Studying engineering, whether it is mechanical, electrical or civil, relies heavily on an understanding of mathematics. This textbook clearly demonstrates the relevance of mathematical principles and shows how to apply them in real-life engineering problems.

It deliberately starts at an elementary level so that students who are starting from a low knowledge base will be able to quickly get up to the level required. Students who have not studied mathematics for some time will find this an excellent refresher.

Each chapter starts with the basics before gently increasing in complexity. A full outline of essential definitions, formulae, laws and procedures is presented, before real world practical situations and problem solving demonstrate how the theory is applied.

Focusing on learning through practice, it contains simple explanations, supported by 1600 worked problems and over 3600 further problems contained within 384 exercises throughout the text. In addition, 35 Revision tests together with 9 Multiple-choice tests are included at regular intervals for further strengthening of knowledge.

An interactive companion website provides material for students and lecturers, including detailed solutions to all 3600 further problems.

Table of Contents

Section A Number and algebra

Chapter 1 Basic arithmetic

Chapter 2 Fractions

Revision Test 1 Basic arithmetic and fractions

Chapter 3 Decimals

Chapter 4 Using a calculator

Chapter 5 Percentages

Revision Test 2 Decimals, calculations and percentages

Chapter 6 Ratio and proportion

Chapter 7 Powers, roots and laws of indices

Chapter 8 Units, prefixes and engineering notation

Revision Test 3 Ratio, proportion, powers, roots, indices and units

Chapter 9 Basic algebra

Chapter 10 Further algebra

Multiple choice questions Test 1

Chapter 11 Solving simple equations

Revision Test 4 Algebra and simple equations

Chapter 12 Transposing formulae

Chapter 13 Solving simultaneous equations

Revision Test 5 Transposition and simultaneous equations

Chapter 14 Solving quadratic equations

Multiple choice questions Test 2

Chapter 15 Logarithms

Chapter 16 Exponential functions

Chapter 17 Inequalities

Revision Test 6 Quadratics, logarithms, exponentials and inequalities

Formulae/ revision hints for Section A

Section B Further number and algebra

Chapter 18 Polynomial division and the factor and remainder theorems

Chapter 19 Partial fractions

Chapter 20 Number sequences

Revision Test 7 Further algebra, partial fractions and number sequences

Chapter 21 The binomial series

Chapter 22 Maclaurin's series

Revision Test 8 The binomial and Maclaurin's series

Chapter 23 Solving equations by iterative methods

Chapter 24 Hyperbolic functions

Revision Test 9 Iterative methods and hyperbolic functions

Chapter 25 Binary, octal and hexadecimal numbers

Chapter 26 Boolean algebra and logic circuits

Revision Test 10 Numbering systems, Boolean algebra and logic circuits

Multiple choice questions Test 3

Formulae/ revision hints for Section B

Section C Areas and volumes

Chapter 27 Areas of common shapes

Chapter 28 The circle and its properties

Revision Test 11 Areas of common shapes and the circle

Chapter 29 Volumes and surface areas of common solids

Chapter 30 Irregular areas and volumes, and mean values

Revision Test 12 Volumes, irregular areas and volumes, and mean values

Formulae/revision hints for Section C

Section D Graphs

Chapter 31 Straight line graphs

Chapter 32 Graphs reducing non-linear laws to linear form

Chapter 33 Graphs with logarithmic scales

Revision Test 13 Graphs

Chapter 34 Polar curves

Chapter 35 Graphical solution of equations

Chapter 36 Functions and their curves

Revision Test 14 Polar curves, graphical solution of equations and functions and their curves

Multiple choice questions Test 4

Formulae/revision hints for Section D

Section E Geometry and trigonometry

Chapter 37 Angles and triangles

Chapter 38 Introduction to trigonometry

Revision Test 15 Angles, triangles and trigonometry

Chapter 39 Trigonometric waveforms

Chapter 40 Cartesian and polar co-ordinates

Chapter 41 Non-right-angled triangles and some practical applications

Revision Test 16 Trigonometric waveforms, Cartesian and polar co-ordinates and non-right-angled triangles

