Abstract
This chapter describes algorithms for repeated numerical differentiation and the numerical evaluation of integrals. The methods introduced allow the evaluation of integrals with both finite and infinite ranges. The accuracy and errors of methods are examined. Methods for dealing with discontinuities and singularities are considered. Algorithms implemented in Matlab include Simpson's rule, Gaussian quadrature, Newton–Coates formulae, and Romberg's method, as well as the Gauss–Laguerre and Gauss–Hermite methods for infinite ranges of integration. The Gauss–Lobatto, Gauss–Chebyshev, and Filon methods are implemented in Matlab and their use is illustrated. Methods for multiple or repeated integrals are also implemented and tested. Examples of the standard Matlab functions for single, double, and triple integration are given. Problems and solutions are provided.
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