Mastering Uncertainty Calculations for Lab Courses and Beyond

[fayan77]

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]

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. $V=V(X,Y,Z,...)$.