Please note - Swinburne University of Technology

Descriptive statistics
Numerical and graphical methods for summarising and
presenting data. Cross-tabulation.
The MlNlTAB 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
Anton, H. Calculus with Analytic Geometry 4th edn, New York, Wiley,
1992
Prescribed calculator
Texas Instruments Advanced Scientific TI-82 Graphics Calculator
s~121o 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
5
-@ Subject description
rn Analytic geometry
2 Vectors in 2- and 3-dimensional space: dot and cross products,
G. and resolution. Plane coordinate geometry. Coordinate
ID
2,
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
8 propagation. Numerical solution of equations by graphical and
4. iterative methods.
.J
Functions of one variable
Standard functions and their graphs. Finite and infinite limits;
continuity.
Calculus
Differentiation: geometric interpretation; derivatives of
standard functions: oroduct. auotient and chain rules: imolicit
, , . ,
differentiation.
Applications of differentiation: graph sketching; related rates;
optimisation; differentials and a~proximations; . .
Tavlor
polynomials.
Inteqration: definite and indefinite inteqrals and their
interpretations; integrals of standard functions; integration by
substitution. Numerical integration. Calculations 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.
Applied Statistics
Topics to be chosen from:
Exploratory data analysis; numerical and graphical methods for
summarising and presenting data. Measures of association for
two variables using Pearson and Spearman correlation coefficients;
scatterplots. Straight line fits to data; residuals;
outliners.
Probability: definition and calculation of probabilities using the
addition and product rules; conditional probability, independent
events.
Applications: probability distributions including binomial,
Poisson, hypergeometric, exponential, normal; expected values
of random variables and applications.
Statistical inference: drawing random samples from finite and
infinite populations. The sampling distributions t and chisquare;
their uses, the MlNlTAB computer package.
Textbook
Anton, H. Calculus with Analytic Geometry. 4th edn, New York, Wiley,
1992
Prescribed calculator
Texas Instruments Advanced Scientific TI-82 Graphics Calculator
~~1215 Mathematical Methods
10 credit points per semester
No. of hours per week: four hours
Assessment: tests/examination and assignments
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
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;
optimisation; differentials and approximations; Taylor
polynomials; L'H6pital1s 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.