The module gives an introduction to practical techniques for carrying out numerical computations on a range of mathematical problems. Students will be expected to have an elementary acquaintance with Matlab. (An introductory session on Matlab will be provided for those who need it.)

1. An Introduction to Practical Computation
- Algorithms
- Simple examples
- Pitfalls

2. Solving single nonlinear equations
- Bisection Method
- Regula Falsi
- Newton's Method

3. Numerical linear algebra
- Gaussian Elimination
- Partial pivoting
- Iterative methods

4. Numerical solution of ordinary differential equations
- Euler's Method
- Runge-Kutta Methods
- Linear Multi-step Methods

5. Simple approximation
- Polynomial interpolation
- Optimal interpolation points
- Fourier and Trigonometric Series

On completion of the module students should be able to:
- appreciate the processes and pitfalls of mathematical approximation
- demonstrate knowledge and understanding of mathematical computing
- motivate and describe the derivation of the numerical algorithms covered in the module
- carry out simple numerical processes "by hand"
- implement and execute algorithms in Matlab
- evaluate, contrast and reflect upon the numerical results arising from different algorithms.