diff --git a/lessons/12_Step_9.ipynb b/lessons/12_Step_9.ipynb
index 8855c39b..c752687c 100644
--- a/lessons/12_Step_9.ipynb
+++ b/lessons/12_Step_9.ipynb
@@ -126,9 +126,7 @@
   {
    "cell_type": "code",
    "execution_count": 1,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "import numpy\n",
@@ -140,9 +138,7 @@
   {
    "cell_type": "code",
    "execution_count": 2,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "def plot2D(x, y, p):\n",
@@ -162,7 +158,13 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The function `plot2D` takes three arguments, an x-vector, a y-vector and our p matrix.  Given these three values, it produces a 3D projection plot, sets the plot limits and gives us a nice viewing angle.  "
+    "The function `plot2D` takes three arguments:\n",
+    "\n",
+    "* `x`: 1D array with point locations along an horizontal gridline,\n",
+    "* `y`: 1D array with point locations along a vertical gridline,\n",
+    "* `p`: 2D array containing the numerical solution in the domain.\n",
+    "\n",
+    "Given these three values, it produces a 3D projection plot, sets the plot limits and gives us a nice viewing angle.  "
    ]
   },
   {
@@ -175,9 +177,7 @@
   {
    "cell_type": "code",
    "execution_count": 3,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "def laplace2d(p, y, dx, dy, l1norm_target):\n",
@@ -204,7 +204,13 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "`laplace2d` takes five arguments, the `p` matrix, the `y`-vector, `dx`, `dy` and the value `l1norm_target`.  This last value defines how close the `p` matrix should be in two consecutive iterations before the loop breaks and returns the calculated `p` value.  \n",
+    "`laplace2d` takes five arguments:\n",
+    "\n",
+    "* `p`: 2D array containing the initial solution in the domain,\n",
+    "* `y`: 1D array with point locations along a vertical gridline,\n",
+    "* `dx`: $x$-distance between two gridlines,\n",
+    "* `dy`: $y$-distance between two gridlines,\n",
+    "* `l1norm_target`: value to define convergence; we stop the iterative process (i.e., exit the `while` loop) when the relative difference between two consecutive solutions (in the $L_1$-norm) is lower or equal than `l1norm_target`.\n",
     "\n",
     "Note that when executing the cells above in your own notebook, there will be no output.  You have *defined* the function but you have not yet *called* the function.  It is now available for you to use, the same as `numpy.linspace` or any other function in our namespace.  "
    ]
@@ -212,9 +218,7 @@
   {
    "cell_type": "code",
    "execution_count": 4,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "##variable declarations\n",
@@ -250,9 +254,7 @@
   {
    "cell_type": "code",
    "execution_count": 5,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -281,9 +283,7 @@
   {
    "cell_type": "code",
    "execution_count": 6,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "p = laplace2d(p, y, dx, dy, 1e-4)"
@@ -299,9 +299,7 @@
   {
    "cell_type": "code",
    "execution_count": 7,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -342,9 +340,7 @@
   {
    "cell_type": "code",
    "execution_count": 8,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -384,9 +380,7 @@
   {
    "cell_type": "code",
    "execution_count": 9,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -419,9 +413,7 @@
   {
    "cell_type": "code",
    "execution_count": 10,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -551,9 +543,9 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.5.2"
+   "version": "3.6.10"
   }
  },
  "nbformat": 4,
- "nbformat_minor": 0
+ "nbformat_minor": 1
 }