Merge pull request #16 from albertobottopoala/minorcorrections

Minor corrections

Author: zingale

advection/advection-higherorder.tex

@@ -355,7 +355,7 @@ \subsection{Limiting}
 
 \begin{exercise}[Limiting and reduction in order-of-accuracy]
 {Show analytically that if you fully limit the slopes
-  (i.e.\ set $\partial a/\partial x |_i = 0$, that the second-order
+	(i.e.\ set $\partial a/\partial x |_i = 0$),then the second-order
   method reduces to precisely our first-order finite-difference discretization,
   Eq.~\ref{eq:fo}.  }
 \end{exercise}
@@ -425,9 +425,9 @@ \subsection{Reconstruct-evolve-average}
  &=& a_{i} - \frac{1}{2} \Delta a_{i} \cfl
 \end{eqnarray}
 
-The final part of the R-E-A procedure is to average the over the 
+The final part of the R-E-A procedure is to average over the 
 advected profiles in the new cell.  The weighted average of the
-amount brought in from the left of the interface and that that remains
+amount brought in from the left of the interface and that remains
 in the cell is
 \begin{align}
 a_i^{n+1} &= \cfl \mathcal{I}_< + (1 - \cfl) \mathcal{I}_>  \\
@@ -896,7 +896,7 @@ \subsection{Timestep limiter for multi-dimensions}
 Eq.~\ref{eq:adv:timestep:multid}.
 
 For the CTU method described above, \cite{colella:1990} argues that
-the inclusion of the transverse information removes some of the some
+the inclusion of the transverse information removes some
 of the instability inherent in simpler schemes, allowing for a larger
 timestep, restricted by Eq.~\ref{eq:adv:timestep:multid}.