How Do You Calculate Error in Complex Physics Equations?

[Exulus]

I really struggle with calculating errors :( I understand what i have to do, find the partial derivative of each variable and multiply it by the error, square it, add up all the others then square root the total. I just seem totally incapable of doing it :( The expression i have to find error on is:

$$E = m_{0}c^2 [\sqrt{1+(\frac{RqB}{m_{0}c\tan{\frac{\Theta}{2}}}) ^2} - 1]$$

Where R, B and theta all have errors associated with them! (to find the error on E)

I've been told its possible to break it down one bit at a time, so evalulating the RqB bit i get:

$$\sigma = \sqrt{ (B\Delta R)^2 + (R\Delta B)^2}$$

But no idea where to go next :( Any help much appreciated!

 

[big man]

So are you having trouble with finding the partial derivatives in the uncertainty expression below??
$$\sigma=\sqrt{(\frac{\delta E}{\delta R})^2*(\Delta R)^2+(\frac{\delta E}{\delta B})^2*(\Delta B)^2+(\frac{\delta E}{\delta\theta})^2*(\Delta\theta)^2}$$

 

[Exulus]

Hi,

Yeah i was having trouble with it. I think I've solved it now. I went an incredibly long way around it by calling everything else inside the bracket which wasnt the variable to be differentiated, a constant, such as C. That made me see what was going on a bit better and i think it worked! *fingers crossed* i can't change it now as the work has been handed in :) Thanks though!

 

[big man]

yeah well that's all you do in partial differentiation anyway. You treat everything else as a constant except the variable you are differentiatin with respect to. Then in your case you had to apply the chain rule and bob's your uncle ;)
Good luck with it then and it sounds like you had the right idea so it should be ok.