This module is not currently running in 2024 to 2025.
The aim of the module is to provide an introduction to the methods, tools and ideas of numerical computation. In applications mathematics frequently generates specific instances of standard problems for which there are no easily obtainable analytic solutions. Examples might be the task of determining the value of a particular integral, or of finding the roots of a certain non- linear equation. Methods are presented for solving such problems on a modern computer. Besides a description of the basic numerical procedure, each method is analysed in terms of when it best works, how it compares with alternative approaches, and the way it may be implemented on a computer. Numerical computations are almost invariably contaminated by errors, and an important concern throughout the module is to understand the source, propagation and magnitude of these errors.The syllabus will cover: Introduction to numerics; solutions of equations in one variable; interpolation and polynomial approximation; numerical differentiation; numerical integration; direct methods for solving linear systems; iterative techniques for solving linear systems.
48
80% Examination, 20% Coursework
RL Burden & JD Faires, Numerical Analysis, Thomson Brooks/Cole, 8th ed., 2005
Samuel D Conte & Carl de Boor, Elementary Numerical Analysis: An Algorithmic Approach, McGraw Hill, New York, 3rd ed., 1980
Robert Plato, Concise Numerical Mathematics, Americal Mathematical Society, Providance (RI), 2003
W Cheney & D Kincaid Numerical Mathematics and Computing (Thomson Brooks/Cle, 2004) (R)
LN Childs A Concrete Introduction to Higher Algebra (2nd ed., Springer, 2000) (R)
DR Knuth The Art of Computer Programming, Vol. 2 (3rd ed., Addison-Wesley, 2003) (B)
See the library reading list for this module (Canterbury)
The intended subject specific learning outcomes.
A first Numerical Analysis encounter provides an introduction to the methods, tools and ideas of numerical computation. More specifically this module creates a bridge for the student between the theoretical activity involved in solving a mathematical problem and the practical task of calculating a numerical answer.
On successful completion of the module students will:
a. have attained a competence with the use of elementary numerical algorithms for undertaking specific tasks of a mathematical character, such as the calculation of the value of a definite integral, when analytical methods can make no headway
b. understand both how numbers are represented in a computer and also the nature of computer arithmetic, and in particular appreciate the difference between human calculation by hand and machine computation
c. understand the inevitability of numerical errors occurring during the course of machine computations, how these errors arise and propagate, and how they may be detected and controlled
d. have encountered basic facilities within matlab, for example how to undertake large-scale matrix calculations, and recognise that such systems encompass diagnostic aids that enable the monitoring of factors such as error growth
The intended generic learning outcomes. On successful completion of the module, students will:
a. have attained a competence in numerical computation of a sophisticated and relatively advanced character
b. have enhanced their ability to communicate mathematical and numerical statements and conclusions, both symbolically and literally
c. have developed advanced study skills by working on challenging problems that require the application of theoretical techniques in specific and practical contexts.
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