Authorised by Academic Registrar, April 1996
Objectives The objectives of this subject are for students to be able to employ any of a suite of numerical approximation techniques, to solve a nonlinear equation in a single variable; find an interpolating polynomial, using limited data; solve a system of linear equations; estimate the eigenvalue (with largest magnitude) for a matrix; estimate the value of a definite integral; solve a nonlinear differential equation or find a `best fit' representation of a function; have a good idea of the likely numerical imprecision inherent in the results, and know (in some instances) ways to reduce such inaccuracies.
Synopsis This subject is intended to introduce some of the methods commonly used in numerical computations; to develop the theoretical bases of the algorithms, as well as assessing their likely accuracy and any possible difficulties. Areas covered include numerical methods for solving non-linear equations; solving systems of linear equations; numerical differentiation and integration; interpolation, least squares fitting, orthogonal polynomials; numerical solution of ordinary differential equations with initial and/or boundary conditions; comparisons of methods by operations count, order of convergence, error bounds, and empirical error estimates; introduction to the use of computer packages for numerical analysis. On-campus students are offered lectures and tutorials, supplemented by a textbook, study guides and readings. Ordinary assignments are corrected but do not count directly towards assessment.
Assessment Two assessment assignments: 40% + Examination: 60%