Course outline: 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.
Lectures: 3 lectures per week.
Tutorials: 1 double tutorial per week
Assessment: June examination no longer than 2 hours: 65%, year mark: 35%.