Please note - Swinburne University of Technology

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Statistics
Mean and standard deviation. Linear regression in fitting
functions to data.
In this subject students learn to use a graphics calculator to
solve problems in functions, graphs, differentiation, matrices,
vectors and statistics.
Prescribed text:
Berry, J., Norcliffe, A. and Humble, 5. Introductory mathematics
through science application* Cambridge: Cambridge University Press,
1989.
Prescribed calculators:
Texas Instruments Advanced Scientific TI-81 graphics calculator.
SM110 Mathematical Methods
7.5 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
Calculations
Reviews of basic mathematical operations; illustrations from
environmental and health applications. Use of electronic
CA
c, calculator.
m
n 3 Numerical methods
m
lntroduction to numerical methods: errors and their
propagation, including rounding errors and loss of
significance. Solution of equations in one variable; numerical
solution of non-linear equations by iterative methods
(bisection, false position, secants, simple iteration,
Newton-Raphson).
Linear algebra
Matrices and matrix algebra; determinants and their
evaluation. Systems of linear equations: Gaussian elimination;
matrix inversion; procedures for numerical solution by direct
or iterative methods.
Functions of one variable
Standard functions and their graphs. Transcendental
functions: exponential; loqarithmic and natural loaarithm
functions; trigonometric and inverse trigonometri;functions.
Curves defined by relations or parametrically.
Calculus
Differentiation: geometric interpretation; derivatives of
standard functions; product, quotient and chain rules;
implicit differentiation.
Applications of differentiation: graph sketching, using first
and higher order derivatives; related rated; optimisation in
finite closed intervals.
Integration: definite and indefinite integrals and their interpretations;
fundamental theorem; integrals of standard
fundions; integration by substitution. Use of integral tables.
Numerical integration (rectangle, trapezium and Simpson's
rules). Separable differential equations, with or without initial
values. Functions of several variables: partial derivatives;
maxima and minima.
SM13 1 Communication Skills
7.5 credit points
No. of hours per week: four hours
Prerequisites: nil
Assessment: individual assignment, participation
and a test
A first year subject of the degree courses in mathematics
and computer science and applied and industrial
mathematics.
Subject description
Communication Skills
In this component written communications skills will be
developed with particular reference to situationally
appropriate letters, memos, reports and essay writing. Study
and research skills will be enhanced by increasing
competence in notetaking from oral and printed input and
in using library technology. Meeting skills and class
presentations will extend oral skills.
Learning Skills
This component introduces students to the skills and
strategies necessary for developing self-managed learning.
Topics will include goal setting and planning, team learning
behaviour, time management, learning and memory
strategies, motivation, evaluation and stress management
skills.
Textbooks and References
McLeod, C. Study Success Without Stress - Resource Notes.
Hawthorn: Swinburne University of Technology, 1992
Vallence, K.E. and McWilliam, T. Communication That Works
Melbourne: Thomas Nelson, 1992 (ISBN 0-17-006918-4)
SM180 Mathematics 1
10.0 credit points per semester
No. of hours per week: four hours
Assessment: tests, examinations and assignments
A first-year subject of the degree courses in mathematics
and computer science and applied and industrial
mathematics.
Subject description
Analytic geometry:
Vectors in 2- and 3- dimensional space: dot and cross
products, and resolution. Plane coordinate geometry.
Coordinate geometry in Cartesian coordinates; graphs of
linear, polynomial, rational and power functions and of conic
sections.
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.
Functions of one variable:
Standard functions and their graphs. Finite and infinite
limits; continuity.
Calculus:
Differentiation: geometric interpretation; derivatives of
standard fundions; product, quotient and chain rules;
implicit differentiation.
Applications of differentiation: graph sketching; related rates;
optimisation; differentials and approximations; Taylor
polynomials; L'Hapital'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
tr~gonometric functions. Numerical integration.
Applications of integration: areas, volumes, lengths of curves
and surface areas of surfaces of revolution; integrals of rates
of change.
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.