this is for holding javascript data
Brian Jackson edited These_details_allow_us_to__.tex
over 8 years ago
Commit id: 2cd4a61d1d79ee9e6a1660bf5bbe465c2f350eca
deletions | additions
diff --git a/These_details_allow_us_to__.tex b/These_details_allow_us_to__.tex
index ab3035c..f9f3e54 100644
--- a/These_details_allow_us_to__.tex
+++ b/These_details_allow_us_to__.tex
...
where we have suppressed the integrand for simplicity. We can then differentiate both sides with respect to $b = \left( \Gamma_{\rm obs}/2\right) \left[ \left( P_{\rm obs} - P_{\rm min} \right)/P_{\rm min} \right]^{1/2}$, but, for the left-hand side, we will convert the $b$-derivative into a $P_{\rm obs}$-derivative:
\begin{equation}
\label{eqn:b_derivative_into_P_obs_derivative}
db = \frac{1}{2}
\left( \dfrac{\Gamma_{\rm obs}}{2} \right) b \left( \dfrac{P_{\rm obs} - P_{\rm min}}{P_{\rm min}}
\right)^{-1/2} \right)^{-1} \dfrac{dP_{\rm obs}}{P_{\rm obs}}.
\end{equation}