Uncertainty in measurements.

[Albert Chan]

(07-22-2019 03:48 PM)StephenG1CMZ Wrote:  ... instead of calculating, say, LOG(10), one can calculate LOG({9.999,10,10.001}) or LOG(10×{.95,1,1.05})
and this could be used to show the upper and lower limits of a calculation based on an uncertain measurement.

this work only if the function is monotonic (at least, locally)

Counter-example: f(x) := (1 .- x) .* (1.1 .- x) .* (1.2 .- x)

x := [1.03, 1.18] // x uncertainly range
f(x) → [-0.000357, 0.000288]

But, in this case, f(x) uncertainly should be evaluated where f'(x) = 0

z := solve(diff(f(x))=0, x) // z ≈ [1.04226, 1.15774], both numbers inside x range
f(z) → [-0.000385, 0.000385]