Please note - Swinburne University of Technology

Subject description
Complex variables: elementary functions, geometry of the
complex plane, mappings, complex differentiation, conformal
mapping, potential problems, contour integration, residue
theory, application to the evaluation of real integrals and
invers~on 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.
Prescribed course material
SM494 - Mathematics for Electrical Engineering. Department of
Mathematics, Swinburne University of Technology, 1993
References
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. Theory and Problems of Complex Variables with An
lntroduction to Conformal Mapping and its Applications. 2nd edn,
New York, McGraw-Hill, 1974.
~ ~ 4 9 9 Engineering Mathematics
No. of hours per week: two hours
Instruction: integrated instruction and practice
Subject description
lntroduction to finite element methods; approximation, basis
functions,quadrature, weighted residual methods, ordinary
and partial differential equations.
References
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
Rade, L. and Westergren, B. Beta Mathematics Handbook. 2nd edn,
Lund, Studentlitteratur, 1990
~ ~ 5 8 1 Discrete Mathematics
10 credit points
No. of hours per week: three hours
Prerequisite: SM180
Assessment: tests/examination and assignments
Subject description
Set theory and relations: review of formal set theory;
operations on sets; ordered sets; Cartesian product. Relations:
binarv relations. es~eciallv eauivalence relations and partitions;
ordeing and partial orde;ing, functions.
Logic: introduction to propositional calculus and to predicate
calculus; traditional and modern symbolic logic.
The nature of formal (pure) mathematics: mathematical proof
and theorems; necessary and sufficient conditions; types of
proof, including mathematical induction.
Boolean alaebra: review of alqebraic structures; rules of
Boolean algrebra, with examges; simplification of Boolean
exoressions. Boolean functions: truth tables and Karnauah -
maps, normal and minimal forms.
Combinatorial analysis: systematic techniques of listing and of
counting for arrangements, selections, partitions etc. Use of
recurrence relations and series. Applications to selected
problems. Use of generating functions.
Elementary number theory: division in integers; greatest
common divisors; congruence; computer applications.
Selected applications of discrete mathematics (e.g. graph
theory). Selective introduction to other areas of pure
mathematics (e.g, abstract algebra).
Textbooks and References
Albertson, M. and Hutchinson, J. Discrete Mathematics with
Algorithms. New York, Wiley, 1988
Gersting, J. Mathematical Structures for Computer Science. 2nd edn,
New York, Freeman, 1987
Mathematics Department notes
Skvarcius, R. and Robinson, W. Discrete Mathematics with Computer
Science Applications. Menlo Park, Calif., BenjaminICummings, 1986
~ ~ 5 8 4 Multivariate Statistical Methods
10 credit points
No. of hours per week: three hours
Prerequisite: SM484
Assessment: testdexamination and assignments
Subject description
Sampling from multivariate populations, the variancecovariance
matrix, the multivariate normal distribution,
multivariate means, Hotelling's T2 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.
Multidimensional scaling.
Computer packages such as Minitab and SAS will be used.
Textbooks and References
Aldenderfer, M.S. and Blashfield, R.K. Cluster Analysis. Beverly Hills,
Sage, 1984
Dillon, W.R. and Goldstein, M. Multivariate Analysis. New York, Wiley,
1984
Everitt, 8.S. and Dunn, G. Advanced Methods of Data Exploration and
Modelling. London, Heinemann, 1983
Johnson, R.A. and Wichern, D.W. Applied Multivariate Statistical
Analysis. 3rd edn, Englewood Cliffs, N.J., Prentice Hall, 1992
Kruskal, 1.8. and Wish, M. MultidimensionalScaling. Beverly Hills,
Sage, 1978
~ ~ 5 8 5 Sample Survey Design
10 credit points
No. of hours per week: three hours
Prerequisite: SM484
Assessment: testdexamination and assignments
Subject description
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.