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Please note - Swinburne University of Technology

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Spaces <strong>of</strong> vectors and linear equations: linear dependence;<br />

subspaces and bases. Matrices: rank; equivalence; nullspace<br />

and range.<br />

Square matrices: eigenvalues and eigenvectors; similarity;<br />

diagonalisation <strong>of</strong> simple matrices.<br />

Infinite sequences; tests for convergence; recurrence relations<br />

Infinite series; tests for convergence; Taylor series;<br />

applications.<br />

Functions <strong>of</strong> several variances; linear and quadratic<br />

approximations to general functions; stationary points; Taylor<br />

polynomials.<br />

~ ~ 3 8 7 lntroduction to Optimisation<br />

10 credit points<br />

No. <strong>of</strong> hours per week: three hours<br />

Prerequisites: nil<br />

Assessment: assignments and examination<br />

Subject description<br />

Linear and integer programming, simplex method,<br />

transaortation and assiqnment alqorithms, branch and bound<br />

methbds, determini~tic~~namic programming.<br />

Computer packages such as SAVOR, Lotus 123/PROPS may be<br />

- used.<br />

Y.<br />

5.<br />

&?.<br />

Textbooks and References<br />

Journal <strong>of</strong> the Operational Research Society<br />

Ravindran, A,, Phillips, D.T. and Solberg, J.J. Operations Research,<br />

Principles and Practice. 2nd edn, New York, Wiley, 1987<br />

Winston, W.L. Operations Research: Applications and Algorithms. 3rd<br />

m edn, Belmont, Calif., Wadsworth, 1994<br />

I<br />

rn<br />

~ ~ 3 8 8 Forecasting and Regression<br />

G.<br />

10 credit points<br />

No. <strong>of</strong> hours per week: three<br />

Prerequisites: SM 185, SM288<br />

Assessment: testdexamination and assignments<br />

u Subject description<br />

. Forecasting: lntroduction to time series forecasting, data<br />

la<br />

patterns, moving average methods, exponential smoothing<br />

methods, calculation <strong>of</strong> seasonal indices using decomposition<br />

methods, ad hoc forecasting methods, measures <strong>of</strong> accuracy.<br />

Mean Absolute Deviation, confidence intervals, analysis <strong>of</strong><br />

error terms, computer packages such as Excel and QSB+ may<br />

be used.<br />

Regression: Linear (single predictor) models, residual plots,<br />

checking <strong>of</strong> assumptions, tests and co-fidence intervals for<br />

parameters. Computer packages such as Minitab may be used.<br />

Case Studies<br />

The students working in groups tackle an unstructured case<br />

study related to a practical situation. The case studies are<br />

drawn from consulting activities conducted by Operation<br />

Researchers and have been carefully modified for student use.<br />

An oral preliminary report on each group's progress towards a<br />

solution is expected. Before the end <strong>of</strong> the semester both oral<br />

and written reports on their proposed solution are presented.<br />

References<br />

Johnson, R. and Bhattacharyya, G. Statistics: Principlesand Methods.<br />

2nd edn, New York, Wiley, 1992<br />

Winston, W.L. Operations Research: Applications and Algorithms. 3rd<br />

edn, Belmont, Calif., Wadsworth, 1994<br />

~ ~ 3 9 3 Engineering Mathematics<br />

No. <strong>of</strong> hours per week: two hours<br />

Instruction: integrated instruction and practice<br />

Subject aims and description<br />

Numerial solution <strong>of</strong> linear and non-linear algebraic equations,<br />

introduction to finite difference methods for ordinary and<br />

partial differential equations, applications. Fourier Series and<br />

partial differential equations.<br />

References<br />

Greenberg, M.D. Foundations <strong>of</strong>Applied Mathematics. Englewood<br />

Cliffs, N.J., Prentice Hall, 1978<br />

Hausler, E.P. Lepack User's Guide and S<strong>of</strong>tware. Version 2, Hawthorn,<br />

SIT, 1989<br />

Kreyszig, E. Advanced Engineering Mathematics. 7th edn, New York,<br />

Wiley, 1993<br />

Rade, L. and Westergren, B. Beta Mathematics Handbook. 2nd edn,<br />

Lund, Studentlitteratur, 1990<br />

Smith, G.D. Numerical Solution <strong>of</strong> Partial Differential Equations: Finite<br />

Difference Methods. 3rd edn, Oxford, Clarendon. 1985<br />

~ ~ 3 9 4 Engineering Mathematics<br />

No. <strong>of</strong> hours per week: three hours<br />

Prerequisites: SM299 Engineering Mathematics<br />

Instruction: lecturedtutorials<br />

Assessment: examination /tutorial assignments<br />

Subject aims<br />

This subject aims to provide the fundamental numerical<br />

techniques and the tools <strong>of</strong> discrete mathematics which are<br />

indispensable to the modern engineer.<br />

Subject description<br />

Numerical methods - numerical solution <strong>of</strong> linear and nonlinear<br />

algebraic equations, introduction to finite difference<br />

methods for ordinary and partial differential equations,<br />

applications.<br />

Z transforms - an introduction to the 2-transforms and its<br />

properties.<br />

Discrete mathematics - mathematical logic, counting<br />

methods, recurrence relations, applications.<br />

Prescribed course material<br />

Hausler, E.P. lntroduction to Numerical Computing. Hawthorn, Vic..<br />

<strong>Swinburne</strong> Institute <strong>of</strong> <strong>Technology</strong>, 1992<br />

Rade, L. and Westergren, B. Beta Mathematics Handbook. 2nd edn,<br />

Lund, Studentlitteratur, 1990<br />

Steiner, J.M. and Clarke, G. T. Discrete Mathematics. 1991<br />

References<br />

Hausler, E.P. Lepack User's Guide and S<strong>of</strong>tware. 1991, (optional)<br />

Knuth, D.E. The Art <strong>of</strong> Computer Programming. Volume 1, 2nd edn,<br />

Fundamental Algorithms, Addison-Wesley, 1991<br />

Skvarcius, R. and Robinson, W.B. Discrete Mathematics with Science<br />

Applications. Menlo Park, Calif., Benjamin/Cummings, 1986<br />

Smith, G. D. Numerical Solution <strong>of</strong> Partial Differential Equations: Finite<br />

Difference Methods. 3rd edn. Oxford, Clarendon Press, 1985<br />

Strum, R.D. and Kirk, D.E. First Principles <strong>of</strong> Discrete Systems and<br />

DigitalSystems Processing. Reading, Mass., Addison-Wesley, 1989

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