Linear Algebra
Prof. Dr. Alan Jeffrey{ 16 Bruce Bldg. University of Newcastle NE1 7RU Newcastle upon Tyne United Kingdom
ISBN 978-90-481-9273-1 e-ISBN 978-90-481-9274-8 DOI 10.1007/978-90-481-9274-8 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2010932003 # Springer Science+Business Media B.V. 2010 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Cover design: eStudio Calamar S.L., Germany Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
This book is based on many courses given by the author to English and American undergraduate students in engineering and the applied sciences. The book separates naturally into two distinct parts, although these are not shown as parts one and two. The first part, represented by Chapters 1–4 and a large part of Chapter 5, gives a straightforward account of topics from the theory of matrices that form part of every basic mathematics course given to undergraduate students in engineering and the applied sciences. However, the presentation of the basic material given in this book is in greater detail than is usually found in such courses. The only unusual topics appearing in the first part of the book are in Chapter 3. These are the inclusion of the technique of least-squares fitting of polynomials to experimental data, and the way matrices enter into a finite difference approximation for the numerical solution of the Laplace equation. The least-squares fitting of polynomials has been included because it is useful and provides a simple application of matrices, while the finite difference approximation for the Laplace equation shows how matrices play a vital part in the numerical solution of this important partial differential equation. This last application also demonstrates one of the ways in which very large matrix equations can be generated when seeking the numerical solution of certain types of problem. The last part of Chapter 5 forms the start of the second part of the book, and contains various important topics which, although belonging to the subject matter of the chapter, are not discussed in courses as often as they deserve. Chapter 6 describes a matrix approach to the study of systems of ordinary differential equations and, although this approach is straightforward and found in courses for mathematics majors, it is still a relatively new topic in courses for engineers and applied scientists. In particular, the chapter shows how to use matrices when solving the homogeneous and nonhomogeneous systems of linear constant coefficient different
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