ActivityGuide_Appendices

ActivityGuide_Append - Appendix A Propagation of Errors This document is a compilation of the formulae we use in this laboratory course for

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
2003 University of Arkansas Department of Physics. Supported in part by a grant from the National Science Foundation 1 Appendix A: Propagation of Errors This document is a compilation of the formulae we use in this laboratory course for propagating errors. It begins with first-order techniques and moves toward the more sophisticated and general. Don‟t panic. I do not expect you to know how to do all of the calculus you see in equations 5 and 6. This is so you can see where the relationships come from, but we will continue to use the values we “guesstimate” from our measuring devices instead. I. First-Order Formulae When a quantity q is calculated from experimentally determined quantities x, …, z, u, …, w, where each of these have uncertainties x, …, z, u, …, w associated with them, then to first order we may use the following formulae for determining q. Adding and Subtracting: If   w u z x q , then w u z x q . Eq. (1) Products and Quotients: If w u z x q , then w w u u z z x x q q . Eq. (2) Multiplying by a constant: If x C q , where C is a constant such as 2, 4/3, , etc., then x C q . Eq. (3) Raising a variable to a power, n: If n x q , then x x n q q . Eq. (4) All of the above first-order approximations to the propagated uncertainties can be derived from two general first-order formulae. For functions of one variable, q = q(x): x dx dq q , Eq. (5) and for functions of many variables, q = q(x, …, z): z z q x x q q , Eq. (6) where partial derivatives are used here. For students who are not yet familiar with partial differentiation, it is easy once you know how to take the ordinary derivative of a function of one variable. Suppose we have a function, q = q(w, x, …, z), of several variables w, x, …, z and we want to calculate its partial derivative with respect to
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2003 University of Arkansas Department of Physics. Supported in part by a grant from the National Science Foundation 2 one of its variables, say x. To do this, we pretend that all variables other than x are just constants and we take the ordinary derivative of q with respect to x. In other words, think of q as being a function of x only [q = q(x)], which it would be if all other variables were constant. When taking the partial derivative of q with respect to another variable, say w, do the same thing but now let all variables except w be constant and think of q as a function of w only: q = q(w). II.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 06/04/2009 for the course PHYS 2054 taught by Professor Stewart during the Spring '08 term at Arkansas.

Page1 / 4

ActivityGuide_Append - Appendix A Propagation of Errors This document is a compilation of the formulae we use in this laboratory course for

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online