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Error_Propagation

# Error_Propagation - PHY 103N Cheat Sheet Average value of a...

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PHY 103N Cheat Sheet : Average value of a series of measurements: ( 29 ( 29 = = = N i i N i i i x x x x 1 2 1 2 1 (eq. 0.1) Uncertainty for average value: ( 29 = = = N i i x x 1 2 1 1 s (eq. 0.2) Error propagation for a function f=f ( x,y,z,… ): ... + + + = z z f y y f x x f f (eq. 0.6) Useful rules of differentiation: ( 29 1 - = n n anx ax dx d where const a = , n ( 29 ( 29 ( 29 q q q a a a d d cos sin = and ( 29 ( 29 ( 29 q q q a a a d d sin cos - = ( 29 ax ax ae e dx d = ( 29 ( 29 ( 29 ( 29 ( 29 dx x dg dx x df x g x f dx d + = + ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 dx x dg x f dx
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