Please note - Swinburne University of Technology

Functions of one variable
Standard functions and their graphs. Transcendental functions:
exponential; logarithmic and natural logarithm functions;
trigonometric and inverse trigonometric 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
functions; 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.
SMIY
Communication Skills
7.5 credit points
No. of hours per week: four hours
Prerequisites: nil
Assessment: individual assignment, participation
and a test
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 note taking 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, Vic., Swinburne University of Technology, 1992
Vallence, K.E. and McWilliam, T. Communication That Works.
Melbourne, Nelson Wadsworth, 1987.
SMI~O Mathematics 1
10 credit points per semester
No. of hours per week: five hours
Assessment: tests, examinations and assignments
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:
Introduction 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 functions; product, quotient and chain rules; implicit
differentiation.
Applications of differentiation: graph sketching; related rates;
optimisation; differentials and approximations; Taylor
polynomials; L'HBpital'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. Calculation of
areas.
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: dot-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.
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
Anton, H. Calculus with Analytic Geometry. New York, Wiley, 4th edn,
1992
Prescribed Calculator: Texas Instruments Advanced Scientific TI-82
Graphics Calculator.