Mathematics for Circuits

Mathematics for Circuits

English | PDF | 1964 | 103 Pages | ISBN : 0333009614 | 6.07 MB

A member of the Royal Society once wrote
' ... besides the great delight and pleasure there is in these mathe- matical and philosophical enquiries there is also much real benefit to be learned, particularly for such gentlemen as employ their estates in those chargeable adventures of draining mines, coal-pits etc ... .'
This is enough to make any mathematician throw up his hands in horror; but it is a hard fact that the elegant language of mathematics has become the medium through which the scientist and engineer express their problem in a quantitative fashion. Mining engineering may have been uppermost in the mind of our seventeenth century philosopher but the sentiments expressed apply to every branch of applied science.
Electrical engineering is one branch in which the subject matter may be broadly divided under two main headings: the study of field theory, and the study of circuit theory. Each facet requires a sound knowledge of mathematical principles: each requires the same basic approach. First, an appraisal of the nature of the problem, second, a knowledge ofthe physical laws relating to the particular study in hand, third, the setting out in mathematical form of the relationships which describe the mode of behaviour of the system, and finally, the extraction of an intelligent solution.
It is in respect of this final point that the broad training in engineer- ing is of such vital importance. In the analysis of a circuit problem, for example, it may very well be that two or more solutions will be found in calculating the value of a particular component: it may equally well be that the use of one of the possible values will result in the circuit becoming a charred mass on being put into service. In other words, at least one function of the engineer is to accept the advice offered by the mathematical solution and reject that which is quite irrelevant.

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