Please note - Swinburne University of Technology

Matrix algebra
Matrices and matrix algebra: determinants. Systems of linear
equations: Cramer's rule; Jordan and Gaussian elimination;
matrix inversion; procedures for numerical solution by direct
and iterative methods.
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; dd-product and resolution; parametric equations
of 2D curves; vector differentiation.
3D space: Cartesian and polar coordinates; simple surfaces
and curves in space.
3D vectors: dot and cross-products; vector equations of lines
and planes; parametric equations of 3D curves.
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Functions of many variables
Graphs of surfaces as functions of two or three variables:
8 partial differentiation and applications; directional derivatives
and gradients; tangent planes to surfaces; differentials and
approximations; optimisation and applications.
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Com~lex numbers
complex numbers: definition and arithmetic; polar form;
exponential notation. Solution of polynomial equations.
Textbook
Hunt, R.A. Cakulus with Analytic Geometry. New York: Harper and
Row, 1988
Prescribed calculator
Texas Instruments Advanced Scientific TI-81 Graphics Calculator
SMI 215
Mathematical Methods
10.0 credit points per semester
No. of hours per week: four hours
Assessment: testslexamination and assignments
A first-year subject of the degree course in medical
biophysics and instrumentation.
Subject description
Vectors
Vectors in 2 and 3 dimensions. Dot and cross products of 2
vectors in space and applications.
Numerical calculations
lntroduction to numerical methods. Errors and their
propagation. Numerical solution of equations by graphical
and iterative methods.
Elementary combinatorial analysis; counting selections and
arrangements.
Plane analytic geometry
Co-ordinate geometry in Cartesian co-ordinates; graphs of
linear, polynomial, rational and power functions and of conic
sections.
Functions of one variable
Standard functions and their graphs. Finite and infinite
limits; continuity.
Calculus
Differentiation: geometric interpretation; derivatives of
standard functions; product quotient and chain rules; implicit
differentiation.
Applications of differentiation: graph sketching; related rates;
optimisation; differentials and approximations; Taylor
polynomials; L'HCpital's rule.
Integration: definite and indefinite integrals and their
interpretations; integrals of standard functions; integration by
substitution and by parts; improper integrals; systematic
integration of rational functions and of products of
trigonometric functions. Numerical integration.
Applications of integration: areas, volumes, lengths of curves
and surface areas of surfaces of revolution; integrals of rates
of change.
2D polar co-ordinates
Definitions: Graphs of equations; transformation to and from
Cartesian co-ordinates.
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 produd-rules; conditional probability and
independence.
Probability distributions: discrete variates, including binomial,
Poisson and hypergeometric distributions; continuous
variates, including normal distribution; mean and variance.
lntroduction to hypothesis tests and confidence intervals for
means and correlation coefficients using the t distribution.
Textbooks
Hunt, R.A., Cakulus with Analytic Geometry. N m York: Harper and
Row, 1988
Prescribed calculator
Texas Instruments Advanced Scientific TI -81 Graphics Calculator
SM2100 Applied Statistics
8.0 credit points
No. of hours per week: three hours
Assessment: testslexamination and assignments
A first-year subject of the degree course in environmental
health.
Subject description
lntroduction 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.
lntroduction to epidemiology: types of study; measures of
risk and of association.