ABSTRACT

Studying engineering, whether it is mechanical, electrical or civil relies heavily on an understanding of mathematics. This new textbook clearly demonstrates the relevance of mathematical principles and shows how to apply them to solve 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 are introduced before real world situations, practicals and problem solving demonstrate how the theory is applied.

Focusing on learning through practice, it contains examples, supported by 1,600 worked problems and 3,000 further problems contained within exercises throughout the text. In addition, 34 revision tests are included at regular intervals.

An interactive companion website is also provided containing 2,750 further problems with worked solutions and instructor materials

part |2 pages

Section A Number and Algebra

chapter |8 pages

Basic arithmetic

chapter |8 pages

Fractions

chapter |6 pages

Decimals

chapter |13 pages

Using a calculator

chapter |8 pages

Percentages

chapter |8 pages

Ratio and proportion

chapter |7 pages

Powers, roots and laws of indices

chapter |8 pages

Basic algebra

chapter |8 pages

Further algebra

chapter |10 pages

Solving simple equations

chapter |8 pages

Transposing formulae

chapter |13 pages

Solving simultaneous equations

chapter |12 pages

Solving quadratic equations

chapter |7 pages

Logarithms

chapter |12 pages

Exponential functions

chapter |10 pages

Inequalities

part |2 pages

Section B Further number and algebra

chapter |10 pages

Number sequences

chapter |11 pages

Binary, octal and hexadecimal numbers

chapter |7 pages

Partial fractions

chapter |10 pages

The binomial series

chapter |9 pages

Maclaurin’s series

chapter |11 pages

Hyperbolic functions

chapter |11 pages

Solving equations by iterative methods

chapter |26 pages

Boolean algebra and logic circuits

part |2 pages

Section C Areas and volumes

chapter |12 pages

Areas of common shapes

chapter |14 pages

The circle and its properties

part |2 pages

Section D Graphs

chapter |18 pages

Straight line graphs

chapter |10 pages

Graphs with logarithmic scales

chapter |4 pages

Polar curves

chapter |9 pages

Graphical solution of equations

chapter |30 pages

Functions and their curves

part |2 pages

Section E Geometry and trigonometry

chapter |16 pages

Angles and triangles

chapter |20 pages

Introduction to trigonometry

chapter |15 pages

Trigonometric waveforms

chapter |5 pages

Cartesian and polar co-ordinates

chapter |7 pages

Trigonometric identities and equations

chapter |21 pages

Compound angles

part |2 pages

Section F Complex numbers

chapter |12 pages

Complex numbers

chapter |10 pages

De Moivre’s theorem

part |2 pages

Section G Matrices and determinants

chapter |10 pages

The theory of matrices and determinants

chapter |16 pages

Applications of matrices and determinants

part |2 pages

Section H Vector geometry

chapter |14 pages

Vectors

chapter |11 pages

Methods of adding alternating waveforms

chapter |17 pages

Scalar and vector products

part |2 pages

Section I Differential calculus

part |2 pages

Section J Integral calculus

chapter |7 pages

Standard integration

chapter |5 pages

Integration using partial fractions

chapter |5 pages

The t = tan substitution

chapter |7 pages

Integration by parts

chapter |9 pages

Reduction formulae

chapter |4 pages

Double and triple integrals

chapter |10 pages

Numerical integration

chapter |9 pages

Areas under and between curves

chapter |5 pages

Mean and root mean square values

chapter |5 pages

Volumes of solids of revolution

chapter |9 pages

Centroids of simple shapes

chapter |16 pages

Second moments of area

part |2 pages

Section L Statistics and probability

chapter |12 pages

Presentation of statistical data

chapter |10 pages

Probability

chapter |7 pages

The binomial and Poisson distributions

chapter |8 pages

The normal distribution

chapter |5 pages

Linear correlation

chapter |7 pages

Linear regression

chapter |13 pages

Sampling and estimation theories

chapter |17 pages

Significance testing

chapter |28 pages

Chi-square and distribution-free tests

part |2 pages

Section M Laplace transforms

part |2 pages

Section N Fourier series