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Maths problems in Engineering - handling infinity

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I am an engineer who uses a lot of maths. One of the difficulties I encounter regularly is dealing with zero and infinity, because these are abstract concepts (nothing in the real world is infinite, and nothing that exists is zero). Mathematical models are comfortable with zero and infinity, for instance Hooke’s law for springs – the spring can extend to infinity, and the maths says that a bouncing ball will bounce an infinite number of times before stopping. As for zero, an infinite wire of finite mass has zero width. But there is more. Can we assume that a rail (on a train track) is infinitely long? This is a useful assumption for sound radiation. What about a power cable between its supports – can that be thought of as infinite? A lot hinges on the answers to the integral over sin and cos from 0 to infinity, which are 1 and 0 respectively. An engineer can prove these results very simply.

This talk is part of the Trinity Mathematical Society series.

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