Modern Engineering Mathematics(5th) 无水印原版pdf

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AO1 JAME0734 05 SE FM. gxd 11703/ 09: 36 Page ii PEARSON At Pearson, we take learning personally. Our courses and resources are available as books, online and via multi gu packages, helping people learn whatever, wherever and owever they choose We work with leading authors to develop the strongest learning experiences, bringing cutting-edge thinking and best learning practice to a global market. We craft our print and digital resources to do more to help learners not onl understand their content, but to see it in action and apply what they learn, whether studying or at work Pearson is the world's leading learning company. Our portfolio includes Penguin, Dorling Kindersley, the Financial T imes and our educational business. Pearson International. We are also a leading provider of electronic learning programmes and of test development, processing and scoring services to educational institutions, corporations and professional bodies around the world Every day our work helps learning flourish, and wherever earning flourishes so do people Tolearnmorepleasevisitusatwww.pearson.com/uk 80302001003801) Modern Engineering Mathematics Fifth edition Glyn James Coventry University an d David burley University of Sheffield Dick Clements University of Bristol Phil Duke University of Plymouth John searl University of Edinburgh Jerry Wright AT&T Shannon Laboratory PEARSON Harlow, Eng and· London New York. Boston: San Francisco· Toronto Sydney· Auckland· Singapore· Hong Kong Tokyo. Seoul, Taipei· New Delhi· Cape Town· Sao paulo· Mexico City. Madrid. Amsterdam. Munich· Paris Milar AO1 JAME0734 05 SE FM. gxd 11// 09: 36 Page iv PEARSON EDUCATION LIMITED Edinburgh Gate Harlow CM20 2JE United Kingdom Tel:+44(0)1279623623 Webwww.pearson.com/k First published 1992(print) Third edition 2001(print) Fourth edition 2008(print) Fourth edition with My Math Lab 2010(print) Fifth edition published 2015 (print and electronic) O Addison-Wesley Limited 1992(print) C Pearson Education Limited 1996(print) O 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 Liccnsing Agency Ltd, Saffron House, 6-10 Kirby Strcct, London ECIN &TS 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 Coral All trademarks used herein are the property uf their respective owners. The use of any trademark in this lext 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 978-1-29208082-6(PD 978-1-29208081-9( 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 Dat A catalog record for the print edition is available from the library of Congress 10987654321 Cover o Spiros gioldasis o. 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 AO1 JAME0734 05 SE FM. gxd 11/03/2015 09: 36 Page y Contents Preface about the author Chapter 1 Numbers, Algebra and Geometry 1 1.1 Introduction 1.2 Number and arithmetic 1.2.1 Number line 1.2.2 Representation of numbers 1.2, 3 Rules of arithmetic 2.4 Exercises(1-9) 1.2.5 Inequalities 10 1.2.6 Modulus and intervals 10 1.2.7 EXercises(10-14) 14 1.3 Algebra 14 1.3.1 Algebraic manipulation 1.3.2 EXercises(15-20 3.3 Equations, inequalities and identities 23 1.3.4 Exercises(21-32) 30 1.3.5 Suffix and sigma notation 30 1.3.6 Factorial notation and the binomial expansion 1.3.7 Exercises(33-35) 35 1.4 Geometry 36 1.4.1 Coordin 36 1.4.2 Straight 36 1. 4. 3 Circles 1.4.4 Exercises (36-42) 1. 4.5 Conics 1.4.6 Exercises(43-45 47 AO1 JAME0734 05 SE FM. gxd 11703/ 09: 36 Page vi VI CONTENTS 1.5 Number and accuracy 47 1.5.1 Rounding, decimal places and significant figures 47 1.5.2 Estimating the effect of rounding errors 49 1.5.3 Exercises(46-55 54 1.5.4 Computer arithmetic 55 1.5.5 Exercises(56-58) 56 1.6 Engineering applications 57 1.7 Review exercises(1-25) 59 Chapter 2 Functions 63 2.1 Introduction 64 2.2 Basic definitions 64 2.2.1 Concept of a function 64 2.2.2 EXercises (1-6) 73 2.2.3 Inverse functions 74 2.2.4 Composite functions 78 2.2.5 Exercises(7-13 81 2.2.6 Odd, even and periodic functions 82 2.2.7 Exercises(14-16) 87 2.3 Linear and quadratic functions 87 2.3.1 Linear functions 87 2.3.2 Least squares fit of a linear function to experimental data 89 2.3.3 Exercises(17-23) 93 2.3.4 The quadratic function 94 2.3.5 Exercises(24-29) 97 2.4 Polynomial functions 98 2.4.1 Basic properties 99 2.4.2 Factorization 100 2.4.3 Nested multiplication and synthetic division 102 2.4.4 Roots of polynomial equations 105 2. 