4. EProp

# 4. EProp - Uncertainty Analysis II Uncertainty of functions...

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Uncertainty Analysis II Uncertainty of functions of more than one variable

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Propagation of uncertainties If y is a real, continuous function of n independent variables, ( ) 1 2 , ,..., n y f x x x = then given small increments, x 1 , x 2 ,…, x n , y , the change in value of y , is ( ) ( ) 1 1 2 2 1 2 , ,..., , ,..., . n n n y f x x x x x x f x x x f = + ∆ + ∆ + ∆ = ∆
The Taylor series expansion around x 1 , x 2 , … , x n is 1 2 1 2 1 1 2 2 ... ... n n n n f f f f x x x x x x x x x ε ε ε = + + + + + + + 1,2,..., 0 n x 1,2,..., 0 n ε Since as

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The total differential is: 1 2 1 2 ... n n f f f f x x x x x x = + + + This is the change in value of a function, f , given small changes in the values of its independent variables, x i . In experimental uncertainty analysis, the 's represent uncertainties in the estimates of physical quantities. 's are equally likely to be of either sign, provided systematic biases have been removed or compensated for.
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