The contents of this book consist of the basic mathematics taught in nearly all first-year service courses in mathematics for science and engineering students. It is based on the experience of the three authors of teaching such material for many years.

There is a growing awareness that we must not teach mathematics in isolation from its applications. In teaching mathematics to scientists, technologists and engineers, there is plenty of opportunity to provide applications as part of the syllabus and teaching approach. There are few textbooks which recognise this. One of the aims of writing this text has been to encourage the teaching of mathematics through its applications in science.

The importance of teaching mathematics through its applications is reflected in the format of this book. Each chapter starts with two or three examples setting the new techniques to be introduced in the context of the scientific world. The aim here is to answer the often posed question from science students: ‘why do we need to learn this mathematics?’

Sections 2 and 4 of each chapter contain the basic mathematical techniques of each chapter, and sections 3 and 5 give worked examples showing the use of the new techniques introduced in the chapter.

Some of the material in the book will have been acquired by most students before entering higher education. For example, in the United Kingdom about half of the contents of the book appears listed in the syllabus of many GCE Advanced level and corresponding BTEC level 3 examinations.