4. 5 Exercises(30-38 112 2.5 Rational functions 114 2.5.1 Partial fractions 116 2.5.2 Exercises(39-42 122 2.5.3 Asymptotes 123 2.5. 4 Parametric representation 126 2.5.5 Exercises(43-47) 128 CONTENTS VI 2.6 Circular functions 128 2.6.1 Trigonometric ratios 129 2.6.2 Exercises(48- 54 131 2.6.3 Circular functions 132 2.6.4 Trigonometric identities 138 2.6.5 Amplitude and phase 142 2.6.6 EXercises(55-66 145 2.6.7 Inverse circular(trigonometric) functions 146 2.6.8 Polar coordinates 148 2.6.9 Exercises (67-71) 151 2.7 Exponential, logarithmic and hyperbolic functions 152 2.7.1 EXponential functions 2.7.2 Logarithmic functions 155 2.7.3 Exercises (72-80) 157 2.7.4 Hyperbolic functions 157 2.7.5 Inverse hyperbolic functions 162 2.7.6 Exercises(81-88 164 2.8 rational functions 164 2.8.1 Algebraic functions 165 2.8.2 Implicit functions 166 2.8. 3 Piecewise defined functions 170 2.8.4 Exercises(89-98) 172 2.9 Numerical evaluation of functions 173 2.9.1 Tabulated functions and interpolation 174 2.9.2 Exercises(99-104) 178 2.10 Engineering application: a design problem 179 2.11 Engineering application: an optimization problem 2.12 Review exercises(1-23) 182 Chapter 3 Complex Numbers 185 3.1 Introduction 186 3.2 Properties 187 3.2.1 The Argand diagram 187 3.2.2 The arithmetic of complex numbers 188 3.2.3 Complex conjugate 3.2.4 Modulus and argument 192 AO1 JAME0734 05 SE FM. qxd 11/03/2015 09: 36 Page viii VI CONTENTS 3.2.5 Exercises(1-18 196 3.2.6 Polar form of a complex number 197 3.2.7 Euler's formula 202 3.2.8 Exercises(19-27) 203 3.2.9 Relationship between circular and hyperbolic functions 204 3.2.10 Logarithm of a complex number 208 3.2.11 Exercises(28-33) 209 3.3 Powers of complex numbers 210 3.3.1 De Moivre's theorem 210 3.3.2 Powers of trigonometric functions and multiple angles 214 3.3.3 Exercises(34-41) 217 3. 4 Loci in the complex plane 218 3.4.1 Straight lines 218 3.4.2 Circles 219 3.4.3 More general loci 221 3.4.4 Exercises(42-50) 222 3.5 Functions of a complex variable 223 3.5.1 Exercises(51-56) 225 3.6 Engineering application: alternating currents in electrical networks 225 3.6.1 Exercises(57-58) 227 3.7 Review exercises(1-34 228 Chapter 4 Vector Algebra 231 4.1 Introduction 232 4.2 Basic definitions and results 233 4.2.1 Cartesian coordinates 233 4.2.2 Scalars and vectors 235 4.2.3 Addition of vectors 237 4.2.4 Exercises(1-10) 243 4.2.5 Cartesian components and basic properties 244 4.2.6 Complex numbers as vectors 250 4.2.7 Exercises (11-26) 252 4.2.8 The scalar product 253 4.2.9 Exercises(27-40) 260 4.2.10 The vector product 261 4.2.11 Exercises(41-56) 271 AO1 JAME0734 05 SE FM. gxd 11/03/ 09: 36 Page ix CONTENTS X 4.2.12 Triple products 272 4.2. 13 Exercises(57-65) 278 4.3 The vector treatment of the geometry of lines and planes 279 4.3.1 Vector equation of a line 279 4.3.2 Exercises(66-72) 286 4.3. 3 Vector equation of a plane 4.3.4 Exercises(73-83) 290 4.4 Engineering application: spin-dryer suspension 291 4.4.1 Point-particle model 291 4.5 Engineering application: cable-stayed bridge 293 4.5.1 A simple stayed bridge 294 4.6 Review exercises(1-22) 295 Chapter 5 Matrix Algebra 298 5.1 Introduction 299 5.2 Basic concepts, definitions and properties 300 5.2.1 Definitions 303 5.2.2 Basic operations of matrices 306 5.2.3 Exercises (1-11) 5.2.4 Matrix multiplication 312 5.2.5 Exercises(12-18) 5.2.6 Properties of matrix multiplicate 318 5.2.7 EXercises(19-33) 327 5.3 Determinants 329 5.3.1 Exercises (34-50) 341 5.4 The inverse matrix 342 5.4.1 Exercises (51-59 346 5.5 Linear equations 348 5.5. 1 Exercises(60-71) 355 5.5.2 The solution of linear equations: elimination methods 357 5.3 Exercises(72-78) 370 5.5. 4 The solution of linear equations: iterative methods 372 5.5.5 Exercises (79-84) 377

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