1993 Swinburne Higher Education Handbook

SM127 Mathematics 1
Five hours per week for one semester
Assessment by tesWexamination and assignments
A first-year subject of the degree course in computer science, and in
mathematics and computer science.
Subject description
Numerical calculations
Simple calculations, including mathematics of finance (interest;
annuities, net present value; internal rate of return). lntroduction to
numerical methods. Errors and their propagation. Numerical solution
of equations by graphical and iterative methods.
Plane analytic geometry
&ordinate geometry in Cartesian cwrdinates; 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;
CHopital's rule.
Intearation: definite and indefinite intearals and their inter~retations:
irn"rals of standard functions; integration by substitution and by parts;
imp-kper integrals; systematic integration d rational functions and of
oroducts of triaonometric - functions. Numerical inte~ration. -
Applications of integration: areas, volumes, lengths of curves and
surface areas of surfaces of revolution; integrals of rates of change.
Textbooks
Hunt, R.A., CaIcuIus with Anslytic Geometfy New York: Harper & Row,
1988
prescribed Calculator
Texas Instrument Advanced Scientific TI81
SM214 Mathematical Methods
Four hours per week for one semester
Prerequisite. SM108
Assessment by testdexamination and assignments
A first-year subject of the degree courses in computer-aided chemistry
and computer-aided biochemistry.
Subject description
Linear algebra
Matrices, determinants and the solution of systems of linear equations.
First order differential equations
The solution of separable first order differential equations with
applications.
Functions of several variables
Partial differentiation; differentials and approximations; an introduction
to optimisation.
Descriptive statistics
Numerical and graphical methods for summarising and presenting
data. Cross-tabulation.
The MlNlTAB computer package is used in the statistical studies.
Pmbability
Pmbability and probability distributions such as binomial, Poisson and
normal.
Inferential statistics
Hypothesis tests and confidence intervals for means, proportions and
variances using the t, chi-square and F disributlons
Regression and correlation
Scatterplots, the Pearson correlation coefficient, and linear least
squares regression for one predictor. Applications to analytical
chemistry.
Faculty of Appiled Science
SM225 Operations Research 2
Two hours per week for one semester
Assessment by examination and assignments
A first-par subject of the degree course in mathematics and computer
science.
Subject description
History and methodology
Development of Operations Research: inter-disciplinary team; in-house
OR teams; consultancy teams; methodology; role of techniques;
application problems; problem formulation; model building; testing;
validating; design and data problems; implementation; OR literature;
OR societies.
Introduction to linear Droarammina
Formulation of linear pbgkmming iroblems: graphical solution of two
variable problems; sensitivity analysis, transportation problems. Use
of computer packages such as SASIOR.
Assignment
Maximum and minimum problems.
Inventory control
Inventorj. systems: economic order quantity; backorders; continuous
replenishment; quantity discount; safety stock under uncertainty.
SM226 Applied Statistics 2
Two hours per week for one semester
Assessment by testslexamination and assignments
A first-year subject of the degree course in mathematics and computer
science.
Subject description
Applications of probability
Continuous Drobabilitv distributions. includina exwnential and normal:
expected values of dontinuous random vazabies; applications.
Statistical inference
Drawing random samples from finite and infinite populations.
The sampling distributions t and chi-square: their use in hypothesis
testing and estimation of means, proportions and variance. Examples
of non-parametric hypothesis tests.
The MlNlTAB computer package will be used in this subject.
SM227 Mathematics 2
Three hours per week for one semester
Assessment by testdexamination and assignments
A first-year subject of the degree course in mathematics and computer
science.
Subject description
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.
Vectors and geometry
2D vectors: dot-product and resolution; parametric equations of 2D
curves; vector differentiation.
30 space: Cartesian and polar co-ordinates; 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.
Textbooks
Hunt, R.A., Calculus with Analytic Geometv. New York: Harper & Row,
1988
Prescribed Calculator
Texas Instrument Advanced Scientific T181