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Abstract

An expression in terms of a contour integral for the remainder
term in a numerical integration formula of a general type is
obtained. Because the function whose integral is under
consideration is allowed to have singularities at the end points of
the interval of integration special emphasis is placed on the
behaviour of the contour at these points. It is then shown how the
corresponding contour integral form of the remainder term in some
of the well-known integration formulae may be derived.
The contour integral in conjunction with known asymptotic
expressions for part of the integrand is used firstly to examine
the convergence properties of certain quadrature schemes (Chapter III)
and secondly to estimate the error in approximating to a real
integral by a quadrature sum (Chapter IV).
In conclusion (Chapter V) we discuss some of the problems which
are to be subjects of further research.

Item Type:	Thesis - PhD
Authors/Creators:	Donaldson, John Dalgleish
Copyright Holders:	The Author
Copyright Information:	Copyright 1967 the Author - The University is continuing to endeavour to trace the copyright owner(s) and in the meantime this item has been reproduced here in good faith. We would be pleased to hear from the copyright owner(s).
Additional Information:	Includes bibliography
Item Statistics:	View statistics for this item

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