Department of Architecture & Civil Engineering, Unit Catalogue 2008/09 |
AR10060 Mathematics 1b |
| Credits: 3 |
| Level: Certificate |
| Semester: 2 |
| Assessment: EX 100% |
| Requisites: |
| Before taking this unit you must take AR10059 |
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Aims: To provide a general mathematical basis for the development of engineering subjects at first year level of the civil engineering programmes, and preparation for year 2 work.
Learning Outcomes: The successful student will be able to demonstrate an understanding and ability to use the following techniques, as detailed in the 'Contents': * Complex numbers; * Determinants and matrices; * Elementary vector analysis; * Statistics; * Concept of probability. Skills: Visualisation of engineering behaviour in terms of mathematical models, solution of mathematically and statistically described engineering problems. Content: Complex numbers: Complex plane, Cartesian, polar and exponential forms, algebra of complex numbers, de Moivre's theorem multiple roots, complex logarithm. Determinants and matrices: Properties of determinants. Matrix algebra. Solution of simultaneous equations using the matrix inverse. Cramer's rule and Gauss elimination. Consistency. Elementary vector analysis: Basic definitions and algebra. Scalar, vector and tensor products. Equations of lines and planes. Geometrical interpretations, orientation of planes, volumes of solids. Statistics: Basic descriptive statistics, histograms, cumulative frequency, measure of location and dispersion, mean, mode and median, upper and lower quartiles, variance and standard deviation. Concept of probability, exclusivity, dependence and independence of events, conditional probability. Binomial and Poisson distributions. |