This new edition gives a detailed consideration of the basic arithmetic, algebraic and graphical methods needed in engineering courses so that it conforms completely with sections A and B of the BTEC Level 2 unit, and it provides the basic tools for the science that follows. A new chapter introduces the basic principles of calculus and more material is given on applications. This includes typical properties of materials and a discussion on the way properties of materials over the ages have changed the basic structures of bridges, weightlessness, snooker, thermal insulation and LEDs, as well as buildings, with a particular look at the engineering behind the collapse of the World Trade Centre.