Course Details in

Module Title	LM Computational Methods for Scientific and Engineering Applications
School	Mathematics
Department	Mathematics
Module Code	06 27713
Module Lead	Dr Chris Good
Level	Masters Level
Credits	20
Semester	Full Term
Pre-requisites	LH Numerical Methods II - (06 27710)
Co-requisites
Restrictions	None
Exclusions
Description	This module exposes students to a range of modern numerical methods for solving partial differential equations models commonly arising in science and engineering. The representative model problems (e.g., diffusion and convection-diffusion equations, heat equation, and wave equation) are solved numerically by using finite difference and finite element methods. The module emphasises mathematical aspects of the design and justification of accurate and stable numerical algorithms. It also covers relevant topics of approximation theory (best approximation in L^p-norms; least-squares approximations; orthogonal polynomials; approximation by splines; curve fitting by polynomials and splines).
Learning Outcomes	By the end of the module students should be able to: understand the concept of best approximation and find best approximations in different norms; develop finite difference schemes and perform relevant error and stability analysis; derive variational formulations of elliptic boundary value problems; develop Galerkin finite element methods and perform relevant error and stability analyses.
Assessment
Assessment Methods & Exceptions	90% on one three hour examination; 10% from coursework and/or class tests.
Other
Reading List