MODERN ENGINEERING MATHEMATICS Fifth Edition This book provides a complete course for first-year engineering mathematics Whichever field of engineering you are studying, you will be most likely to require knowledge of the mathematics presented in this textbook Taking a thorough approach, the authors put the concepts into an engineering context, so you can understand the relevance of mathematical techniques presented and gain a fuller appreciation of how to draw upon them throughout your studies Key features Comprehensive coverage of first-year engineering mathematics Fully worked examples and exercises provide relevance and reinforce the role of mathematics in the various branches of engineering Excellent coverage of engineering applications Over 1200 exercises to help monitor progress with your learning and provide a more progressive level of difficulty Online ‘refresher units’ covering topics you should have encountered previously but may not have used for some time MATLAB and MAPLE are fully integrated, showing you how these powerful tools can be used to support your work in mathematics Glyn James is currently Emeritus Professor in Mathematics at Coventry University, having previously been Dean of the School of Mathematical and Information Sciences As in previous editions he has drawn upon the knowledge and experience of his co-authors to provide an excellent revision of the book MODERN ENGINEERING MATHEMATICS Fifth Edition Glyn James Fifth Edition MODERN ENGINEERING MATHEMATICS Glyn James Glyn James www.pearson-books.com Cover: Rio-Antirio Bridge © Spiros Gioldasis - eikazo.com CVR_JAME0734_05_SE_CVR.indd 10/03/2015 11:27 A01_JAME0734_05_SE_FM.qxd 11/03/2015 09:36 Page i Modern Engineering Mathematics A01_JAME0734_05_SE_FM.qxd 11/03/2015 09:36 Page ii A01_JAME0734_05_SE_FM.qxd 11/03/2015 09:36 Page iii Modern Engineering Mathematics Fifth Edition Glyn James and David Burley Dick Clements Phil Dyke John Searl Jerry Wright Coventry University University of Sheffield University of Bristol University of Plymouth University of Edinburgh AT&T Shannon Laboratory A01_JAME0734_05_SE_FM.qxd 11/03/2015 09:36 Page iv PEARSON EDUCATION LIMITED Edinburgh Gate Harlow CM20 2JE United Kingdom Tel: +44 (0)1279 623623 Web: www.pearson.com/uk First published 1992 (print) Second edition 1996 (print) Third edition 2001 (print) Fourth edition 2008 (print) Fourth edition with MyMathLab 2010 (print) Fifth edition published 2015 (print and electronic) © Addison-Wesley Limited 1992 (print) © Pearson Education Limited 1996 (print) © Pearson Education Limited 2015 (print and electronic) The rights of Glyn James, David M Burley, Richard Clements, Philip Dyke, John W Searl and Jeremy Wright to be identified as authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988 The print publication is protected by copyright Prior to any prohibited reproduction, storage in a retrieval system, distribution or transmission in any form or by any means, electronic, mechanical, recording or otherwise, permission should be obtained from the publisher or, where applicable, a licence permitting restricted copying in the United Kingdom should be obtained from the Copyright Licensing Agency Ltd, Saffron House, 6–10 Kirby Street, London EC1N 8TS The ePublication is protected by copyright and must not be copied, reproduced, transferred, distributed, leased, licensed or publicly performed or used in any way except as specifically permitted in writing by the publishers, as allowed under the terms and conditions under which it was purchased, or as strictly permitted by applicable copyright law Any unauthorised distribution or use of this text may be a direct