diff --git a/lab/Second order sections in matrix form.ipynb b/lab/Second order sections in matrix form.ipynb
index b8a45fe..a619a0d 100644
--- a/lab/Second order sections in matrix form.ipynb	
+++ b/lab/Second order sections in matrix form.ipynb	
@@ -42,16 +42,18 @@
       "the output, and a scalar for the zero-delay contribution of the input to the output. For mathematical convenience, we group\n",
       "the last two into a single 3-vector. Thus, a filter is described as the tuple $(\\mathbf{A}, B, C)$, and each step is as follows:\n",
       "\n",
+      "$$\n",
       "\\begin{align}\n",
       "    out_n & = C \\cdot concat([[x_n], y_n]) \\\\\n",
-      "    y_{n+1} & = B \\cdot x_n + \\mathbf{A} \\cdot y_n\n",
+      "    y_{n+1} & = B \\cdot x_n + \\mathbf{A} \\cdot y_n \\\\\n",
       "\\end{align}\n",
+      "$$\n",
       "\n",
       "Where the $\\cdot$ notation represents dot product, vector times scalar, or matrix times vector multiplication, respectively.\n",
       "\n",
       "Question: would it be more convenient to have a single 3x3 matrix?\n",
       "\n",
-      "There is some redundancy in this representation. Obviously, multiplying A and B times some scalar, and dividing C by the same,\n",
+      "There is some redundancy in this representation. Obviously, multiplying B times some scalar, and dividing C by the same,\n",
       "is a filter with the same results. More subtly, the y vector can be transformed by any non-degenerate linear transformation.\n",
       "However, these transforms do matter when the filter parameters are modulated, which is especially common in synthesizers, and\n",
       "also matter for roundoff behavior (particularly important when evaluating the filters using 32 bit floating point arithmetic).\n",
@@ -85,7 +87,7 @@
       "y vector represents the two state variables in transposed direct form II. For review, the transfer function of this\n",
       "filter is:\n",
       "\n",
-      "\\begin{equation} H(z) = \\frac{b_0 + b_1 z^{-1} + b_2 z^{-2}}{1  + a_1 z^{-1} + a_2 z^{-2}} \\end{equation}"
+      "$$ H(z) = \\frac{b_0 + b_1 z^{-1} + b_2 z^{-2}}{1  + a_1 z^{-1} + a_2 z^{-2}} $$"
      ]
     },
     {
@@ -208,7 +210,7 @@
      "source": [
       "Simper prefers a resonance control that ranges from 0 to 1. If you prefer the classic Q, just use this conversion:\n",
       "\n",
-      "\\begin{equation} res = 1 - .5/Q \\end{equation}\n",
+      "$$ res = 1 - .5/Q $$\n",
       "\n",
       "Let's test the filter out:"
      ]