From ad7dcd1ee92087d55c503e02c9a031ae87fd3c5a Mon Sep 17 00:00:00 2001
From: Jannis Portmann <jannisp@student.ethz.ch>
Date: Thu, 2 Feb 2023 18:13:28 +0100
Subject: [PATCH] First formulas

---
 main.tex | 18 +++++++++++++++++-
 1 file changed, 17 insertions(+), 1 deletion(-)

diff --git a/main.tex b/main.tex
index c41fb1e..f2ebbef 100644
--- a/main.tex
+++ b/main.tex
@@ -144,7 +144,23 @@
 \rule{\linewidth}{0.25pt}
 \end{center}
 
-\section{First}
+\section{Equations}
+\subsection{Navier-Stokes}
+\begin{equation}
+    \frac{D}{Dt}
+\end{equation}
+
+\subsection{Circulation}
+\begin{equation}
+    C = \oint_c u \, dc = \oint (u \, dx + v \, dy + w \, dz)
+\end{equation}
+
+\section{Concepts}
+\subsection{Thermal wind}
+\textit{Thermal wind} describes the vertical change of geostrophic (i.e. horizontal) wind
+\begin{equation}
+    \frac{\partial}{\partial z} v_G = \bigg(\frac{1}{f}\frac{g}{\theta_0}\bigg)(k \times \nabla_h \theta^*)
+\end{equation}
 
 \scriptsize