Mathematics of Scientific and Industrial Computation

This course has a long and successful history (previously under the title "Numerical Solution of Differential Equations") and is highly regarded by industrial practitioners, both for the training that it provides and for its employment record. It provides a link between theory and application and an insight into modern computational methods. Students also take part in a modelling week, working in teams to address problems presented by industry stakeholders, subject to realistic time pressure.

Differential equations form the basis of mathematical models for many problems in the physical and engineering sciences and as well as in the biological sciences. Very often the involved nature of these problems leads to equations that can be solved only approximately, by numerical methods. The study of such methods is therefore of practical importance to industry and business and the need for people who can develop and apply numerical techniques to problems in these areas is growing rapidly.

The numerical methods themselves often behave in a complicated way. The study of their stability, convergence and approximation properties forms an important part of numerical analysis. A proper understanding is needed of the differential equations being approximated; for example, it is important to know the conditions for a unique solution to exist and the characterisation of such solutions. The provision of a firm foundation in both the mathematical theory of differential equations and in numerical analysis is therefore an important part of the course.

Some understanding of typical practical application areas is also essential. Examples are drawn mainly from fluid dynamics and control engineering, which together cover a very wide range of practical problems and types of differential equations. They include for instance, models of the flow of compressible fluids (like air), incompressible fluids (like water), flows in porous media (such as water or oil underground), atmospheric flows (weather prediction) as well as mechanical, electrical and electronic control systems and chemical and bio-chemical reaction processes.

Further information

A full Programme Specification is also available with further details of the programme structure.