infringement of the author’s and the publishers’ rights and those responsible may be liable in law accordingly All trademarks used herein are the property of their respective owners The use of any trademark in this text does not vest in the author or publisher any trademark ownership rights in such trademarks, nor does the use of such trademarks imply any affiliation with or endorsement of this book by such owners Pearson Education is not responsible for the content of third-party internet sites ISBN: 978-1-292-08073-4 (print) 978-1-292-08082-6 (PDF) 978-1-292-08081-9 (eText) British Library Cataloguing-in-Publication Data A catalogue record for the print edition is available from the British Library Library of Congress Cataloging-in-Publication Data A catalog record for the print edition is available from the Library of Congress 10 19 18 17 16 15 Cover © Spiros Gioldasis – eikazo.com Print edition typeset in 10/12pt Times by 35 Print edition printed and bound in Slovakia by Neografia NOTE THAT ANY PAGE CROSS REFERENCES REFER TO THE PRINT EDITION A01_JAME0734_05_SE_FM.qxd 11/03/2015 09:36 Page v Contents Preface About the authors Chapter Numbers, Algebra and Geometry 1.1 Introduction 1.2 Number and arithmetic 1.2.1 1.2.2 1.2.3 1.2.4 1.2.5 1.2.6 1.2.7 1.3 1.4 xxi xxiv Number line Representation of numbers Rules of arithmetic Exercises (1–9) Inequalities Modulus and intervals Exercises (10–14) 10 10 14 Algebra 14 1.3.1 1.3.2 1.3.3 1.3.4 1.3.5 1.3.6 1.3.7 15 22 23 30 30 32 35 Algebraic manipulation Exercises (15–20) Equations, inequalities and identities Exercises (21–32) Suffix and sigma notation Factorial notation and the binomial expansion Exercises (33–35) Geometry 36 1.4.1 1.4.2 1.4.3 1.4.4 1.4.5 1.4.6 36 36 38 41 41 47 Coordinates Straight lines Circles Exercises (36–42) Conics Exercises (43–45) A01_JAME0734_05_SE_FM.qxd 11/03/2015 09:36 Page vi vi C O NTEN TS 1.5 Number and accuracy 47 1.5.1 1.5.2 1.5.3 1.5.4 1.5.5 47 49 54 55 56 Rounding, decimal places and significant figures Estimating the effect of rounding errors Exercises (46–55) Computer arithmetic Exercises (56–58) 1.6 Engineering applications 57 1.7 Review exercises (1–25) 59 Chapter Functions 63 2.1 Introduction 64 2.2 Basic definitions 64 2.2.1 2.2.2 2.2.3 2.2.4 2.2.5 2.2.6 2.2.7 64 73 74 78 81 82 87 2.3 2.4 Linear and quadratic functions 87 2.3.1 2.3.2 2.3.3 2.3.4 2.3.5 87 89 93 94 97 Linear functions Least squares fit of a linear function to experimental data Exercises (17–23) The quadratic function Exercises (24–29) Polynomial functions 2.4.1 2.4.2 2.4.3 2.4.4 2.4.5 2.5 Concept of a function Exercises (1–6) Inverse functions Composite functions Exercises (7–13) Odd, even and periodic functions Exercises (14–16) Basic properties Factorization Nested multiplication and synthetic division Roots of polynomial equations Exercises (30–38) 98 99 100 102 105 112 Rational functions 114 2.5.1 2.5.2 2.5.3 2.5.4 2.5.5 116 122 123 126 128 Partial fractions Exercises (39–42) Asymptotes Parametric representation Exercises (43–47) A01_JAME0734_05_SE_FM.qxd 11/03/2015 09:36 Page vii CO N T E N T S 2.6 2.7 2.8 128 2.6.1 2.6.2 2.6.3 2.6.4 2.6.5 2.6.6 2.6.7 2.6.8 2.6.9 129 131 132 138 142 145 146 148 151 Trigonometric ratios Exercises (48–54) Circular functions Trigonometric identities Amplitude and phase Exercises (55–66) Inverse circular (trigonometric) functions Polar coordinates Exercises (67–71) Exponential, logarithmic and hyperbolic functions 152 2.7.1 2.7.2 2.7.3 2.7.4 2.7.5 2.7.6 152 155 157 157 162 164 Exponential functions Logarithmic functions Exercises (72–80) Hyperbolic functions Inverse hyperbolic functions Exercises (81–88) 164 2.8.1 2.8.2 2.8.3 