ABSTRACT

This compendium of essential formulae, definitions, tables and general information provides the mathematical information required by engineering students, technicians, scientists and professionals in day-to-day engineering practice. A practical and versatile reference source, now in its fifth edition, the layout has been changed and streamlined to ensure the information is even more quickly and readily available – making it a handy companion on-site, in the office as well as for academic study. It also acts as a practical revision guide for those undertaking degree courses in engineering and science, and for BTEC Nationals, Higher Nationals and NVQs, where mathematics is an underpinning requirement of the course.

All the essentials of engineering mathematics – from algebra, geometry and trigonometry to logic circuits, differential equations and probability – are covered, with clear and succinct explanations and illustrated with over 300 line drawings and 500 worked examples based in real-world application. The emphasis throughout the book is on providing the practical tools needed to solve mathematical problems quickly and efficiently in engineering contexts. John Bird’s presentation of this core material puts all the answers at your fingertips.

section Section 1|1 pages

Engineering conversions, constants and symbols

chapter Chapter 1|2 pages

General conversions and Greek alphabet

chapter Chapter 2|3 pages

Basic SI units, derived units and common prefixes

chapter Chapter 3|3 pages

Some physical and mathematical constants

chapter Chapter 4|3 pages

Recommended mathematical symbols

chapter Chapter 5|8 pages

Symbols for physical quantities

section Section 2|1 pages

Some algebra topics

chapter Chapter 6|5 pages

Introduction to algebra

chapter Chapter 7|2 pages

Polynomial division

chapter Chapter 8|2 pages

The factor theorem

chapter Chapter 9|1 pages

The remainder theorem

chapter Chapter 10|2 pages

Continued fractions

chapter Chapter 11|6 pages

Solving simple equations

chapter Chapter 12|5 pages

Transposing formulae

chapter Chapter 13|7 pages

Solving simultaneous equations

chapter Chapter 14|4 pages

Solving quadratic equations by factorising

chapter Chapter 15|3 pages

Solving quadratic equations by completing the square

chapter Chapter 16|3 pages

Solution of quadratic equations by formula

chapter Chapter 17|5 pages

Logarithms

chapter Chapter 18|3 pages

Exponential functions

chapter Chapter 19|4 pages

Napierian logarithms

chapter Chapter 20|5 pages

Hyperbolic functions

chapter Chapter 21|4 pages

Partial fractions

section Section 3|1 pages

Some number topics

chapter Chapter 22|2 pages

Simple number sequences

chapter Chapter 23|2 pages

Arithmetic progressions

chapter Chapter 24|3 pages

Geometric progressions

chapter Chapter 25|8 pages

Inequalities

chapter Chapter 26|5 pages

The binomial series

chapter Chapter 27|4 pages

Maclaurin’s theorem

chapter Chapter 28|2 pages

Limiting values – L’Hopital’s rule

chapter Chapter 32|8 pages

Computer numbering systems

section Section 4|2 pages

Areas and volumes

chapter Chapter 33|4 pages

Areas of plane figures

chapter Chapter 34|6 pages

Circles

chapter Chapter 35|6 pages

Volumes and surface areas of regular solids

chapter Chapter 37|3 pages

The frustum and zone of a sphere

chapter Chapter 38|6 pages

Areas and volumes of irregular figures and solids

chapter Chapter 39|5 pages

The mean or average value of a waveform

section Section 5|2 pages

Geometry and trigonometry

chapter Chapter 40|1 pages

Types and properties of angles

chapter Chapter 41|3 pages

Properties of triangles

chapter Chapter 42|2 pages

The theorem of Pythagoras

chapter Chapter 43|2 pages

Trigonometric ratios of acute angles

chapter Chapter 44|2 pages

Evaluating trigonometric ratios

chapter Chapter 45|2 pages

