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Aboslute error calculation

  1. Oct 16, 2014 #1
    The absolute error of the quantity p should be calculated.
    p=a*b where a and b are two variables.
    By taking ln on both sides:
    lnp=lna+lnb, then differentiating:
    dp/p=da/a+db/b
    dp=abolute error
    Should I have used total or partial differential in the differentiation step?
     
  2. jcsd
  3. Oct 16, 2014 #2

    ShayanJ

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    Doesn't matter. [itex] da [/itex] or [itex] \partial a [/itex] or [itex] \Delta a [/itex], they all represent the error in measuring a.
     
  4. Oct 16, 2014 #3
    Which is the most correct to use when I differentiate a function of two variables? Partial derivative?
     
  5. Oct 16, 2014 #4

    ShayanJ

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    Well, now that I think, [itex] d [/itex] is the correct one. Because you're actually differentiating [itex] \ln p [/itex] w.r.t. p regardless of what p depends on! The same for other two logarithms.
    Anyway, I've heard several methods for calculating absolute errors. But the one I prefer, is the following:
    [itex]E[f(x_1,x_2,...,x_n)]=\sqrt{\sum_{k=1}^n (\frac{\partial f}{\partial x_k} dx_k)^2}[/itex]
    Because it obviously gives the maximum change in f for given changes in its arguments.
     
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