From: W. Trevor King <wking@tremily.us>
Date: Sun, 5 May 2013 18:42:00 +0000 (-0400)
Subject: calibcant/discussion.tex: POE is approximate (first order Taylor)
X-Git-Tag: v1.0~262
X-Git-Url: http://git.tremily.us/?a=commitdiff_plain;h=10dd56b61196dcf7e8890b326ce8520a69136b39;p=thesis.git

calibcant/discussion.tex: POE is approximate (first order Taylor)
---

diff --git a/src/calibcant/discussion.tex b/src/calibcant/discussion.tex
index 62d60b3..8b0f9e2 100644
--- a/src/calibcant/discussion.tex
+++ b/src/calibcant/discussion.tex
@@ -95,17 +95,17 @@ standard deviation of $\kappa$ from the standard deviation of the
 measured parameters\citep{ku66}.
 
 \begin{align}
-  \sigma_\kappa &= \sqrt{
+  \sigma_\kappa &\approx \sqrt{
       \p({\deriv{\sigma_p}{\kappa}})^2 \sigma_{\sigma_p}^2 +
       \p({\deriv{T}{\kappa}})^2 \sigma_{T}^2 +
       \p({\deriv{\avg{V_p(t)^2}}{\kappa}})^2 \sigma_{\avg{V_p(t)^2}}^2
       } \\
-    &= \sqrt{
+    &\approx \sqrt{
       \frac{4\kappa^2}{\sigma_p^2} \sigma_{\sigma_p}^2 +
       \frac{\kappa^2}{T^2} \sigma_{T}^2 +
       \frac{\kappa^2}{\avg{V_p(t)^2}} \sigma_{\avg{V_p(t)^2}}^2
       } \\
-  \frac{\sigma_\kappa}{\kappa} &= \sqrt{
+  \frac{\sigma_\kappa}{\kappa} &\approx \sqrt{
       4\p({\frac{\sigma_{\sigma_p}}{\sigma_p}})^2 +
       \p({\frac{\sigma_{T}}{T}})^2 +
       \p({\frac{\sigma_{\avg{V_p(t)^2}}^2}{\avg{V_p(t)^2}}^2})