Please note - Swinburne University of Technology

~ ~ 2 9 9 Engineering Mathematics
No. of hours per week: three hours for two
semesters
Instruction: integrated instruction and practice
Subject aims and description
Integration-integration methods, plane polar coordinates,
double integrals and applications, cylindrical and spherical
coordinates, triple integrals and applications.
Vector calculus - scalar and vector fields, gradient of a scalar
field, the potential, surface integrals, flux of a vector field,
divergence Gauss' theorem, continuity of fluid flow, line
integrals, curl, Stokes theorem, introduction to fluid dynamics,
introduction to tensors and tensor notation.
Linear algebra - orthogonal matrices, eigenvalue problems,
real symmetric matrices and applications.
Statistics - review of data analysis, probability, probability
distributions for discrete variates and continuous variates,
sampling distributions. The t distribution, F and Chi-Square,
hypothesis testing, goodness of fit, ANOVA (One and Twoway),
correlation and simple regression, experimental design.
Minitab packaged used.
Differential equations - revision of differential equations,
Laplace transforms, solution of differential equations by series,
applications.
Textbook
Smith, P.J. Into Statistics. Melbourne, Nelson, 1993
References
Hogg, R.V and Ledolter, 1. Engineering Statistio. New York, Macmillan, 1989
Kreyszig, E. Advanced Engineering Mathematics. 7th edn, New York,
Wiley, i993
Rade, L. and Westergren, B. Beta Mathematics Handbook. 2nd edn,
Lund, Studentlitteratur, 1990
Ryan, B.F., Jo~ner, B.L. and Ryan, T.A. Minitab Handbook, 2nd edn,
Boston. PWS-Kent, 1992
Stroud, K.A. Engineering Mathematics: Programmes and Problems. 3rd
edn, London, Macmillan, 1987
Stroud, K.A. Further Engineering Mathematics: Programmes and
Problems. London, Macmillan, 1986
Thomas, G.B. and Finney, R.L. Calculus and Analytic Geometry. 8th
edn, Reading, Mass., Addison Wesley, 1992
5~378 Design and Measurement 3
No. of hours per week: four hours day-time
Prerequisite: SM278
Assessment: continuous
Subject aims and description
A stage three, first semester subject in research design and
statistical analysis that is designed to complement concurrent
and future studies in psychology.
In this subject the topics included in SM278 are extended and
further topics in design and analysis are considered. The SPSS
package will be used to perform the various statistical
analyses.
Topics to be studied include correlation and an introduction to
multiple regression, analysis of covariance and factor analysis.
References
Ferguson, G.A. Statistical Analysis in Psychology & Education. 5th edn,
New York, McGraw-Hill, 1981
Kerlinger, F. N. and Pedhazur, E.J. Multiple Regression in Behavioural
Research, 2nd edn, New York, Holt Rinehart and Winston, 1982
Norusis, M. SPSS-X. IntroductoryStatistics Guide. Chicago, Ill., SPSS
Inc., 1990
Norusis, M. SPSS/PC+ Studentware Plus. Chicago, Ill., SPSS Inc., 1991
Roscoe, J. T. Fundamental Research for the Behavioral Sciences. 2nd
edn, New York, Holt Rinehart and Winston, 1975
SM381
Linear Algebra and Geometry
10 credit points
No. of hours per week: three hours
Prerequisite: SM 180
Assessment: tests/examination and assignments
Note: In any year there will be offered either SM383 only, or
one or both of SM381 and SM480. Students may not receive
credit for both SM383 and SM381 or SM480.
Subject description
Spaces of vectors and linear equations: real n-dimensional
space; linear dependence of vectors; vector spaces, subspaces
and bases; inner product and orthogonality; Gramm-Schmidt
process; convex sets. Spaces of solutions for linear equations.
Matrices: rank; elementary operations and equivalence;
nullspace and range. Matrices as operations on vector spaces.
Square matrices: eigenvalues and eigenvectors; similarity of
simple matrices; real symmetric matrices; applications including
quadratic forms, Markov chains.
Linear operations on 2- and 3-dimensional spaces: elementary
types; geometry of projections, rotations and reflections.
General linear and non-linear operations on finite dimensional
spaces; geometric aspects of linear and affine functions; affine
approximations to non-linear functions.
Computational aspects of matrix and related problems.
Applications of matrix methods e.g. in computer graphics and
in statistics.
Textbooks and References
Hohn, F.E. Elementary Matrix Algebra. 3rd edn, New York, Macmillan,
London, Collier Macmillan, 1973
Johnson, R.A. and Wichern, D.W. Applied Multivariate Statistical
Analysis. 3rd edn, Englewood Cliffs, N.J., Prentice Hall, 1992
Mathematics Department notes
Mortenson, M.E. Computer Graphics. Oxford: Heinemann Newness,
1989
Searle, S.R. Matrix Algebra Useful for Statistics. New York, Wiley, 1982
~ ~ 3 8 3 Mathematics 2
10 credit points
No. of hours per week: three
Prerequisite: nil
Assessment: tests/examination and assignments
Note: In any year there will be offered either SM383 only, or
one or both of SM381 and SM480. Students may not receive
credit for both SM383 and SM381 or SM480.
Subject description
Ordinary differential equations: first-order linear;
homogeneous, exact; second-order linear; numerical methods
of solution.
Ordinary difference equations: first and second-order linear
with constant coefficients.
Introduction to partial differential equations.