Understanding Engineering Mathematics

Studying engineering, whether it is mechanical, elec- trical, aeronautical, communications, civil, construction or systems engineering, relies heavily on an understand- ing of mathematics. In fact, it is not possible to study any engineering discipline without a sound knowledge of mathematics. What happens, then, when a student realises he/she is very weak at mathematics – an increas- ingly common scenario?
The answer may hopefully be found in this textbook Understanding Engineering Mathematics which explains as simply as possible the steps needed to become better at mathematics and hence gain real confidence and understanding in their chosen engineering subject.

Understanding Engineering Mathematics is an amal- gam of three books – Basic Engineering Mathemat- ics, Engineering Mathematics and Higher Engineering Mathematics, all currently published by Routledge. The point about Understanding Engineering Mathematics is that it is all-encompassing. We do not have to think ‘what course does this book apply to?’. The answer is that it encompasses all courses that include some engineering content in their syllabus, from beginning courses up to degree level.

The primary aim of the material in this text is to provide the fundamental analytical and underpinning knowl- edge and techniques needed to successfully complete scientific and engineering principles modules covering a wide range of programmes. The material has been designed to enable students to use techniques learned for the analysis, modelling and solution of realistic engi- neering problems. It also aims to provide some of the more advanced knowledge required for those wishing to pursue careers in a range of engineering disciplines.

In addition, the text will be suitable as a valuable reference aid to practising engineers. In Understanding Engineering Mathematics, theory is introduced in each chapter by a full outline of essential definitions, formulae, laws, procedures, etc. The theory is kept to a minimum, for problem solving is extensively used to establish and exemplify the theory. It is intended that readers will gain real understanding through see- ing problems solved and then through solving similar problems themselves. The material has been ordered into the following four- teen convenient categories: number and algebra, fur- ther number and algebra, areas and volumes, graphs, geometry and trigonometry, complex numbers, matrices and determinants, vector geometry, differential calcu- lus, integral calculus, differential equations, statistics and probability, Laplace transforms and Fourier series. Each topic considered in the text is presented in a way that assumes in the reader very little previous knowledge. With a plethora of engineering courses worldwide it is not possible to have a definitive ordering of material; it is assumed that both students and instructors/lecturers alike will ‘dip in’ to the text according to their particular course structure.

The text contains some 1500 worked problems, 2750 further problems (with answers), arranged within 370 Exercises, 255 multiple choice questions arranged into 9 tests, 34 Revision Tests, 750 line diagrams and 14 lists of formulae/revision hints. Worked solutions to all 2750 further problems have been prepared and can be accessed free via the pub- lisher’s website (see below). At intervals throughout the text are some 34 Revision Tests to check understanding. For example, Revision Test 1 covers the material in Chapters 1 and 2, Revision Test 2 covers the material in Chapters 3 to 5, Revi- sion Test 3 covers the material in Chapters 6 to 8, and so on. ‘Learning by example’ is at the heart of Understand- ing Engineering Mathematics.