1 Numerical methods

Many mathematical problems which arise in the modelling of engineering situations are too difficult, or too lengthy, to tackle by hand. Instead it is often good enough to resort to an approximation given by a computer. Indeed, the process of modelling a “real world" situation with a piece of mathematics will involve some approximation, so it may make things no worse to seek an approximate solution of the theoretical problem.

Evidently there are certain issues here. Computers do not know what a function is, or a vector, or an integral, or a polynomial. Loosely speaking, all computers can do is remember long lists of numbers and then process them (very quickly!). Mathematical concepts must be posed as something numerical if a computer is to be given a chance to help. For this reason a topic known as numerical analysis has grown in recent decades which is devoted to the study of how to get a machine to address a mathematical problem.