Background knowledge
No book like this can go right back to the very beginning, so we must expect you to have some general ideas from earlier study of applied mathematics or physics. In particular it will help considerably if you have some acquaintance with the following.
(i) Newtonian dynamics, including energy, momentum and angular momentum (moment of momentum).
(ii) The physics of any sort of wave motion, including the ideas of standing and travelling waves and reflection at barriers.
(iii) The atomic nature of matter, and especially that a gas is made up of well-separated rapidly moving molecules.
Naturally it will be a help if you have further background, but there will be quite a lot of explanation for everything that is essential. If you find there is not enough description in some areas, you must go to other texts.
Mathematical modelling
The activity of modelling (in a mathematical sense) is one that causes unprepared students some trouble. The theories and examples that we deal with in a course like this seem too unreal to be worth the trouble, and unless the reasons behind the theories and the choice of examples are explained, applied mathematics gets a bad name. This happened many years ago in elementary statics and dynamics with interminable questions about ladders leaning against smooth walls and particles sliding down rough wedges with smooth bases.
The problems of the real subject of fluid dynamics are of great complexity, involving many physical effects and a considerable set of non-linear partial differential equations. These problems cannot be solved either by advanced techniques or by ‘putting them on the computer’: the techniques do not exist and the machines are neither powerful enough nor sophisticated enough (to reject spurious solutions). The problems can only be approached by omitting, after much careful thought and perhaps some experiments, a large number of the physical effects; then perhaps a special case can be dealt with analytically, and this will show what sort of calculation the machine must be programmed for in the more general case.
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