TF ErrorAna PropOfErr: Difference between revisions
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A quantity which is calculated using quantities with known uncertainties will have an uncertainty based upon the uncertainty of the quantities used in the calculation. | A quantity which is calculated using quantities with known uncertainties will have an uncertainty based upon the uncertainty of the quantities used in the calculation. | ||
To determine the uncertainty in a quantity which is a function of other quantities, you can consider the dependence of these quantities in terms of a tayler expansion | |||
A Taylor expansion | Consider a calculation of a Table's Area | ||
<math>A= L \times W</math> | |||
The mean that the Area (A) is a function of the Length (L) and the Width (W) of the table. | |||
<math>A = f(L,W)</math> | |||
The Taylor series expansion of a function f(x) about the point a is given as | |||
<math>f(x) = f(a) + f^{\prime}(x)|_{x=a} \frac{x}{1!} + f^{\prime \prime}(x)|_{x=a} \frac{x^2}{2!} + ...</math> | |||
;<math>= \sum_{n=0}^{infty} f^{(n)}(x)|_{x=a} \frac{x^n}{n!}</math> | |||
Revision as of 19:56, 9 January 2010
A quantity which is calculated using quantities with known uncertainties will have an uncertainty based upon the uncertainty of the quantities used in the calculation.
To determine the uncertainty in a quantity which is a function of other quantities, you can consider the dependence of these quantities in terms of a tayler expansion
Consider a calculation of a Table's Area
[math]\displaystyle{ A= L \times W }[/math]
The mean that the Area (A) is a function of the Length (L) and the Width (W) of the table.
[math]\displaystyle{ A = f(L,W) }[/math]
The Taylor series expansion of a function f(x) about the point a is given as
[math]\displaystyle{ f(x) = f(a) + f^{\prime}(x)|_{x=a} \frac{x}{1!} + f^{\prime \prime}(x)|_{x=a} \frac{x^2}{2!} + ... }[/math]
- [math]\displaystyle{ = \sum_{n=0}^{infty} f^{(n)}(x)|_{x=a} \frac{x^n}{n!} }[/math]