Please note - Swinburne University of Technology

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.
lntroduction to hypothesis tests and confidence intervals for
means and correlation coefficients using the t distribution.
Textbooks
Hunt, R.A., Calculus with Analytic Geometry. New York: Harper and
Row, 1988
Prescribed Calculator:
Texas Instruments Advanced Scientific TI-81 Graphics Calculator
SMI 208 Mathematics
10.0 credit points in semester one and 8.0 credit
points in semester two
No. of hours per week: five hours in semester
one and four hours in semester two
Assessment: tests, examination and assignments
A first-year subject of the degree courses in computer-aided
chemistry and computer-aided biochemistry.
Subject description
Vectors
Veaors in 2 and 3 dimensions. Dot and cross products of 2
vectors in space and applications.
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.
Plane analytic geometry
Coordinate geometry in Cartesian coordinates; 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;
obimisation: differentials and a~~roximations;
. . . Tavlor .
polynomials;. LIHopital'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.
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 MINITAB computer package is used in the statistical
studies.
Probability
Probability 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
distributions.
Regression and correlation
Scatterplots, the Pearson correlation coefficient, and linear
least squares regression for one predictor. Applications to
analytical chemistry.
Textbooks
Hunt, R.A. Calculus with Analytic Geomety NRN York: Harper and
ROW, 1988
Prescribed calculator
Texas Instruments Advanced Scientific TI-81 Graphics Calculator
SM 1210
Mathematics
12.5 credit points in semester one and 7.5 credit
points in semester two
No. of hours per week: five hours in semester
one and three hours in semester two
Assessment: tests, examinations and assignments
A first-year subject of the degree courses in mathematics
and computer science and software engineering.
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 functions: 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: definie 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.