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6 changes: 3 additions & 3 deletions chapter2/helmholtz.md
Original file line number Diff line number Diff line change
Expand Up @@ -88,8 +88,8 @@ The last term can be written using the Neumann and Robin BCs, that is:
$$
\begin{align}
\int_{\partial \Omega} \frac{\partial p}{\partial n} \bar v ~\mathrm{d}s =
-\int_{\partial \Omega_v} j \omega \rho_0 \bar v ~\mathrm{d}s
- \int_{\partial \Omega_Z} \frac{j \omega \rho_0 \bar{v}_n}{\bar{Z}} p \bar v ~\mathrm{d}s.
-\int_{\partial \Omega_v} j \omega \rho_0 \bar{v}_n \bar v ~\mathrm{d}s
- \int_{\partial \Omega_Z} \frac{j \omega \rho_0}{\bar{Z}} p \bar v ~\mathrm{d}s.
\end{align}
$$

Expand All @@ -111,7 +111,7 @@ We define the sesquilinear form $a(p,v)$ is
$$
\begin{align}
a(p,v) = \int_{\Omega} \nabla p \cdot \nabla \bar v ~\mathrm{d}x
+ \frac{j \omega }{\bar{Z}} \int_{\partial \Omega_Z} \rho_0 p \bar v ~\mathrm{d}s,
+ \frac{j \omega }{\bar{Z}} \int_{\partial \Omega_Z} \rho_0 p \bar v ~\mathrm{d}s
- k^2 \int_{\Omega} p \bar v ~\mathrm{d}x
\end{align}
$$
Expand Down