update: auto commit

report.tex

@@ -257,10 +257,14 @@
     \begin{equation}
       \pdvt[2]{\phi} - \pdv[2]{\phi}{x} = 0,
     \end{equation}
-  \end{frame}
+    we can introduce $\pi := \pdvt{\phi}$ and $\psi := \pdv{\phi}{x}$, and rewrite the wave equation as
-
+    \begin{equation}
-  \begin{frame}{Towards first order Z4c}{Example: wave equation}
+      \begin{cases}
-    
+        \pdvt{\phi} = \pi, \\
+        \pdvt{\psi} = \pdv{\pi}{x}, \\
+        \pdvt{\pi} = \pdv{\psi}{x}.
+      \end{cases}
+    \end{equation}
   \end{frame}
 
   \begin{frame}{Existing first order formulations}