The Engineer’S Approach to Mathematics*

Extract

When faced with a problem, for example the design of a piece of equipment to meet a customer’s requirements, an engineer will seek to find an answer to it by the quickest and cheapest means at his disposal. Of those means mathematics is but one, even though a powerful one. The first stage in invoking its aid is to formulate the engineering problem in mathematical terms. This involves first, the separation of non-quantitative considerations which are not expressible mathematically (which requires engineering experience), second, the formulation of the problem in such a way that the required information (and no more) will be obtained with as little labour as possible; and third, the making of simplifying assumptions so that the mathematics becomes tractable and yet is a sufficiently good representation of the physical situation. Both these last processes require a balanced knowledge both of engineering and of mathematics. (This is an aspect of undergraduate training which could with advantage receive better treatment.) But even when the resulting equations have been solved the engineer’s task is by no means over; the solution to a mathematical equation is a long way from being the answer to an engineering problem. Given the solution the next step (the inverse of formulation) is the interpretation of it. This often involves investigating the effect of variation of the parameters of the problem and requires much computation. The place of electronic computers in the scheme of things becomes evident. Finally, when a satisfactory interpretation has been achieved the engineer may proceed to the answer to his problem.