In this country today there are two conflicting forces acting on the mathematical curriculum and these are thrown into sharp contract when we consider Engineering Mathematics. Engineering Mathemat­ ics consists of a large body of material and techniques which is tra­ ditionally used by Engineers and Scientists in order to develop their theoretical work. As more of this work is developed the pressure is in­ creased for students to acquire the necessary mathematical skills and techniques earlier. Set against this, there has been a general reduction in the numbers of young people who choose to study A-level math­ ematics at school. The examination boards have responded to this unpopularity by reducing the quantity of material which is included in the A-level syllabus and the level of skill required. Consequently, knowledge and facility, regarded as routine 10 years ago, is now not generally acquired until the student becomes an undergraduate. The 'one still point in this turning world' is the unfortunate stu­ dent. It can be argued that students are getting brighter but, due to the pressures which have already been mentioned, their mathematical experience on entering University does not reflect this. This new edi­ tion attempts, in some measure, to resolve these opposing forces by adopting on the one hand a very elementary starting point and includ­ ing, on the other, some relatively advanced material. The first two chapters have been rewritten to make them more accessible.