Fix integrals in notebook (#179)

Author: jorgensd

chapter1/nitsche.ipynb

@@ -64,19 +64,19 @@
     "As opposed to the first tutorial, we now have to have another look at the variational form.\n",
     "We start by integrating the problem by parts, to obtain\n",
     "\\begin{align}\n",
-    "\\int*{\\Omega} \\nabla u \\cdot \\nabla v~\\mathrm{d}x - \\int*{\\partial\\Omega}\\nabla u \\cdot n v~\\mathrm{d}s = \\int*{\\Omega} f v~\\mathrm{d}x.\n",
+    "\\int_{\\Omega} \\nabla u \\cdot \\nabla v~\\mathrm{d}x - \\int_{\\partial\\Omega}\\nabla u \\cdot n v~\\mathrm{d}s = \\int_{\\Omega} f v~\\mathrm{d}x.\n",
     "\\end{align}\n",
     "As we are not using strong enforcement, we do not set the trace of the test function to $0$ on the outer boundary.\n",
     "Instead, we add the following two terms to the variational formulation\n",
     "\\begin{align}\n",
-    "-\\int*{\\partial\\Omega} \\nabla v \\cdot n (u-u*D)~\\mathrm{d}s + \\frac{\\alpha}{h} \\int*{\\partial\\Omega} (u-u*D)v~\\mathrm{d}s.\n",
+    "-\\int_{\\partial\\Omega} \\nabla v \\cdot n (u-u*D)~\\mathrm{d}s + \\frac{\\alpha}{h} \\int_{\\partial\\Omega} (u-u*D)v~\\mathrm{d}s.\n",
     "\\end{align}\n",
     "where the first term enforces symmetry to the bilinear form, while the latter term enforces coercivity.\n",
     "$u_D$ is the known Dirichlet condition, and $h$ is the diameter of the circumscribed sphere of the mesh element.\n",
     "We create bilinear and linear form, $a$ and $L$\n",
     "\\begin{align}\n",
-    "a(u, v) &= \\int*{\\Omega} \\nabla u \\cdot \\nabla v~\\mathrm{d}x + \\int*{\\partial\\Omega}-(n \\cdot\\nabla u) v - (n \\cdot \\nabla v) u + \\frac{\\alpha}{h} uv~\\mathrm{d}s,\\\\\n",
-    "L(v) &= \\int*{\\Omega} fv~\\mathrm{d}x + \\int\\_{\\partial\\Omega} -(n \\cdot \\nabla v) u_D + \\frac{\\alpha}{h} u_Dv~\\mathrm{d}s\n",
+    "a(u, v) &= \\int_{\\Omega} \\nabla u \\cdot \\nabla v~\\mathrm{d}x + \\int_{\\partial\\Omega}-(n \\cdot\\nabla u) v - (n \\cdot \\nabla v) u + \\frac{\\alpha}{h} uv~\\mathrm{d}s,\\\\\n",
+    "L(v) &= \\int_{\\Omega} fv~\\mathrm{d}x + \\int\\_{\\partial\\Omega} -(n \\cdot \\nabla v) u_D + \\frac{\\alpha}{h} u_Dv~\\mathrm{d}s\n",
     "\\end{align}\n"
    ]
   },