Engineering_Mathematics_4E.pdf

Engineering Mathematics

In memory of Elizabeth

Engineering Mathematics

Fourth Edition

JOHN BIRD, BSc(Hons) CMath, FIMA, CEng, MIEE, FCollP, FIIE

Newnes

OXFORD AMSTERDAM BOSTON LONDON NEW YORK PARIS

SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO

Newnes

An imprint of Elsevier Science

Linacre House, Jordan Hill, Oxford OX2 8DP

200 Wheeler Road, Burlington MA 01803

First published 1989

Second edition 1996

Reprinted 1998 (twice), 1999

Third edition 2001

Fourth edition 2003

The right of John Bird to be identiﬁed as the author of this work

has been asserted in accordance with the Copyright, Designs and

Patents Act 1988

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British Library Cataloguing in Publication Data

A catalogue record for this book is available from the British Library

ISBN 0 7506 5776 6

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Typeset by Laserwords Private Limited, Chennai, India

Printed and bound in Great Britain

Contents

Preface xi

Part 1 Number and Algebra 1

1 Revision of fractions, decimals and

percentages 1

1.1 Fractions 1

1.2 Ratio and proportion 3

1.3 Decimals 4

1.4 Percentages 7

2 Indices and standard form 9

2.1 Indices 9

2.2 Worked problems on indices 9

2.3 Further worked problems on

indices 11

2.4 Standard form 13

2.5 Worked problems on standard

form 13

2.6 Further worked problems on standard

form 14

3 Computer numbering systems 16

3.1 Binary numbers 16

3.2 Conversion of binary to decimal 16

3.3 Conversion of decimal to binary 17

3.4 Conversion of decimal to binary via

octal 18

3.5 Hexadecimal numbers 20

4 Calculations and evaluation of

formulae 24

4.1 Errors and approximations 24

4.2 Use of calculator 26

4.3 Conversion tables and charts 28

4.4 Evaluation of formulae 30

Assignment 1 33

5 Algebra 34

5.1 Basic operations 34

5.2 Laws of Indices 36

5.3 Brackets and factorisation 38

5.4 Fundamental laws and precedence 40

5.5 Direct and inverse proportionality 42

6 Further algebra 44

6.1 Polynomial division 44

6.2 The factor theorem 46

6.3 The remainder theorem 48

7 Partial fractions 51

7.1 Introduction to partial fractions 51

7.2 Worked problems on partial fractions

with linear factors 51

7.3 Worked problems on partial fractions

with repeated linear factors 54

7.4 Worked problems on partial fractions

with quadratic factors 55

8 Simple equations 57

8.1 Expressions, equations and

identities 57

8.2 Worked problems on simple

equations 57

8.3 Further worked problems on simple

equations 59

8.4 Practical problems involving simple

equations 61

8.5 Further practical problems involving

simple equations 62

Assignment 2 64

9 Simultaneous equations 65

9.1 Introduction to simultaneous

equations 65

9.2 Worked problems on simultaneous

equations in two unknowns 65

9.3 Further worked problems on

simultaneous equations 67

9.4 More difﬁcult worked problems on

simultaneous equations 69

9.5 Practical problems involving

simultaneous equations 70

10 Transposition of formulae 74

10.1 Introduction to transposition of

formulae 74

10.2 Worked problems on transposition of

formulae 74

10.3 Further worked problems on

transposition of formulae 75

10.4 Harder worked problems on

transposition of formulae 77

11 Quadratic equations 80

11.1 Introduction to quadratic equations 80

11.2 Solution of quadratic equations by

factorisation 80

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