This book is based on a course of introductory lectures that I have given for a number of years in Cambridge. I hope that it will be useful not only to students but also more generally to those who need to make use of a digital computer for scientific and engineering purposes. I have endeavoured to give the subject a modern slant and to confine myself to essentials.

The longest chapter is that on interpolation. This is not because of the practical importance of interpolation as such (it is, in fact, a rare operation to perform in a digital computer) but because the idea of the interpolating polynomial is fundamental to the use of finite difference methods in numerical analysis generally. The chapter on interpolation should, therefore, be regarded as laying the theoretical foundations for what is to follow.

Systematic use is made of difference operators for deriving finite difference formulae, although alternative methods are given in the more important cases. Since the view taken is that finite difference formulae are only proved when the functions concerned are polynomials, expressions containing difference operators may be regarded as convenient abbreviations for finite expressions that could be written out in full. No elaborate theoretical justification of the use of such operators is therefore called for. The finite difference formulae once derived are, of course, applied at user's risk to functions which can only approximately be represented by polynomials.