From 46c42b62ff6eddbc8532c52601dcaeab888a0daf Mon Sep 17 00:00:00 2001
From: Sia Ghelichkhan <mail@sia.earth>
Date: Fri, 29 Apr 2022 09:31:39 +1000
Subject: [PATCH] Adjusting the text

---
 07-GD-2D-cylindrical.ipynb | 10 ++++------
 1 file changed, 4 insertions(+), 6 deletions(-)

diff --git a/07-GD-2D-cylindrical.ipynb b/07-GD-2D-cylindrical.ipynb
index acece24..32092e4 100644
--- a/07-GD-2D-cylindrical.ipynb
+++ b/07-GD-2D-cylindrical.ipynb
@@ -48,7 +48,7 @@
     "  + \\int_\\Omega \\left(\\nabla q\\right) \\cdot \\left(\\kappa \\nabla T\\right) \\ dx = 0   \\text{ for all } q\\in Q.$$\n",
     "\n",
     "\n",
-    "In the Cartesian examples considered below, zero-slip and free-slip boundary conditions for \\eqref{eq:weak_mom} and \\eqref{eq:weak_cont} are imposed through strong Dirichlet boundary conditions for velocity $\\vec{u}$. This is achieved by restricting the velocity function space $V$ to a subspace $V_0$\n",
+    "In the Cartesian examples we saw earlier are imposed through strong Dirichlet boundary conditions for velocity $\\vec{u}$. This is achieved by restricting the velocity function space $V$ to a subspace $V_0$\n",
     "of vector functions for which all components (zero-slip) or only the normal\n",
     "component (free-slip) are zero at the boundary. Since this restriction also\n",
     "applies to the test functions $\\vec{v}$, the weak form only needs to be\n",
@@ -57,13 +57,11 @@
     "  -\\int_{\\partial\\Omega} \\vec{v}\\cdot \\left(\\mu \\left[\\nabla\\vec{u}\n",
     "    + \\left(\\nabla\\vec{u}\\right)^T\\right]\\right)\\cdot \\vec{n} ds\n",
     "\\end{equation}\n",
-    "that was required to obtain the integrated by parts viscosity term in Equation\n",
-    "\\eqref{eq:weak_mom}, automatically vanishes for zero-slip boundary conditions as\n",
+    "that was required to obtain the integrated by parts viscosity term, automatically vanishes for zero-slip boundary conditions as\n",
     "$\\bf v =0$ at the domain boundary, $\\partial\\Omega$. In the case of a free-slip\n",
     "boundary condition for which the tangential components of $\\vec{v}$ are\n",
-    "non-zero, the boundary term does not vanish, but by omitting that term in\n",
-    "\\eqref{eq:weak_mom} we weakly impose a zero shear stress condition. The boundary\n",
-    "term obtained by integrating the pressure gradient term in \\eqref{eq:cmass} by parts,\n",
+    "non-zero, the boundary term does not vanish, but by omitting that term, we weakly impose a zero shear stress condition. The boundary\n",
+    "term obtained by integrating the pressure gradient term by parts,\n",
     "\\begin{equation}\n",
     "  \\int_{\\partial\\Omega} \\vec{v}\\cdot\\vec{n} p ds ,\n",
     "\\end{equation}\n",