Department of Architecture & Civil Engineering, Unit Catalogue 2008/09 |
AR20061 Mathematics 2 |
| Credits: 6 |
| Level: Intermediate |
| Semester: 1 |
| Assessment: CW 20%, EX 80% |
| Requisites: |
| Before taking this unit you must take AR10060 |
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Aims: To provide a general mathematical basis for the development of engineering subjects at second year level of the civil engineering programmes, and preparation for year 3 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': * Ordinary Differential equations; * Functions of several variables; * Numerical Methods; * Elementary computer programming using C++. Skills: An understanding of the mathematical tools used in engineering analysis and how they can be applied to civil engineering problems. Content: Ordinary Differential equations Simple first order using separation of variables and integrating factor. Linear equations with constant coefficients using trial method for particular integral. Simultaneous equations. Application of differential equations to mechanical systems and structural problems. Functions of several variables: Multiple Integration, Partial differentiation. Separation of variables, Laplace's equation, diffusion and wave equations. Fourier series Full and half-range series. Odd and even functions, odd harmonics. Numerical Methods: Method of least squares, Finite differences, interpolation using Lagrange and Newton difference formulae. Error estimation, splines, Numerical solution of ordinary differential equations. Euler, improved Euler, Runge-Kutta methods. Accuracy and stability. Initial and boundary value problems. Numerical integration. Root finding Newton Raphson, Secant method. An introduction to the principles and techniques of computer programming using C++. |