Please note - Swinburne University of Technology
Please note - Swinburne University of Technology
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