THE previous chapter developed tools for predicting values of a function f(~x) given asampling of points (~xi, f(~xi)) in the domain of f . Such methods are useful in themselves for completing functions that are known to be continuous or differentiable but whose values only are sampled at a set of isolated points, but in some cases we instead wish to compute “derived quantities” from the sampled function. Most commonly, many applications must approximate the integral or derivatives of f rather than its values.