Numerical quadrature is one of the classical topics of numerical analysis. Of the
basic areas of analysis, the processes of differentiation and integration arise early in
the development of the subject, and students quickly meet integrals with no standard
closed form. Even so-called closed forms are no more than definitions of transcendental
functions in terms of integral representations. [Continues.]
A doctoral thesis submitted in partial fulfilment of the requirements for the award of Doctor of Science at Loughborough University. This thesis consists of copies of separate publications. It has been redacted for reasons relating to the law of copyright. For more information please contact the author.