update: auto commit

2026-04-09 22:24:22 -04:00
parent a90b45c122
commit 26fe34b8d1
1 changed files with 1 additions and 0 deletions
@@ -256,6 +256,7 @@
  \end{frame}

  \begin{frame}{Towards first order Z4c}{First order reduction}
+    \subsection{First order reduction: wave equation}
    We can introduce auxiliary variables to reduce a second order PDE system to a first order one. For example, for the wave equation on flat spacetime:
    \begin{equation}
      \Partial{t}^2 {\phi} - \tensor{\delta}{^i^j} \Partial{i} \Partial{j} \phi = 0,