Please note - Swinburne University of Technology

SMl85 Applied Statistics 1
10 credit points
No. of hours per week: four hours
Prerequisites: nil
Assessment: testdexaminations and assignments.
Subject description
Data summaries - displaying and describing distributions.
Relationship between variables - scatterplots, correlation,
cross-tabulation, regression. Basic probability. Random
variables. Discrete distributions; binomial, poisson, geometric,
hypergeometric. Continuous distributions; exponential,
normal. Comparing distributions using Q-Q plots; normal
plots. Bootstrap estimation of means and proportions;
confidence intervals. The sampling distribution of the mean;
Central Limit Theorem. Estimation and hypothesis tests based
on small and large samples. The t-distribution. Simple nonparametric
methods.
Textbooks and References
Moore, D.S. and McCabe, G.P., Introduction to the Practise of
Statistics, 2nd edn, New York, Freeman, 1993
Groeneveld, R.A., htroductory Statistical Methods, Boston, PWS Kent,
1988
Johnson, R.A. and Bhattacharyya, G.K., Statistics: Principles and
Methods, 2nd edn, New York, Wiley, 1992
Ott, L. and Mendenhall, W., Understanding Statistics, 6th edn,
E! Belmont, Calif., Duxbury Press. 1994
1.
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0, ~ ~ 1 9 3 Mathematics
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No. of hours per week: three hours in first
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3 semester and two hours in second semester
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Instruction: lectures, tutorials
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Assessment: examination SO%, assessed work
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50%
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m Subject aims and description
2. This subject is designed to provide the students with the
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mathematical basis for many construction subjects. Topics
include: vectors, trigonometry, calculus, matrices, algebra,
statistics, financial mathematics and computer studies.
z.
'a References
3 Dobinson, J. Mathematics for Technolog)! Vols. 1 and 2,
Harmondsworth, Penguin, 1972
Gottfried, B.S. Schaum's Outline of Theory and Problems of
Programming With Structured BASIC, New York, McGraw-Hill, 1993
Greer, A. and Taylor, G.W. Mathematics for Technicians: Level 11:
Building Construction Mathematics. Cheltenham, Thornes, 1980
Jones, M.K. Construction Mathematics. Vols. 1 and 2, London,
Longman, 1979
Lang, D.W. Critical Path Analysis. London, Teach Yourself Books, 1970
~ ~ 1 9 9 Engineering Mathematics
No. of hours per week: three hours for two
semesters
Instruction: lectures, tutorials
Assessment: examinations, tests
Subject aims and description
This subject covers the basic mathematical knowledge
considered to be minimally essential for an adequate
understanding of the concurrent first-year studies in
engineering.
The subject presents some additional material relevant to later
engineering studies which will enable those students with
ability and interest to develop further their mathematical
knowledge and skills.
Functions and graphs: graphs for functions of one and two
variables; surfaces; derivatives and partial derivatives;
indefinite integrals; integration of partial derivatives.
Linear algebra: linear transformations, matrices and inverse
matrix, determinants, solution of linear equations - Cramer's
Rule and Gaussian elimination.
Analytic geometry: algebra of vectors, dot product and cross
product, vector projections, the plane, parametric specification
of plane curves and curves in space, velocity and acceleration
vectors, the straight line.
Functions of several variables and complex numbers: small
variation, chain rule, curve fitting, algebra of complex
numbers, polar form, exponential notation, roots of complex
numbers, solution of polynominal equations.
Directional derivative, maxima and minima, hyperbolic and
inverse functions.
Integration: methods of integration, including substitution,
integration by parts, partial fractions, substitution of circular or
hyperbolic functions, square completion, integration using
complex numbers. Appliations of integration, including area,
mean square, centroid, moments, volume, curved surface area.
Differential equations: first order separable, first order linear,
second order linear.
Infinite series: Taylor's theorem, infinite series, Taylor and
Maclaurin series, power series manipulation.
Also included in the course is a choice of project work.
Students select six from the following:
Minitab. Contour IinedSurfaces. Probability. Iterative methods.
The general linear system. Beam theory. Curve fitting nonlinear
models. Vectors - an extension. Fluid mechanics.
Bisection and false position methods. Newton's method and
simple iteration. Computer programming. Centroids and
second moments of area. Trapezoidal and Simpson's Rule.
Diagnosis of integration. Centroids and Pappus's theorems.
Applications of differential equations. Boolean Algebra. Electric
circuits.
Textbook
Thomas, G.B. and Finney, R.L. CalculusandAnalytic Geometry 8th
edn, Reading, Mass., Addison-Wesley, 1992
References
Anton, H. Calculus with Analytic Geometry: 4th edn, New York, Wiley,
1992
~ade, L. and Westergren, B. Beta Mathematics Handbook. 2nd edn,
Lund, Studentlitteratur, 1990
Shenk, A. Calculus and Analytic Geometry 4th edn, Glenview, Scott,
Foresman. 1988
~ ~ 1 9Engineering 9 ~ Mathematics Pathways
No. of hours per week: five hours for first
semester, four hours for second semester with an
extra two weeks in each semester
Instruction: lectures, tutorials
Assessment: examinations, tests
Subject aims and description
The subject covers the basic mathematical knowledge
considered to be minimally essential for an adequate
understanding of the concurrent first year studies in
engeineering, but also covers extra mathematical
groundwork.