Chapter 42 Trigonometric identities and equations

Chapter 43 The relationship between trigonometric and hyperbolic functions

Chapter 44 Compound angles

Revision Test 17 Trigonometric identities and equations and compound angles

Multiple choice questions Test 5

Formulae/ revision hints for Section E

Section F Complex numbers

Chapter 45 Complex numbers

Chapter 46 De Moivre’s theorem

Revision Test 18 Complex numbers and De Moivre's theorem

Formulae/ revision hints for Section F

Section G Matrices and determinants

Chapter 47 The theory of matrices and determinants

Chapter 48 Applications of matrices and determinants

Revision Test 19 Matrices and determinants

Formulae/ revision hints for Section G

Section H Vector geometry

Chapter 49 Vectors

Chapter 50 Methods of adding alternating waveforms

Chapter 51 Scalar and vector products

Revision Test 20 Vectors

Multiple choice questions Test 6

Formulae/ revision hints for Section H

Section I Differential calculus

Chapter 52 Introduction to differentiation

Chapter 53 Methods of differentiation

Chapter 54 Some applications of differentiation

Revision Test 21 Methods of differentiation and some applications

Chapter 55 Differentiation of parametric equations

Chapter 56 Differentiation of implicit functions

Chapter 57 Logarithmic differentiation

Revision Test 22 Parametric, implicit and logarithmic differentiation

Chapter 58 Differentiation of hyperbolic functions

Chapter 59 Differentiation of inverse trigonometric and hyperbolic functions

Chapter 60 Partial differentiation

Chapter 61 Total differential, rates of change and small changes

Chapter 62 Maxima, minima and saddle points for functions of two variables

Revision Test 23 Further differentiation and applications

Multiple choice questions Test 7

Formulae/revision hints for Section I

Section J Integral calculus

Chapter 63 Standard integration

Chapter 64 Integration using algebraic substitutions

Chapter 65 Integration using trigonometric and hyperbolic substitutions

Revision Test 24 Standard integration and some substitution methods

Chapter 66 Integration using partial fractions

Chapter 67 The t = tan ,/2 substitution

Chapter 68 Integration by parts

Revision Test 25 Integration using partial fractions, tan ,/2 and 'by parts

Chapter 69 Reduction formulae

Chapter 70 Double and triple integrals

Chapter 71 Numerical integration

Revision Test 26 Reduction formulae, double and triple integrals, and numerical integration

Chapter 72 Areas under and between curves

Chapter 73 Mean and root mean square values

Chapter 74 Volumes of solids of revolution

Chapter 75 Centroids of simple shapes

Chapter 76 Second moments of area

Revision Test 27 Applications of integration

Multiple choice questions Test 8

Formulae/ revision hints for Section J

Section K Differential equations

Chapter 77 Solution of first-order differential equations by separation of variables

Chapter 78 Homogeneous first-order differential equations

Chapter 79 Linear first-order differential equations

Chapter 80 Numerical methods for first-order differential equations

Revision Test 28 First-order differential equations

Chapter 81 Second-order differential equations of the form a d2y dx2 +b dy dx +cy=O

Chapter 82 Second-order differential equations of the form a d2y dx2 +b dy dx +cy=f (x

Chapter 83 Power series methods of solving ordinary differential equations

Chapter 84 An introduction to partial differential equations

Revision Test 29 Second-order differential equations, power series methods and partial differential equations

Formulae/ revision hints for Section K

Section L Statistics and probability

Chapter 85 Presentation of statistical data

Chapter 86 Mean, median, mode and standard deviation

Chapter 87 Probability

Revision Test 30 Presentation of statistical data, mean, median, mode, standard deviation and probability

Chapter 88 The binomial and Poisson distributions

Chapter 89 The normal distribution

Chapter 90 Linear correlation

Chapter 91 Linear regression

Revision Test 31 Binomial, Poisson and normal distributions, correlation and regression

Chapter 92 Sampling and estimation theories

Chapter 93 Significance testing

Chapter 94 Chi-square and distribution-free tests

Revision Test 32 Sampling and estimation theories, significance testing, chi-square and distribution-free tests

Multiple choice questions Test 9

Formulae/revision hints for Section L

Section M Laplace transforms

Chapter 95 Introduction to Laplace transforms

Chapter 96 Properties of Laplace transforms

Chapter 97 Inverse Laplace transforms

Chapter 98 The Laplace transform of the Heaviside function

Chapter 99 The solution of differential equations using Laplace transforms

Chapter 100 The solution of simultaneous differential equations using Laplace transforms

Revision Test 33 Laplace transforms

Formulae/revision hints for Section M

Section N Fourier series

Chapter 101 Fourier series for periodic functions of period 2p

Chapter 102 Fourier series for a non-periodic function over range 2p

Chapter 103 Even and odd functions and half-range Fourier series

Chapter 104 Fourier series over any range

Chapter 105 A numerical method of harmonic analysis

Chapter 106 The complex or exponential form of a Fourier series

Revision Test 34 Fourier series

Formulae/revision hints for Section N

Section O Z-transforms

Chapter 107 An introduction to z-transforms

Revision Test 35 Z-transforms

Formulae/revision hints for Section O

Answers to practice exercises

Answers to multiple choice questions

Index

Review

"Bird is totally comprehensive and is recommended as the ‘bible’ of maths to all students"

-- David Kennedy, Trafford College Centre for STEM

"This will be on my new essential reading book list for new students and students moving into Higher Education… Once more John Bird has written a book which will allow the beginner to expert engineer [to] build a sound foundation in engineering mathematics."

-- Brian Rowe BA (Hons) BENG (Hons), Head of Engineering, East Durham College

About the Author

John Bird (BSc(Hons), CMath, CEng, CSci, FITE, FIMA, FCollT) is the former Head of Applied Electronics in the Faculty of Technology at Highbury College, Portsmouth, UK. More recently he has combined freelance lecturing and examining, and is the author of over 130 textbooks on engineering and mathematical subjects with worldwide sales of over one million copies. He is currently lecturing at the Defence School of Marine Engineering in the Defence College of Technical Training at HMS Sultan, Gosport, Hampshire, UK.