2.8.4 Algebraic functions Implicit functions Piecewise defined functions Exercises (89–98) 165 166 170 172 Numerical evaluation of functions 173 2.9.1 Tabulated functions and interpolation 2.9.2 Exercises (99–104) 174 178 2.10 Engineering application: a design problem 179 2.11 Engineering application: an optimization problem 181 2.12 Review exercises (1–23) 182 Complex Numbers 185 Chapter Circular functions Irrational functions 2.9 vii 3.1 Introduction 186 3.2 Properties 187 3.2.1 3.2.2 3.2.3 3.2.4 187 188 191 192 The Argand diagram The arithmetic of complex numbers Complex conjugate Modulus and argument A01_JAME0734_05_SE_FM.qxd 11/03/2015 09:36 Page viii viii CONTENTS 3.2.5 3.2.6 3.2.7 3.2.8 3.2.9 3.2.10 3.2.11 3.3 3.4 3.5 3.6 3.7 Chapter Exercises (1–18) Polar form of a complex number Euler’s formula Exercises (19–27) Relationship between circular and hyperbolic functions Logarithm of a complex number Exercises (28–33) 196 197 202 203 204 208 209 Powers of complex numbers 210 3.3.1 De Moivre’s theorem 3.3.2 Powers of trigonometric functions and multiple angles 3.3.3 Exercises (34–41) 210 214 217 Loci in the complex plane 218 3.4.1 3.4.2 3.4.3 3.4.4 218 219 221 222 Straight lines Circles More general loci Exercises (42–50) Functions of a complex variable 223 3.5.1 Exercises (51–56) 225 Engineering application: alternating currents in electrical networks 225 3.6.1 Exercises (57–58) 227 Review exercises (1–34) 228 Vector Algebra 231 4.1 Introduction 232 4.2 Basic definitions and results 233 4.2.1 4.2.2 4.2.3 4.2.4 4.2.5 4.2.6 4.2.7 4.2.8 4.2.9 4.2.10 4.2.11 233 235 237 243 244 250 252 253 260 261 271 Cartesian coordinates Scalars and vectors Addition of vectors Exercises (1–10) Cartesian components and basic properties Complex numbers as vectors Exercises (11–26) The scalar product Exercises (27–40) The vector product Exercises (41–56) A01_JAME0734_05_SE_FM.qxd 11/03/2015 09:36 Page ix CO N TE NT S 4.3 4.4 4.5 4.6 Chapter 272 278 The vector treatment of the geometry of lines and planes 279 4.3.1 4.3.2 4.3.3 4.3.4 279 286 287 290 Vector equation of a line Exercises (66–72) Vector equation of a plane Exercises (73–83) Engineering application: spin-dryer suspension 291 4.4.1 Point-particle model 291 Engineering application: cable-stayed bridge 293 4.5.1 A simple stayed bridge 294 Review exercises (1–22) 295 Matrix Algebra 298 Introduction 299 5.2 Basic concepts, definitions and properties 300 5.2.1 5.2.2 5.2.3 5.2.4 5.2.5 5.2.6 5.2.7 303 306 311 312 317 318 327 5.4 5.5 4.2.12 Triple products 4.2.13 Exercises (57–65) 5.1 5.3 ix Definitions Basic operations of matrices Exercises (1–11) Matrix multiplication Exercises (12–18) Properties of matrix multiplication Exercises (19–33) Determinants 329 5.3.1 Exercises (34–50) 341 The inverse matrix 342 5.4.1 Exercises (51–59) 346 Linear equations 348 5.5.1 5.5.2 5.5.3 5.5.4 5.5.5 355 357 370 372 377 Exercises (60–71) The solution of linear equations: elimination methods Exercises (72–78) The solution of linear equations: iterative methods Exercises (79–84) ...A01_JAME0734_05_SE_FM.qxd 11/03 /2015 09:36 Page i Modern Engineering Mathematics A01_JAME0734_05_SE_FM.qxd 11/03 /2015 09:36 Page ii A01_JAME0734_05_SE_FM.qxd 11/03 /2015 09:36 Page iii Modern Engineering Mathematics. .. Department of Engineering Mathematics (1973–2007) He has an MA A01_JAME0734_05_SE_FM.qxd 11/03 /2015 09:36 Page xxv ABO UT TH E AUTH O RS xxv in Mathematics and a PhD in Aeronautical Engineering. .. of mathematics to students of engineering, and became Senior Lecturer in Engineering Mathematics He held a Royal Society Industrial Fellowship for 1994, and is a Fellow of the Institute of Mathematics