diff --git a/lessons/05_Step_4.ipynb b/lessons/05_Step_4.ipynb
index ec8e076f..038cdb65 100644
--- a/lessons/05_Step_4.ipynb
+++ b/lessons/05_Step_4.ipynb
@@ -86,7 +86,7 @@
     "\n",
     "$$u(0) = u(2\\pi)$$\n",
     "\n",
-    "This is called a *periodic* boundary condition. Pay attention! This will cause you a bit of headache if you don't tread carefully."
+    "This is called a *periodic* boundary condition. Pay attention! This will cause you a bit of headache if you don't read carefully."
    ]
   },
   {
diff --git a/lessons/08_Step_6.ipynb b/lessons/08_Step_6.ipynb
index 59559a8b..aaa9e055 100644
--- a/lessons/08_Step_6.ipynb
+++ b/lessons/08_Step_6.ipynb
@@ -69,9 +69,9 @@
    "source": [
     "Rearranging both equations, we solve for $u_{i,j}^{n+1}$ and $v_{i,j}^{n+1}$, respectively.  Note that these equations are also coupled.  \n",
     "\n",
-    "$$u_{i,j}^{n+1} = u_{i,j}^n - u_{i,j} \\frac{\\Delta t}{\\Delta x} (u_{i,j}^n-u_{i-1,j}^n) - v_{i,j}^n \\frac{\\Delta t}{\\Delta y} (u_{i,j}^n-u_{i,j-1}^n)$$\n",
+    "$$u_{i,j}^{n+1} = u_{i,j}^n - u_{i,j}^n \\frac{\\Delta t}{\\Delta x} (u_{i,j}^n-u_{i-1,j}^n) - v_{i,j}^n \\frac{\\Delta t}{\\Delta y} (u_{i,j}^n-u_{i,j-1}^n)$$\n",
     "\n",
-    "$$v_{i,j}^{n+1} = v_{i,j}^n - u_{i,j} \\frac{\\Delta t}{\\Delta x} (v_{i,j}^n-v_{i-1,j}^n) - v_{i,j}^n \\frac{\\Delta t}{\\Delta y} (v_{i,j}^n-v_{i,j-1}^n)$$"
+    "$$v_{i,j}^{n+1} = v_{i,j}^n - u_{i,j}^n \\frac{\\Delta t}{\\Delta x} (v_{i,j}^n-v_{i-1,j}^n) - v_{i,j}^n \\frac{\\Delta t}{\\Delta y} (v_{i,j}^n-v_{i,j-1}^n)$$"
    ]
   },
   {
@@ -160,9 +160,7 @@
   {
    "cell_type": "code",
    "execution_count": 3,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -188,20 +186,18 @@
   {
    "cell_type": "code",
    "execution_count": 4,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "for n in range(nt + 1): ##loop across number of time steps\n",
     "    un = u.copy()\n",
     "    vn = v.copy()\n",
     "    u[1:, 1:] = (un[1:, 1:] - \n",
-    "                 (un[1:, 1:] * c * dt / dx * (un[1:, 1:] - un[1:, :-1])) -\n",
-    "                  vn[1:, 1:] * c * dt / dy * (un[1:, 1:] - un[:-1, 1:]))\n",
+    "                 (un[1:, 1:] * dt / dx * (un[1:, 1:] - un[1:, :-1])) -\n",
+    "                  vn[1:, 1:] * dt / dy * (un[1:, 1:] - un[:-1, 1:]))\n",
     "    v[1:, 1:] = (vn[1:, 1:] -\n",
-    "                 (un[1:, 1:] * c * dt / dx * (vn[1:, 1:] - vn[1:, :-1])) -\n",
-    "                 vn[1:, 1:] * c * dt / dy * (vn[1:, 1:] - vn[:-1, 1:]))\n",
+    "                 (un[1:, 1:] * dt / dx * (vn[1:, 1:] - vn[1:, :-1])) -\n",
+    "                 vn[1:, 1:] *  dt / dy * (vn[1:, 1:] - vn[:-1, 1:]))\n",
     "    \n",
     "    u[0, :] = 1\n",
     "    u[-1, :] = 1\n",
@@ -217,9 +213,7 @@
   {
    "cell_type": "code",
    "execution_count": 5,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -245,9 +239,7 @@
   {
    "cell_type": "code",
    "execution_count": 6,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -286,9 +278,7 @@
   {
    "cell_type": "code",
    "execution_count": 7,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -321,9 +311,7 @@
   {
    "cell_type": "code",
    "execution_count": 8,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -453,9 +441,9 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.5.2"
+   "version": "3.6.4"
   }
  },
  "nbformat": 4,
- "nbformat_minor": 0
+ "nbformat_minor": 1
 }