1997 Swinburne Higher Education Handbook

conformal mapping, potential problems, contour
integration, residue theory, application to the evaluation of
real integrals and inversion of Laplace transforms.
Curvilinear coordinates: revison of potential theory; general
coordinate systems, coordinate surfaces, curves and vectors,
orthogonal systems; grad, div, curl and Laplacian in
orthogonal systems.
Linear algebra: background, transmission matrices, vector
spaces, solution of linear equations; the eigenvalue problem,
the Cayley-Hamilton theorem, numerical evaluation using
power method, characteristic impedance, propogation
function; systems of linear differential equations, solution of
first order systems by reducing to an eigenvalue problem,
the phase plane, equilibrium, quadratic forms and matrices,
Liapunov's direct method, linerisation of non-linear sytems.
Recommended reading
SM494 - Mathematicsfor Electrical Engineering. Department of
Mathematics, Swinburne University of Technology, 1993
Kreyszig, E. Advanced Engineering Mathematics. 7th ed, New
York, Wiley, 1993
Rade, L. and Westergren, B. Beta Mathematics Handbook:
Concepts, Theorems, Methods, Algorithms, Fomulae, Graphs, Tables.
2nd edn, Lund, Studentlitteratur, 1990
Spiegel, M.R. 7beory and Problems of Complex Variables with An
Introduction to Conformal Mapping and its Applications. 2nd edn,
New York, McGraw-Hill, 1974.
SM499 Engineering Mathematics
4 credit points 2 hours per week Hawthorn Prerequisites:
W99 Assessmat: examination tests and assignments
A fourth year subject in the Bachelor of Engineering
(Mechanical)
Obiedives
To introduce the mathematical concepts of approximation
and the finite element method.
Content
Concepts of finite element methods; approximation, basis
functions, quadrature, weighted residual methods, ordinary
and partial differential equations.
Recommended reading
Davies, A.J., The Finite Element Method. A First Approach. Oxford,
Oxford University Press, 1980
Easton, A.K., Robb, P.J. and Singh, M., Approximation and the Finite
Element Method 1995
SM584 Multivariate Statistical Methods
10 credit points 3 hours per week Hawthorn
Prerequisite: SM484 Assessment: tests/examinution and
assignments
A third year subject in the Bachelor of Applied Science
(Mathematics and Computer Science)
0 b jedives
Extend hypothesis testing to multivariate data;
Introduce methods of data classification.
Content
Joint distributions and the analysis of bivariate data. Some
theory of estimation. Point and interval estimators.
Properties of estimators. Method of moments and method of
maximum likelihood.
The multivariate normal distribution, multivariate means,
Hotelling's T 2 statistic, the multivariate analysis of variance,
Wilk's lambda.
An introduction to principal components analysis and factor
analysis.
Classification methods: cluster analysis, linear discriminant
analysis.
Computer packages such as Minitab and SAS will be used.
Recommended readina
Aldenderfer, M.S. and lashg geld, R.K., Cluster Analysis. Beverly
Hills, Sage, 1984
Dillon, W.R. and Goldstein, M., Multivariate Analysis. New York,
Wiley, 1984
Everitt, B.S. and Dunn, G., Advanced Method of Data Exploration
and Modelling. London, Heinemann, 1983
Johnson, R.A. and Wichern, D.W., Applied Multivariate Statisticid
Analysis. 3rd edn, Englewood Cliffs, N.J., Prentice Hall, 1992
Kruskal, J.B. and Wish, M., Multidimensional Scaling. Beverly Hills,
Sage, 1978
SM585 Sample Survey Design
10 credit points 3 hours per week Hawthorn Prerequin'te:
M484 Assessmar tests/examinution and assignments
A third year subject in the Bachelor of Applied Science
(Mathematics and Computer Science)
Obiedives
Introduce basic methods for sample design and analysis.
Develop skills in writing questionnaire items.
Content
The basic designs for sample surveys: simple random
sampling, stratified sampling, systematic sampling and
cluster sampling.
Estimators for the mean, total and proportion for simple
random samples and stratified samples; variance estimation.
The design effect; sample size determination; EPSEM
samples.
Ratio estimation;
Cluster sampling, multi-stage sampling, PPS sampling;
variance estimation.
Practical issues and methods; questionnaire design; pilot
surveys, mail, interviewer-based and telephone surveys; nonsampling
errors; weighting.
Recommended reading
Cochran, W.G., Sampling T~hiques. New York, Wiley, 1977
Jolliffe, F.R., Sunny Design and Analysis. Chichester, Ellis Horwood,
1986
Kalton, G., Introduction to Surwy Sampling. Beverly Hills, Sage, 1983
Stuart, A,, Basic Ideas of Sciatiftc Sampling. London, 3rd edn,
Griffin, 1968
Sudman, S., Applied Sampling. New York, Academic Press, 1976
Swinburne Univenity of Technology 1997 Handbook 51 3