From 330852afb5a2e29e09d1d01040821f7c6b4f96d8 Mon Sep 17 00:00:00 2001
From: Yingjie Wang <phywyj@gmail.com>
Date: Thu, 9 Apr 2026 16:13:08 -0400
Subject: [PATCH] update: auto commit

---
 report.tex | 1 +
 1 file changed, 1 insertion(+)

diff --git a/report.tex b/report.tex
index cd301a7..a30296f 100644
--- a/report.tex
+++ b/report.tex
@@ -245,6 +245,7 @@
     \begin{equation}
       \pdvt{u^I} + \tensor{A}{^i^I_J} \pdv{u^J}{x^i} = S^I,
     \end{equation}
+    where both $A$ and $S$ can depend on $u^I$ but not their derivatives. For any unit covector $\xi_i$, the \emph{Principal symbol} matrix is defined as $P(\xi) := \tensor{A}{^i^I_J} \xi_i$.
   \end{frame}
 
   \begin{frame}{Existing first order formulations}