Abstract :
It is often possible to model the behaviour of devices or systems using analytical techniques, but the complexity of such models may make such calculations impracticable without computer support. In the past, the only solution to this problem was to write specialised code to implement the required calculations. The subsequent appearance of spreadsheets provided a mechanism for avoiding this requirement in some limited applications, but these tools are not well suited to working with complex numbers, vectors or complicated equations. In recent years, however, a wide range of general purpose tools have become available which permit the user to carry out extensive mathematical analysis without recourse to writing code. The capabilities of these tools range from rapid prototyping of numerical methods (e.g. finite element solvers or signal processing algorithms) through to purely symbolic manipulation of equations. Between these two extremes, however, there is frequently an important role for the evaluation of complex analytical expressions over a range of parameter values. The study of a preliminary model is also frequently found to be beneficial in gaining a better understanding of more complicated systems, which may ultimately require more sophisticated numerical modelling. However, this type of analytical study is often sufficient in itself to guide the design or understanding of some systems, and some representative examples of this are outlined below
