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An Introduction to Programming and Numerical Methods in MATLAB

S.R. Otto and J.P. Denier

An Introduction to Programming and Numerical Methods in MATLAB
With 111 Figures

S.R. Otto, BSc, PhD The R & A St Andrews Fife KY16 9JD Scotland J.P. Denier, BSc (Hons), PhD School of Mathematical Sciences The University of Adelaide South Australia 5005 Australia

British Library Cataloguing inPublication Data Otto, S. R. (Stephen Robert) An introduction to programming and numerical methods in MATLAB 1. MATLAB (Computer file) 2. Numerical analysis — Data processing I. Title II. Denier, J. P. 518′.02855 ISBN 1852339195 Library of Congress Control Number: 2005923332 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under theCopyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to thepublishers. ISBN-10: 1-85233-919-5 ISBN-13: 978-185233-919-7 Springer Science+Business Media springeronline.com © Springer-Verlag London Limited 2005 The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant laws and regulations and therefore free for general use. The publisher makes norepresentation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Typesetting: Camera-ready by authors Printed in the United States of America 12/3830-543210 Printed on acid-free paper SPIN 11317333

For Julie and Jill and Megan.

Preface

This text providesan introduction to the numerical methods that are typically encountered (and used) in science and engineering undergraduate courses. The material is developed in tandem with MATLAB which allows rapid prototyping and testing of the methods. The package MATLAB (matrix laboratory) provides an environment in which students can learn to programme and explore the structure of the numerical methods. Themethods included here are of a basic nature and only rely on material which should have been explored prior to the first year undergraduate stage. The methods presented are supplemented with a set of tasks at the end of each chapter (full solutions of these are given in Appendix C). The tasks are introduced in such a way as to allow students to explore the topics as they evolve. Some are of amathematical nature, but in the main they involve manipulating codes which are given in the text of the chapter (or section). Those tasks which we regard as being harder are marked with an asterisk. Throughout the text MATLAB commands appear using this font in the text. In the main the names of MATLAB commands reflect the commands rˆle. We o have taken particular care to highlight many of the problemsthat occur with interpreting the syntax of MATLAB commands. In Appendix B we provide a glossary of all MATLAB commands within the text and short examples of how these commands can be used. Reference is made to the comprehensive help facility within MATLAB: however examples are given which are similar to those given in other places within the text. Throughout the text we derive the numericaltechniques we use, but also emphasise that MATLAB’s rich vocabulary provides commands for performing most of the fundamental tasks encountered in numerical methods. This approach serves to introduce students to the methods and also provides an

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Preface

understanding of their inner workings.

Why Do We Need Numerical Methods?
Mathematics is an elegant and precise subject: however when...
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