- #1

ShayanJ

Gold Member

- 2,788

- 587

## Main Question or Discussion Point

Consider a physical quantity e.g. w,related to some other quantities by [itex] w=f(x,y,z) [/itex].

Imagine an experiment is done for finding the value of w and the measurement errors for x,y and z are known.

I wanna know what is the standard method for calculating the error in w resulting from the errors in x,y and z?

I can think of several ways but don't know which is better!

1-[itex] \Delta w=\frac{\partial f}{\partial x}\Delta x+\frac{\partial f}{\partial y}\Delta y+\frac{\partial f}{\partial z}\Delta z[/itex]

2-[itex]\Delta w^2=(\frac{\partial f}{\partial x})^2 \Delta x^2+(\frac{\partial f}{\partial y})^2 \Delta y^2+(\frac{\partial f}{\partial z})^2 \Delta z^2 [/itex]

and some others...!

Thanks

Imagine an experiment is done for finding the value of w and the measurement errors for x,y and z are known.

I wanna know what is the standard method for calculating the error in w resulting from the errors in x,y and z?

I can think of several ways but don't know which is better!

1-[itex] \Delta w=\frac{\partial f}{\partial x}\Delta x+\frac{\partial f}{\partial y}\Delta y+\frac{\partial f}{\partial z}\Delta z[/itex]

2-[itex]\Delta w^2=(\frac{\partial f}{\partial x})^2 \Delta x^2+(\frac{\partial f}{\partial y})^2 \Delta y^2+(\frac{\partial f}{\partial z})^2 \Delta z^2 [/itex]

and some others...!

Thanks