more math

[lectures/latex.git] / posic / thesis / d_tersoff.tex

diff --git a/posic/thesis/d_tersoff.tex b/posic/thesis/d_tersoff.tex
index c4273b23ce6c2956e5a94fd5c4e83453f9e36be8..b031be2f58ecd016152de51b4e26e136c23450aa 100644 (file)
--- a/posic/thesis/d_tersoff.tex
+++ b/posic/thesis/d_tersoff.tex
@@ -38,7 +38,7 @@ For a three body potential, if $V_{ij}$ is not equal to $V_{ji}$, the derivative
 \begin{equation}
 \nabla_{{\bf r}_i} E = \frac{1}{2} \big[ \sum_j ( \nabla_{{\bf r}_i} V_{ij} + \nabla_{{\bf r}_i} V_{ji} ) + \sum_k \sum_j \nabla_{{\bf r}_i} V_{jk} \big] \textrm{ .}
 \end{equation}
-In the following all the necessary derivatives to calculate $\nabla_{{\bf r}_i} E$ are written down.
+In the following, all the necessary derivatives to calculate $\nabla_{{\bf r}_i} E$ are written down.
 
   \section[Derivative of $V_{ij}$ with respect to ${r}_i$]{\boldmath Derivative of $V_{ij}$ with respect to ${\bf r}_i$}