Fractional and surd forms of trigonometric ratios

chapter Chapter 46|3 pages

Solution of right-angled triangles

chapter Chapter 47|3 pages

Cartesian and polar co-ordinates

chapter Chapter 48|5 pages

Sine and cosine rules and areas of any triangle

chapter Chapter 49|1 pages

Graphs of trigonometric functions

chapter Chapter 50|2 pages

Angles of any magnitude

chapter Chapter 51|6 pages

Sine and cosine waveforms

chapter Chapter 52|5 pages

Trigonometric identities and equations

chapter Chapter 54|7 pages

Compound angles

section Section 6|2 pages

Graphs

chapter Chapter 55|3 pages

The straight-line graph

chapter Chapter 56|6 pages

Determination of law

chapter Chapter 57|5 pages

Graphs with logarithmic scales

chapter Chapter 58|2 pages

Graphical solution of simultaneous equations

chapter Chapter 59|5 pages

Quadratic graphs

chapter Chapter 60|2 pages

Graphical solution of cubic equations

chapter Chapter 61|6 pages

Polar curves

chapter Chapter 62|2 pages

The ellipse and hyperbola

chapter Chapter 63|8 pages

Graphical functions

section Section 7|1 pages

Complex numbers

chapter Chapter 64|1 pages

General complex number formulae

chapter Chapter 65|4 pages

Cartesian form of a complex number

chapter Chapter 66|3 pages

Polar form of a complex number

chapter Chapter 67|3 pages

Applications of complex numbers

chapter Chapter 68|2 pages

De Moivre’s theorem

chapter Chapter 69|2 pages

Exponential form of a complex number

section Section 8|1 pages

Vectors

chapter Chapter 70|1 pages

Scalars and vectors

chapter Chapter 71|3 pages

Vector addition

chapter Chapter 72|2 pages

Resolution of vectors

chapter Chapter 73|3 pages

Vector subtraction

chapter Chapter 74|3 pages

Relative velocity

chapter Chapter 75|2 pages

i, j, k notation

chapter Chapter 76|3 pages

Combination of two periodic functions

chapter Chapter 77|4 pages

The scalar product of two vectors

chapter Chapter 78|3 pages

Vector products

section Section 9|1 pages

Matrices and determinants

chapter Chapter 79|2 pages

Addition, subtraction and multiplication of matrices

chapter Chapter 80|2 pages

The determinant and inverse of a 2 by 2 matrix

chapter Chapter 81|2 pages

The determinant of a 3 by 3 matrix

chapter Chapter 82|2 pages

The inverse of a 3 by 3 matrix

chapter Chapter 83|4 pages

Solution of simultaneous equations by matrices

chapter Chapter 84|4 pages

Solution of simultaneous equations by determinants

chapter Chapter 87|5 pages

Eigenvalues and eigenvectors

section Section 10|1 pages

Boolean algebra and logic circuits

chapter Chapter 88|4 pages

Boolean algebra and switching circuits

chapter Chapter 89|2 pages

Simplifying Boolean expressions

chapter Chapter 90|2 pages

Laws and rules of Boolean algebra

chapter Chapter 91|2 pages

De Morgan’s laws

chapter Chapter 92|6 pages

Karnaugh maps

chapter Chapter 93|4 pages

Logic circuits and gates

chapter Chapter 94|4 pages

Universal logic gates

section Section 11|2 pages

Differential calculus and its applications

chapter Chapter 95|2 pages

Common standard derivatives

chapter Chapter 96|2 pages

Products and quotients

chapter Chapter 97|2 pages

Function of a function

chapter Chapter 98|2 pages

Successive differentiation

chapter Chapter 99|2 pages

Differentiation of hyperbolic functions

chapter Chapter 100|2 pages

Rates of change using differentiation

chapter Chapter 101|2 pages

Velocity and acceleration

chapter Chapter 102|4 pages

Turning points

chapter Chapter 103|2 pages

Tangents and normals

chapter Chapter 104|1 pages

Small changes using differentiation

chapter Chapter 105|3 pages

Parametric equations

chapter Chapter 106|3 pages

Differentiating implicit functions

chapter Chapter 107|3 pages

Differentiation of logarithmic functions

chapter Chapter 108|4 pages

Differentiation of inverse trigonometric functions

