TABLE OF CONTENTS In this chapter we first consider the basic concepts of mathematical modelling in 1. In reducing a real-life problem to a manageable mathematical problem it is important to know which parameters are relevant. The resulting dimension analysis and Buckingham s theorem are treated in 2. The subsequent sections each contain an interesting application. We consider vehicle control through steering of rear wheels in 3. Next a mechanical problem, viz. inverse resonance, is dealt with in 4. Water waves and in particular solitary solutions of the Korteweg-de Vries equation are considered in 5. The next two sections are devoted to epidemics models: diffusive effects are neglected in 6 and taken into account in 7. In 8 we consider nerve impulse propagation and solitary wave solutions of the Fitzhugh-Nagumo equation. The next case study is the torsion in a crank shaft, which is carried out in 9. Finally, chaos is shown to play an important r le in studying the dripping of a faucet, cf. 10.
When mathematics is applied to real-life problems, a translation is needed to put the subject into a mathematically tractable form. This process is usually referred to as mathematical modelling, and a possible definition reads: mathematical modelling is the description of an experimentally verifiable phe nomenon by means of the mathematical language.
See also [12, 18]. The phenomenon to be described will be called the system, and the mathematics used, together with its interpretation in the context of the system, will be called the mathematical...
