The aim of this course is to introduce a selection of advanced topics in numerical methods. Topics include: Computational issues: finite precision, speed of algorithm, Matlab Polynomial interpolation: Lagrange form, Newton Form, error formulae, splines. Solutions to non-linear equations: bisection method, inverse interpolation, Newton's method in one dimension, error formulae, rates of convergence, Newton's method for systems. Solutions to linear equations: Gaussian elimination, pivoting, LU factorisation, QR factorisation, iterative methods. Numerical differentiation: derivation of finite difference formulae. Numerical integration: derivation of Newton-Cotes formulae, adaptive composite trapezium rule, Gaussian integration. Solutions to systems of
explicit first-order ODEs: Euler, modified Euler, Runge-Kutta. Stiffness: stability, backward Euler. Conversion of higher order explicit equations to first-order systems. Solution to PDE BVP on a rectangular domain by finite differences on a regular mesh.

DP requirements: attendance at all class tests, submission of all assignments, 40% average for class tests and assignments.

Assessment: 6 computer class tests (40%), 2 assignments(10%), computer final examination (50%).

*Course content subject to change