chapter Chapter 109|5 pages

Differentiation of inverse hyperbolic functions

chapter Chapter 110|4 pages

Partial differentiation

chapter Chapter 111|2 pages

Total differential

chapter Chapter 112|2 pages

Rates of change using partial differentiation

chapter Chapter 113|2 pages

Small changes using partial differentiation

section Section 12|2 pages

Integral calculus and its applications

chapter Chapter 115|4 pages

Standard integrals

chapter Chapter 116|1 pages

Non-standard integrals

chapter Chapter 117|3 pages

Integration using algebraic substitutions

chapter Chapter 119|3 pages

Integration using partial fractions

chapter Chapter 120|4 pages

The t = tan θ 2 substitution

chapter Chapter 121|4 pages

Integration by parts

chapter Chapter 122|5 pages

Reduction formulae

chapter Chapter 123|4 pages

Double and triple integrals

chapter Chapter 124|4 pages

Numerical integration

chapter Chapter 125|7 pages

Area under and between curves

chapter Chapter 126|3 pages

Mean or average values

chapter Chapter 127|3 pages

Root mean square values

chapter Chapter 128|3 pages

Volumes of solids of revolution

chapter Chapter 129|5 pages

Centroids

chapter Chapter 130|4 pages

Theorem of Pappus

chapter 131|6 pages

Second moments of area

section Section 13|2 pages

Differential equations

chapter Chapter 132|1 pages

The solution of equations of the form dy dx = f ( x )

chapter Chapter 133|2 pages

The solution of equations of the form dy dx = f ( y )

chapter Chapter 135|2 pages

Homogeneous first order differential equations

chapter Chapter 136|2 pages

Linear first order differential equations

section Section 14|1 pages

Laplace transforms

chapter Chapter 152|5 pages

Standard Laplace transforms

chapter Chapter 153|3 pages

The initial and final value theorems

chapter Chapter 154|4 pages

Inverse Laplace transforms

chapter Chapter 155|3 pages

Poles and zeros

chapter Chapter 156|8 pages

The Laplace transform of the Heaviside function

chapter Chapter 157|4 pages

Solving differential equations using Laplace transforms

section Section 15|1 pages

Z-transforms

chapter Chapter 159|4 pages

Sequences

chapter Chapter 160|6 pages

Some properties of z-transforms

chapter Chapter 161|5 pages

Inverse z-transforms

chapter Chapter 162|4 pages

Using z-transforms to solve difference equations

section Section 16|2 pages

Fourier series

chapter Chapter 163|4 pages

Fourier series for periodic functions of period 2π

chapter Chapter 165|4 pages

Even and odd functions

chapter Chapter 166|3 pages

Half range Fourier series

chapter Chapter 167|4 pages

Expansion of a periodic function of period L

chapter Chapter 169|6 pages

The complex or exponential form of a Fourier series

chapter Chapter 170|4 pages

A numerical method of harmonic analysis

chapter Chapter 171|4 pages

Complex waveform considerations

section Section 17|4 pages

Statistics and probability

chapter Chapter 172|4 pages

Presentation of ungrouped data

chapter Chapter 173|4 pages

Presentation of grouped data

chapter Chapter 174|4 pages

Measures of central tendency

chapter Chapter 175|3 pages

Quartiles, deciles and percentiles

chapter Chapter 176|3 pages

Probability

chapter Chapter 177|3 pages

Permutations and combinations

chapter Chapter 178|2 pages

Bayes’ theorem

chapter Chapter 179|3 pages

The binomial distribution

chapter Chapter 180|2 pages

The Poisson distribution

chapter Chapter 181|6 pages

The normal distribution

chapter Chapter 182|2 pages

Linear correlation

chapter Chapter 183|2 pages

Linear regression

chapter Chapter 184|7 pages

Sampling and estimation theories

chapter Chapter 185|4 pages

Chi-square values

chapter Chapter 186|3 pages

The sign test

chapter Chapter 187|4 pages

Wilcoxon signed-rank test

chapter Chapter 188|7 pages

The Mann-Whitney test