Numerical Differentiation and Integration

Abstract

Differentiation and integration are infinitary concepts of calculus; that is, they are defined by means of a limit process – the limit of the difference quotient in the first instance, the limit of Riemann sums in the second. Since limit processes cannot be carried out on the computer, we must replace them by finite processes. The tools to do so come from the theory of polynomial interpolation (Chap. 2, Sect. 2.2). They not only provide us with approximate formulae for the limits in question, but also permit us to estimate the errors committed and discuss convergence.