Please note - Swinburne University of Technology

The subject presents some additional material relevant to later
engineering studies which will enable those students with
ability and interest to develop further their mathematical
knowledge and skills.
Basic algebra: algebraic methods, indices and logarithms,
circular functions and formulae.
Functions and graphs: graphs for functions of one and two
variables; surfaces; derivatives, including product, quotient and
chain rule, implicit and logarithmic differentiation; partial
derivatives; indefinite integrals, integration of partial
derivatives.
Linear algebra: linear transformations, matrices and inverse
matrix, determinants, solution of linear equations - Cramer's
Rule and Gaussian elimination.
Analytic geometry: algebra of vectors, dot product and cross
product, vector projections, the plane, parametric specification
of plane curves and curves in space, velocity and acceleration
vectors, the straight line.
Functions of several variables and complex numbers: small
variation, chain rule, curve fitting, algebra of complex
numbers, polar form, exponential notation, roots of complex
numbers, solution of polynomial equations.
Directional derivative, maxima and minima, hyperbolic and
inverse functions.
Integration: methods of integration, including substitution,
integration by parts, partial fractions, substitution of circular or
hyperbolic functions, square completion, integration using
complex numbers. Applications of integration, including area,
mean square, centroid, moments, volume, curved surface area.
Differential equations: first order separable, first order linear,
second order linear.
Infinite series: Taylor's theorem, infinite series, Taylor and
Maclaurin series, power series manipulation.
Also included in the course is a choice of project work.
Students select six from the following:
Minitab. Contour lines/Surfaces. Probability. Iterative methods.
The general linear system. Beam theory. Curve fitting nonlinear
models. Vectors - an extension. Fluid mechanics.
Bisection and false position methods. Newton's method and
simple iteration. Computer programming. Centroids and
second moments of area. Trapezoidal and Simpon's Rule.
Diagnosis of integration. Centroids and Pappus's theorems.
Applications of differential equations. Boolean Algebra. Electric
circuits.
Textbook
Thomas, G.B. and Finney, R.L. Calculus and Analytic Geometry 8th
edn, Reading, Mass., Addison-Wesley, 1992
References
Anton, H. Calculus with Analytic Geometry 4th edn, New York, Wiley,
1992
Berkey, D.D. and Blanchard, P., Calculus 3rd edn, Forth Worth,
Saunders College, 1988
Rade, L. and Westergren, 9. Beta Mathematics Handbook. 2nd edn,
Lund, Studenlitteratur, 1990
Shenk, A. Calculus and Analytic Geometry 4th edn, Glenview, Scott
Foresman, 1988
Watson, R. et al. Xpace and Numbec Pilot ed, Sydney, McGraw-Hill,
1989
~ ~ 2 7 8 Design and Measurement 2A
No. of hours per week: four hours daytime or
three and a half hours evening
Prerequisites: AYl 00 and AYI 01
Assessment: hands-on SPSS computer test, SPSS
and statistics written test and exam
Subject aims and description
A stage two, first-semester subject in research design and
statistical analysis is planned to complement concurrent and
future studies in psychology.
In this subject the emphasis is on understanding the
methodology of basic research design and how the associated
statistical analysis can provide answers to research questions.
Students also receive instruction in the use of the Statistical
Package for the Social Sciences (SPSS). This computer package
will be used to analyse data both in this course and second and
third stage courses in psychology.
Topics to be studied include an introduction to computer based
data analysis, one and two-way factorial designs and the
corresponding analysis of variance.
Textbook
To be advised.
~ ~ 2 8 % Operations Research: An
lntroduction to Problem Solving
10 credit points
No. of hours per week: three hours
Prerequisites: nil
Assessment: assignments and examination
Subject description
History and methodolouv:
~evelopment of operationfiesearch: inter-disciplinary team;
methodolouv: role of techniaues: aroblem formulation: model
building; t@s of models; testing:validating; design and data
problems; implementation; operations research literature;
operations research societies. Special lectures on the
application of operations research will also be given.
lntroduction to linear programming:
Applications of linear programming; formulation of linear
programming problems; graphical solution of two variable
problems; sensitivity analysis; computer based solution using
SAS.
Markov chains:
Applications of Markov chains; formulation of Markov chain
problems; n-step and steady state probabilities.
Heuristics:
Definition of an heuristic; examples of heuristics as applied to
travelling salesman problems and scheduling problems.
lntroduction to the SAS system:
The SAS system, the SAS program manager, inputting data,
sorting and printing, summarising and plotting data, graphing
data, transferring data and output between packages,
programming in SAS, using SAS to solve linear programming
and other operations research problems.
Textbooks and References
Journal of the Operations Research Society
Winston, W.L. Operations Research: Applications andAlgorithms. 3rd
edn, Belmont, Calif., Wadsworth, 1994