Department of Architecture & Civil Engineering, Unit Catalogue 2008/09 |
AR10059 Mathematics 1a |
| Credits: 3 |
| Level: Certificate |
| Semester: 1 |
| Assessment: EX 100% |
| Requisites: |
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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.
Learning Outcomes: The successful student will be able to demonstrate an understanding and ability to use the following techniques, as detailed in the 'Contents': * Elementary functions; * Differentiation and its applications; * Integration and its applications; * Infinite series. Skills: Ability to manipulate and solve mathematical problems, graphical representation of mathematical functions, development of mathematical ideas relevant to engineering Content: Elementary functions Exponential and logarthmic functions, hyperbolic functions and inverses in logarithmic form, inverse circular functions, plotting graphs. Differentiation and its applications Maximum and minimum values, inflection points, tangents, normals, curvature, solution of non-linear equations using Newton's method, limits. Integration and its applications General revision of techniques, by parts, use of partial fractions, substitution, length of curves, areas and volumes, first and second moments, centre of gravity, parallel and perpendicular axes theorem. Infinite series Maclaurin and Taylor's series, binomial expansion, ideas of convergence, geometrical series, comparison, ratio and integral tests, l' Hôpital's rule. |