this is for holding javascript data
Brian Jackson edited These_details_allow_us_to__.tex
over 8 years ago
Commit id: 2e4c21137dcf915adc3bf952816f5025ee6bc39a
deletions | additions
diff --git a/These_details_allow_us_to__.tex b/These_details_allow_us_to__.tex
index 81422b3..8d9dbfe 100644
--- a/These_details_allow_us_to__.tex
+++ b/These_details_allow_us_to__.tex
...
\begin{eqnarray}
\label{eqn:difference_between_observed_density_points}
\rho(\Gamma_{\rm obs}, P_{\rm obs}) - \rho(\Gamma_0, P_{\rm min}) &=& &\int_{(\Gamma_{\rm obs}, P_{\rm obs})}^{(\Gamma_1, P_{\rm max})} \cdots db^\prime& - \int_{(\Gamma_0, P_{\rm min})}^{(\Gamma_1, P_{\rm max})} \cdots db^\prime \\ &=& &\int_{(\Gamma_0, P_{\rm min})}^{(\Gamma_{\rm obs}, P_{\rm obs})} \cdots
db^\prime&, db^\prime& = &\int_{b^\prime = 0}^{b} \cdots db^\prime& ,
\end{eqnarray}
where we have suppressed the integrand for simplicity. We can then differentiate both sides with respect to $b$