Please note - Swinburne University of Technology

2D polar coordinates
Definitions: Graphs of equations; transformation to and from
Cartesian coordinates.
Complex numbers
Definition and arithmetic: polar form; de Moivre's theorem and
exponential notation.
Ordinary differential equations
General and particular solutions. First order equations of
separable, linear and homogeneous types. Second order linear
equations with constant coefficients. Applications. Numerical
methods of solution.
Vector functions
Calculus of vector functions of one variable with application to
displacement, velocity and acceleration and to mechanics.
Equations to lines and planes, gradient of a scalar field,
directional derivative.
Functions of many variables
Partial differentiation and applications: differentials and
approximations; optimisation and applications (including least
squares) with first and second derivative tests.
Data presentation and analysis
Frequency distributions: tabulation; graphical presentation;
measures of central tendency and of dispersion; measures of
association.
Probability
Definitions and concepts of probability: calculation using
addition and product-rules; conditional probability and
independence.
Probability distributions: discrete variates, including binomial,
Poisson and hypergeometric distributions; continuous variates,
including normal distribution; mean and variance.
Introduction to hypothesis tests and confidence intervals for
means and correlation coefficients using the t distribution.
Textbooks
Anton, H., Cakulus with Analytic Geometry. 4th edn, New York,
Wiley, 1992
Prescribed calculator
Texas Instruments Advanced Scientific TI-82 Graphics Calculator
~~2100 Applied Statistics
8 credit points
No. of hours per week: three hours
Assessment: testdexamination and assignments
Subject description
lntroduction to health statistics: morbidity and mortality, vital
statistics, standardisation, life tables.
Probability: concepts and basic formulas. Probability
distributions: discrete, includinq 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). lntroduction to experimental design. Chisquared
tests on goodness of fit.
Correlation and regression. Selected non-parametric methods.
lntroduction to epidemiology: types of study; measures of risk
and of association.
~~3400 Mathematical Methods
8 credit points per semester
No. of hours per week: three hours
Prerequisite: SMI 200 or SM1215
Assessment: testdexaminations and assignments
Subject description
Linear algebra and vectors
Matrices and matrix algebra. Systems of linear equations:
Guassian elimination; procedures for numerical solution by
direct or iterative methods, (Jacobi and Gauss-Seidel),
transformation matrices.
Real analysis
Partial differentiation, chain rule, approximations. Application
to maximum and minimum problems constrained optima and
Lagrange multipliers. Change of variable. Multiple integrals.
Applications of single, double and triple integrals. Jacobians.
Surface integrals. Fourier series of general periodic functions.
Laplace transforms. Use of tables. Partial differential equations,
solution via separation of variables (Fourier series).
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. Line, surface and volume
integrals. Field theory.
Complex analysis
Algebra and geometry of complex numbers. Functions of a
complex variable. Elementary functions such as polynomial,
exponential, trigonometric, hyperbolic, logarithm and power.
Differentiability and Cauchy-Reimann equations. Harmonic
functions. Contour integration, Cauchy integral and residue
theorems. Evaluation of definite integrals. Conformal mapping
and applications.
Random processes
Review of probability, Markov chains, Poisson processes, birthdeath
processes, Chapman-Kolmogorov equations. Steady
state probabilities. Simple queueing processes.
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.
Prescribed text
Semesters 1 and 2
Boas, M.L. Mathematical Methods in the Physical Sciences. 2nd edn,
New York, Wiley, 1983
Semester 2 only
Hill, R. A First Course in Coding Theory. Oxford, Oxford University Press,
1990
~~3415 Mathematical Methods
8 credit points for semesters one and two
No. of hours per week: three hours
Prerequisite: SM 1200 or SM 121 5
Assessment: tests/examinations and assignments
Subject description
Linear algebra and vectors
Matrices and matrix algebra. Systems of linear equations:
Guassian elimination; procedures for numerical solution by
direct or iterative methods, (Jacobi and Gauss-Seidel),
transformation matrices.