Table Of ContentMATHEMATICS ENGINEERS CROFT AND ANTHONY CROFT AND ROBERT DAVISON
FOR
DAVISON MATHEMATICS
Fifth edition
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Understanding key mathematical concepts and applying them successfully to solve problems are vital skills
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that all engineering students must acquire. Mathematics for Engineers introduces, teaches, develops and ENGINEERS
nurtures those skills. Practical, informal and accessible, it begins with the foundations and gradually builds A FOR
upon this knowledge as it introduces more complex concepts. Learn everything you will need for your fi rst year G
engineering mathematics course, together with a wealth of introductory material for even more advanced T
topics such as Laplace and Fourier transforms and partial diff erential equations.
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Key features FIFTH EDITION
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• Applications of mathematics are drawn from a wide range of engineering areas: aeronautical, automotive,
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chemical, civil, computer, electrical and electronic, manufacturing, materials, mechanical, production,
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reliability, and systems engineering.
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• Hundreds of interactive examples are provided in the context of various engineering disciplines, so you
are able to both engage with the problems and also see the relevance of the maths to your wider studies.
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• A wealth of practice and revision exercises with solutions help test your knowledge.
• Key points and important results are highlighted throughout. ST
• Computer and calculator examples and exercises are incorporated in relevant sections.
• Specimen examination papers give further opportunity to practise. I
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• A foundation section gives you a fi rm base in arithmetic, the building block of many high-level
mathematical topics.
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New to this 5th edition
• Signifi cant enhancements integrating the use of computer software in the solution of engineering
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mathematics problems.
• Widening of the applications base to include more from mechanical, materials and aeronautical O
engineering.
• Introductory material on the solution of partial diff erential equations, loci in the complex plane and the R
equation of a circle.
FIFTH
Anthony Croft is Emeritus Professor of Mathematics Education at Loughborough University and
EDITION
Robert Davison spent over 30 years teaching and writing mathematics for higher education students.
They have authored many best-selling mathematics textbooks including several for engineering students.
Cover image: © shutterstock Premier/ Ekaphon maneechot www.pearson-books.com
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Mathematics for Engineers
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Mathematics for
Engineers
Fifth Edition
Anthony Croft
Loughborough University
Robert Davison
Harlow, England • London • New York • Boston • San Francisco • Toronto • Sydney • Dubai • Singapore • Hong Kong
Tokyo • Seoul • Taipei • New Delhi • Cape Town • São Paulo • Mexico City • Madrid • Amsterdam • Munich • Paris • Milan
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PEARSON EDUCATION LIMITED
KAO Two
KAO Park
Harlow CM17 9NA
United Kingdom
Tel: +44 (0)1279 623623
Web: www.pearson.com/uk
First published 1998 (print)
Second edition published 2004 (print)
Third edition published 2008 (print)
Fourth edition published 2015 (print and electronic)
Fifth edition published 2019 (print and electronic)
© Pearson Education Limited 1998, 2004, 2008 (print)
© Pearson Education Limited 2015, 2019 (print and electronic)
The rights of Anthony Croft and Robert Davison 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, Barnard’s Inn, 86 Fetter Lane, London
EC4A 1EN.
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 authors’ and the publisher’s
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: 978-1-292-25364-0(print)
978-1-292-25370-1 (eText)
978-1-292-25369-5 (ePub)
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
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23 22 21 20 19
Cover: © Shutterstock / Ekaphon Maneechot
Print edition typeset in 10/12 Times by Pearson CSC
Print edition printed in Slovakia by Neografia
NOTE THAT ANY PAGE CROSS REFERENCES REFER TO THE PRINT EDITION
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ToKateandHarvey(AC)
To Kathy (RD)
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Brief contents
Contents ix
Publisher’s acknowledgements xv
Preface xvi
Using mathematical software packages xx
1 Arithmetic 1
2 Fractions 18
3 Decimal numbers 35
4 Percentage and ratio 45
5 Basic algebra 57
6 Functions and mathematical models 136
7 Polynomial equations, inequalities,
partial fractions and proportionality 215
8 Logarithms and exponentials 289
9 Trigonometry 335
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viii Brief contents
10 Further trigonometry 401
11 Complex numbers 450
12 Matrices and determinants 521
13 Using matrices and determinants to solve equations 600
14 Vectors 669
15 Differentiation 740
16 Techniques and applications of differentiation 771
17 Integration 826
18 Applications of integration 895
19 Sequences and series 943
20 Differential equations 977
21 Functions of more than one variable
and partial differentiation 1048
22 The Laplace transform 1094
23 Statistics and probability 1129
24 An introduction to Fourier series
and the Fourier transform 1213
Typical examination papers 1242
Appendix 1: SI units and prefixes 1248
Index 1249
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Contents
Publisher’s acknowledgements xv
Preface xvi
Using mathematical software packages xx
1 Arithmetic 1
Block 1 Operations on numbers 3
Block 2 Prime numbers and prime factorisation 10
End of chapter exercises 17
2 Fractions 18
Block 1 Introducing fractions 20
Block 2 Operations on fractions 25
End of chapter exercises 33
3 Decimal numbers 35
Block 1 Introduction to decimal numbers 37
Block 2 Significant figures 42
End of chapter exercises 43
4 Percentage and ratio 45
Block 1 Percentage 47
Block 2 Ratio 51
End of chapter exercises 56
