Please note - Swinburne University of Technology

2D polar coordinates:
Definitions: graphs of equations; transformation to and from
Cartesian coordinates; curve length and area.
Differential equations:
Ordinary differential equations of first order: general and
particular solutions; separable and linear types.
Vectors and geometry:
2D vectors: dot-product and resolution; parametric equations
of 2D curves; vector differentiation.
3D space: Cartesian and polar coordinates; simple surfaces
and cums in space.
3D vectors: dot and cross-products; vector equations of lines
and planes; parametric equations of 3D curves.
Functions of many variables:
Graphs of surfaces as functions of two or three variables:
partial differentiation and applications; directional derivatives
and gradients; tangent planes to surfaces; differentials and
approximations; optimisation and applications.
Complex numbers:
Complex numbers: definition and arithmetic; polar form;
exponential notation. Solution of polynomial equations.
Textbooks
Hunt, R.A. Calculus with Analytic Geometry. New York: Harper and
Row, 1988
Prescribed Calculator: Texas Instruments Advanced Scientific TI-81
Graphics Calculator
~ ~ 1 8 Applied 5 Statistics 1
10.0 credit points
No. of hours per week: three hours
At the time of printing full subject details were unavailable.
Please contact the course convener for further details
(Mathematics Department).
SM278 Design and Measurement 2A
Please see Faculty of Arts subject details for further
information.
sM288 Operations Research: An Introduction to
Problem Solving
10.0 credit points
No. of hours per week: two hours
Prerequisites: nil
Assessment: assignments and examination
A first-year subject of the degree courses in mathematics
and computer science and applied and industrial
mathematics.
Subject description
History and methodology:
Development of operations research: inter-disciplinary team;
methodology; role of techniques; problem formulation;
model building; types 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.
Textbooks and References
Journal of the Operations Research Society
Winston, W.L. Operations Research Applications and Algorithms. 2nd
ed, Boston: FWS-Kent, 1991
SM378 Design and Measurement 3
Please see Faculty of Arts subject details for further
information.
SM381
Linear Algebra Geometry
10.0 credit points
No. of hours per week: three hours
Prerequisite: SM180
Assessment: testslexamination and assignments
A second-year subject of the degree courses in mathematics
and computer science and applied and industrial
mathematics.
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. Wiley. 1972
Johnson, R.A. and Wichern, D.W. Applied Multivariate Statistical
Analysis, 2nd ed, Englewood Cliffs, N.J.: Prentice-Hall. 1988
Mathematics Department notes
Mortenson. M.E. Computer Graphics. Oxford: Heinemann, 1989
Searle, S.R. Matrix Algebra Useful for Statistics. New York: Wiley,
1982
SM384 Inference and Regression
10.0 credit points
No. of hours per week: three hours
Prerequisite: SM284
Assessment: testslexamination and assignments
A second-year subject of the degree courses in mathematics
and computer science and applied and industrial
mathematics.
Subject description
Revision of hypothesis testing and confidence intervals.
The power of a test: (i) against a specific alternative; (ii) the
power curve.
Two independent samples: tests and confidence intervals.
Differences in location; nonparametric tests, differences in
spread; the F test.
Differences between proportions in large samples.
Goodness of fit, observed and expected frequencies, chisquare
test.