Computing uncertainties

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Hello, took a year off school and starting school soon. So I'm shaking off the rust and remembered in my previous lab courses we were supposed to compute uncertainties but I never really understood how that works. All I remember was its something to do with pythagorean theorem. I want to really understand this mathematical concept for I will be taking many more labs at university level and want to be prepared.
 

Charles Link

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What you are referring to I believe is e.g. if ## V=V(X,Y) ## where ## X ## has uncertainty ## \Delta X ##, and ## Y ## has uncertainty ## \Delta Y ##, then the uncertainty ## \Delta V ## satisfies ## (\Delta V)^2=(\frac{\partial{V}}{\partial{X}})^2 (\Delta X)^2+(\frac{\partial{V}}{\partial{Y}})^2 (\Delta Y)^2 ##. Perhaps someone can find a link to something that spells this idea out in more detail. ## \\ ## A simple example of the above is the case where ## V=X+Y ##. Then ## (\Delta V)^2=(\Delta X )^2+(\Delta Y )^2 ##. ## \\ ## Meanwhile, the above can be generalized to more variables, e.g. ## V=V(X,Y,Z,...) ##.
 
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