ApdxPropErrVer1 - Appendix - Propagation of Errors (...

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Appendix - Propagation of Errors ( Calculus Method ) PROPAGATION OF ERRORS When taking measurements in the laboratory, there is an uncertainty associated with each measurement. All of the measurements are then combined in some way to give a final experimental value. Since there is an uncertainty in the individual measurements, there has to be an uncertainty in the final answer. The correct way to find this associated uncertainty of the final answer is through the method of propagation of errors. In this method, which is described below, you will see how to take into account these individual measurement errors and how they are propagated through to the final answer. This technique requires the use and knowledge of partial derivatives. Since you may or may not know how to take partial derivatives, we will teach you the method, but not the theory. The theory will be taught in Calculus III and you do not need to be exposed to it to understand the techniques of taking partial derivatives. The method of taking partial derivatives is very similar to taking the derivative of a function with a single variable. The best way to learn how to do partial derivatives is by example. The important thing to notice here is that when taking the partial derivative of a function of several variables with respect to one of those variables, you treat all of the other variables as constants . This should hopefully become clear in the following example. Example 1 - Let's look at the function f(x,y,z) = 2xy 2 z 3 + {x 3 /z 2 } = 2xy 2 z 3 + x 3 z -2 (14.1) As you can see, the function depends on three variables. This means that there are three partial derivatives that you can take of this function f . The proper way to write the partial derivative of
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ApdxPropErrVer1 - Appendix - Propagation of Errors (...

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