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2013-10-26 19:02:16 +0100 | received badge | ● Student (source) |
2013-10-26 16:19:12 +0100 | commented answer | Propagation of uncertainty Thank you for your answer. To the second point (wrong method/calculation): I haven't read the whole Wikipedia article, because I got it first from the other site. Thanks for pointing that out. Also your "custom functions" are really nice. |
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2013-10-26 16:14:42 +0100 | marked best answer | Propagation of uncertainty Your approach with You should understand that the product of the middles is usually not equal to the middle of the products, not every map is flat! Actually, the result $32\pm 16$ given by The result using the "sophisticated" formula is wrong: the smallest product between $10\pm 2$ and $3\pm 1$ is $8\times 2 = 16$, and is smaller than $30-11.67 = 18.33$. It uses a truncated Taylor estimation, so it can only be used to have a quick rough estimate of the error, not a guaranteed upper bound, see the Caveats and warnings section. If you want to use custom functions instead of Then you can do: |
2013-10-26 15:11:45 +0100 | received badge | ● Editor (source) |
2013-10-26 15:06:51 +0100 | asked a question | Propagation of uncertainty Is there any simple method in sage to do a calculation with uncertainties? Something like this: $(10\pm2) * (3\pm1) = (30\pm18)$. Or with a more "sophisticated" formula: $(30\pm11.67)$ because of $(10 \times 3 \times \sqrt{(2/10)^2 + (1/3)^2} = 11.67)$. Both ways are taken from here, but the second way is also described on wikipedia. To do such calculations I have already seen a method using RIF's like the following: Which outputs: But with as one can see the center result is $32$ ($\frac{16+48}{2}$) instead of $30$ ($10*3$). Also I think it is a bit complex, because one has to calculate the upper an lower limits before, instead of a simple thing like: (And as last point, I think result with the question mark is not very nice) If one of my calculations is wrong please let me know, because I am new to error calculations. |