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Luke_A_Somers comments on Local truth - Less Wrong Discussion
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Just about every approximation, ever. The further you are from math, the more of these there are, and you don't need to go far (all physics other than fundamental physics) to be loaded with them.
Simple harmonic oscillators? In 99% of cases, that's locally true around the minimum.
PV = nRT? Ideal gases are an approximation that is often strong, but right around condensation points or if there are long-ranged forces in the gas, it isn't.
So on, so on.
You don't even have to leave fundamental physics. Firstly the existing equations are (presumably) approximations to the underlying unified theory; secondly, we can't solve them exactly anyway, and even in the relatively tractable electroweak case we use the approximation of a truncated sum. As for the strong force, where that technique doesn't converge, don't even ask.
I meant actual fundamental physics, not the standard model, which is already known to be a (very good) approximation. There are some statements we can make which at least have the possibility of being exactly correct - the general form of the Schrodinger equation, General Relativity, conservation of momentum... that sort of thing.
As for truncated series etc, that fits exactly into the sort of approximation I was talking about.