phy-4660/Error Analysis/error propagation

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2017-01-13 08:30:24 +00:00
Z = X + Y OR Z = X - Y
_________
ΔZ = √ΔX² + ΔY²
Z = X * Y OR Z = X / Y
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_ΔZ_ = / ⎛_ΔX_⎞² + ⎛_ΔY_⎞²
Z √ ⎝ X ⎠ ⎝ Y ⎠
Z = Xⁿ
ΔZ = n X⁽ⁿ⁻¹⁾ ΔX, i.e. _ΔZ_ = n _ΔX_
Z X
Z = 𝑓(X,Y,...)
ΔZ² = ⎛_∂f(X,Y)_ ΔX⎞² + ⎛_∂f(X,Y)_ ΔY⎞² + ...
⎝ ∂X ⎠ ⎝ ∂Y ⎠