--- trunk/tengDissertation/Introduction.tex	2006/05/26 17:56:36	2778
+++ trunk/tengDissertation/Introduction.tex	2006/05/26 18:25:41	2779
@@ -846,12 +846,11 @@ can obtain
 \]
 Applying Baker-Campbell-Hausdorff formula to Sprang splitting, we
 can obtain
-\begin{eqnarray}
+\begin{eqnarray*}
 \exp (h X/2)\exp (h Y)\exp (h X/2) & = & \exp (h X + h Y + h^2 [X,Y]/4 + h^2 [Y,X]/4 \\
                                    &   & \mbox{} + h^2 [X,X]/8 + h^2 [Y,Y]/8 \\
-                                   &   & \mbox{} + h^3 [Y,[Y,X]]/12 - h^3[X,[X,Y]]/24\\
-                                   &   & \mbox{} + \ldots )
-\end{eqnarrary}
+                                   &   & \mbox{} + h^3 [Y,[Y,X]]/12 - h^3[X,[X,Y]]/24 + \ldots )
+\end{eqnarray*}
 Since \[ [X,Y] + [Y,X] = 0\] and \[ [X,X] = 0\], the dominant local
 error of Spring splitting is proportional to $h^3$. The same
 procedure can be applied to general splitting,  of the form
@@ -859,7 +858,7 @@ Careful choice of coefficient $a_1 ,\ldot , b_m$ will 
 \varphi _{b_m h}^2  \circ \varphi _{a_m h}^1  \circ \varphi _{b_{m -
 1} h}^2  \circ  \ldots  \circ \varphi _{a_1 h}^1 .
 \end{equation}
-Careful choice of coefficient $a_1 ,\ldot , b_m$ will lead to higher
+Careful choice of coefficient $a_1 \ldot b_m$ will lead to higher
 order method. Yoshida proposed an elegant way to compose higher
 order methods based on symmetric splitting. Given a symmetric second
 order base method $ \varphi _h^{(2)} $, a fourth-order symmetric