1997 Swinburne Higher Education Handbook

Coordindate geometry in Cartesian coordinates.
Standard functions and their graphs; finite and infinite limits.
Differentiation and its applications; optimisation;
approximations; Taylor polynominals.
Integration and its applications; numerical integration.
Matrices and determinants; systems of linear equations.
Exploratory data analysis; descriptive statistics.
Probability: basic theory; probability distributions, mean
and variance.
Statistical inference: sampling distributions, estimation and
testing of hypotheses.
The MINITAB computer package.
Recommended reading
Prrescribed text: to be advised.
Prescribed Calculator
Texas Instruments Advanced Scientific TI-82 Graphics
Calculator or equivalent.
SM1215 Mathematical Methods
10 credit points per semester. 4 hours per week Prerequisite: nil
Hawthorn Assessment: tests/examination and assignments
This is a first year subject of the Bachelor of Applied Science
(Medical Biophysics and Instrumentation)
Content
Vectors in the two-and three-dimensional space.
Introduction to numerical methods; errors; solution of
equations. Coordinate geometry in Cartesian coordinates.
Standard functions and their graphs; finite and infinite
limits.
Differentiation and its applications; optimisation;
approximations; Taylor polynomials. Integration and its
applications, numerical integration.
Polar coordinates, complex numbers. Ordinary differential
equations. Vector functions and functions of many
variables. Data analysis and probability.
Recommended reading
To be advised.
Prescribed calculator
Texas Instruments Advanced Scientific TI-82 Graphics Calculator
SM2 1 00 Applied Statistics
8 credit points 3 hours per week. Hawthorn Assessment:
tests/examination and assignments
This is a first year subject of the Bachelor of Applied Science
(Environmental Health)
Content
Introduction to health statistics: morbidity and mortality,
vital statistics, standardisation, life tables.
Probability: concepts and basic formulas. Probability
distributions: discrete, including binomial and Poisson;
continuous, including normal. Sampling distributions of
mean, variance and proportion.
Estimation of means, variances and proportions from single
samples. Tests of hypotheses in means, variances and
proportions; comparisons of two groups and of several
groups (analysis of variance). Introduction to experimental
design. Chi-squared tests on goodness of fit.
Correlation and regression. Selected non-parametric
methods.
Introduction to epidemiology: types of study; measures of
risk and of association.
SM3400 Mathematical Methods
10 credit points per semester 3 hours per week Hawthorn
Prerequisite: SM1200 or SMI21S Assessmar tests,
examinations and assignments
A second year subject in the Bachelor of Applied Science
(Computing and Instrumentation)
Objectives
Broaden students mathematical techniques and apply to
physics.
Content
A selection of topics from the following:
Real analysis, fourier series of general periodic functions.
Vector analysis
Basic vector manipulation including calculus of vector
functions. Space curves, Serret-Frenet formulas. Special
emphasis on gradient of a scalar field, directional derivative,
divergence and curl of a vector field.
Complex analysis
Algebra and geometry of complex numbers. Functions of a
complex variable. Harmonic functions. Contour integration,
Cauchy integral and residue theorems. Evaluation of definite
integrals. Conformal mapping and applications.
Modern algebra with applications
Groups, rings fields (including Galois fields). Vector spaces,
polynomials with binary coefficients. Linear block codes,
parity check matrices and standard arrays. Cyclic codes,
generator polynomials. Hamming codes.
Recommended reading
Semesters 1 and 2
Boas, M.L., Mathematical Methods in the Physical Sciences. 2nd edn,
New York, Wiley, 1983
Semester 2 only
Anton, H., Calculus with Analytic Geometry, 5th ed. New York,
Wiley, 1995
Hill, R., A First Course in Coding Theo y. Oxford, Oxford
University Press, 1990
Wong, Chien Wa, Introduction to Mathematical Physics, Oxford
University Press, 1991
Swinburne University of Technology 1 997 Handbook 5 1 9