From b3c8ff2a0b355ab7e66ccadc7fcc85ea0d429cc6 Mon Sep 17 00:00:00 2001
From: sibagherian <si.bagherian@gmail.com>
Date: Sun, 15 Dec 2019 20:05:58 +0330
Subject: [PATCH 1/2] Correction on pressure equation typo, Step_11 and Step_12

---
 lessons/14_Step_11.ipynb | 22 ++++++++++++++++------
 lessons/15_Step_12.ipynb |  6 +++---
 2 files changed, 19 insertions(+), 9 deletions(-)

diff --git a/lessons/14_Step_11.ipynb b/lessons/14_Step_11.ipynb
index 81ce5f30..a74d409a 100644
--- a/lessons/14_Step_11.ipynb
+++ b/lessons/14_Step_11.ipynb
@@ -63,7 +63,8 @@
     "\n",
     "$$\\frac{\\partial v}{\\partial t}+u\\frac{\\partial v}{\\partial x}+v\\frac{\\partial v}{\\partial y} = -\\frac{1}{\\rho}\\frac{\\partial p}{\\partial y}+\\nu\\left(\\frac{\\partial^2 v}{\\partial x^2}+\\frac{\\partial^2 v}{\\partial y^2}\\right) $$\n",
     "\n",
-    "$$\\frac{\\partial^2 p}{\\partial x^2}+\\frac{\\partial^2 p}{\\partial y^2} = -\\rho\\left(\\frac{\\partial u}{\\partial x}\\frac{\\partial u}{\\partial x}+2\\frac{\\partial u}{\\partial y}\\frac{\\partial v}{\\partial x}+\\frac{\\partial v}{\\partial y}\\frac{\\partial v}{\\partial y} \\right)$$"
+    "$$\\frac{\\partial^2 p}{\\partial x^2}+\\frac{\\partial^2 p}{\\partial y^2} = \\rho\\left(\\frac{\\partial }{\\partial t} \\left( \\frac{\\partial u}{\\partial x}+\\frac{\\partial v}{\\partial y} \\right)-\\frac{\\partial u}{\\partial x}\\frac{\\partial u}{\\partial x}-2\\frac{\\partial u}{\\partial y}\\frac{\\partial v}{\\partial x}-\\frac{\\partial v}{\\partial y}\\frac{\\partial v}{\\partial y} \\right)\n",
+    "$$"
    ]
   },
   {
@@ -216,7 +217,10 @@
    "cell_type": "code",
    "execution_count": 1,
    "metadata": {
-    "collapsed": true
+    "collapsed": true,
+    "jupyter": {
+     "outputs_hidden": true
+    }
    },
    "outputs": [],
    "source": [
@@ -383,7 +387,10 @@
    "cell_type": "code",
    "execution_count": 6,
    "metadata": {
-    "collapsed": true
+    "collapsed": true,
+    "jupyter": {
+     "outputs_hidden": true
+    }
    },
    "outputs": [],
    "source": [
@@ -435,7 +442,10 @@
    "cell_type": "code",
    "execution_count": 8,
    "metadata": {
-    "collapsed": true
+    "collapsed": true,
+    "jupyter": {
+     "outputs_hidden": true
+    }
    },
    "outputs": [],
    "source": [
@@ -660,9 +670,9 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.5"
+   "version": "3.7.4"
   }
  },
  "nbformat": 4,
- "nbformat_minor": 2
+ "nbformat_minor": 4
 }
diff --git a/lessons/15_Step_12.ipynb b/lessons/15_Step_12.ipynb
index 30d1a927..b45deb59 100644
--- a/lessons/15_Step_12.ipynb
+++ b/lessons/15_Step_12.ipynb
@@ -54,7 +54,7 @@
     "\n",
     "$$\\frac{\\partial v}{\\partial t}+u\\frac{\\partial v}{\\partial x}+v\\frac{\\partial v}{\\partial y}=-\\frac{1}{\\rho}\\frac{\\partial p}{\\partial y}+\\nu\\left(\\frac{\\partial^2 v}{\\partial x^2}+\\frac{\\partial^2 v}{\\partial y^2}\\right)$$\n",
     "\n",
-    "$$\\frac{\\partial^2 p}{\\partial x^2}+\\frac{\\partial^2 p}{\\partial y^2}=-\\rho\\left(\\frac{\\partial u}{\\partial x}\\frac{\\partial u}{\\partial x}+2\\frac{\\partial u}{\\partial y}\\frac{\\partial v}{\\partial x}+\\frac{\\partial v}{\\partial y}\\frac{\\partial v}{\\partial y}\\right)\n",
+    "$$\\frac{\\partial^2 p}{\\partial x^2}+\\frac{\\partial^2 p}{\\partial y^2} = \\rho\\left(\\frac{\\partial }{\\partial t} \\left( \\frac{\\partial u}{\\partial x}+\\frac{\\partial v}{\\partial y} \\right)-\\frac{\\partial u}{\\partial x}\\frac{\\partial u}{\\partial x}-2\\frac{\\partial u}{\\partial y}\\frac{\\partial v}{\\partial x}-\\frac{\\partial v}{\\partial y}\\frac{\\partial v}{\\partial y} \\right)\n",
     "$$"
    ]
   },
@@ -669,9 +669,9 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.4"
+   "version": "3.7.4"
   }
  },
  "nbformat": 4,
- "nbformat_minor": 1
+ "nbformat_minor": 4
 }

From df8297ad8ff61c75345273a137dc234071645538 Mon Sep 17 00:00:00 2001
From: sibagherian <43025796+sibagherian@users.noreply.github.com>
Date: Sun, 15 Dec 2019 20:58:24 +0330
Subject: [PATCH 2/2] Update 14_Step_11.ipynb

Correction on pressure equation
---
 lessons/14_Step_11.ipynb | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/lessons/14_Step_11.ipynb b/lessons/14_Step_11.ipynb
index 81ce5f30..0296f4c9 100644
--- a/lessons/14_Step_11.ipynb
+++ b/lessons/14_Step_11.ipynb
@@ -63,7 +63,9 @@
     "\n",
     "$$\\frac{\\partial v}{\\partial t}+u\\frac{\\partial v}{\\partial x}+v\\frac{\\partial v}{\\partial y} = -\\frac{1}{\\rho}\\frac{\\partial p}{\\partial y}+\\nu\\left(\\frac{\\partial^2 v}{\\partial x^2}+\\frac{\\partial^2 v}{\\partial y^2}\\right) $$\n",
     "\n",
-    "$$\\frac{\\partial^2 p}{\\partial x^2}+\\frac{\\partial^2 p}{\\partial y^2} = -\\rho\\left(\\frac{\\partial u}{\\partial x}\\frac{\\partial u}{\\partial x}+2\\frac{\\partial u}{\\partial y}\\frac{\\partial v}{\\partial x}+\\frac{\\partial v}{\\partial y}\\frac{\\partial v}{\\partial y} \\right)$$"
+    
+    "$$\\frac{\\partial^2 p}{\\partial x^2}+\\frac{\\partial^2 p}{\\partial y^2} = \\rho\\left(\\frac{\\partial }{\\partial t} \\left( \\frac{\\partial u}{\\partial x}+\\frac{\\partial v}{\\partial y} \\right)-\\frac{\\partial u}{\\partial x}\\frac{\\partial u}{\\partial x}-2\\frac{\\partial u}{\\partial y}\\frac{\\partial v}{\\partial x}-\\frac{\\partial v}{\\partial y}\\frac{\\partial v}{\\partial y} \\right)\n",
+    "$$"
    ]
   },
   {