Integrable

From QED

A function is said to be integrable if some type of integral, with the function as an integrand, exists. Note that this doesn't mean "exists and can be written in terms of elementary functions", I mean "exists as a definite function". This admittedly useless answer is basically all that mathworld yields, so I'll elaborate for the physicist audience.

You've probably heard of the Lebesgue Integral, and you're wondering what on earth this thing is, and what it's useful for. Essentially, it's an integral which is defined on a type of measure which admits hairier spaces than would otherwise like, or deal with on a regular basis. Nearly everything modern physicists deal with is on manifolds, which are really a whole heck of a lot nicer than the bizarre spaces which occasionally terrorize the mathematicians that worry about this kind of stuff.

If you plan on dealing with scientific computing, rigorous analysis calls for discretization of the space -- an approximation of which this leads us into the Lebesgue integral! If we're feeling particularly adventurous, it's possible that other types of integrals make possible the avoidance of singularities which you'd otherwise be killed by. So if you feel like looking at incompressible, inviscid flows, you might be able to handle something you would normally be stumped by.

But the bottom line is, for standard affairs: don't worry about it. Don't waste your time, as I have, worrying about a mathematical obscurity. You can become an expert if and when the need arises.

This page was recovered in October 2009 from the Plasmagicians page on Integrable dated 20:41, 1 November 2006.