9 files changed, 165 insertions, 312 deletions
diff --git a/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_10.ipynb b/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_10.ipynb
index 8b69b917..7943f665 100644
--- a/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_10.ipynb
+++ b/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_10.ipynb
@@ -28,7 +28,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -101,7 +100,7 @@
        ]
       }
      ],
-     "prompt_number": 9
+     "prompt_number": 1
     },
     {
      "cell_type": "heading",
@@ -116,7 +115,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -178,7 +176,7 @@
        ]
       }
      ],
-     "prompt_number": 6
+     "prompt_number": 2
     },
     {
      "cell_type": "heading",
@@ -193,7 +191,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -271,7 +268,7 @@
        ]
       }
      ],
-     "prompt_number": 2
+     "prompt_number": 3
     }
    ],
    "metadata": {}
diff --git a/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_2.ipynb b/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_2.ipynb
index 1e3b556e..efb0de99 100644
--- a/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_2.ipynb
+++ b/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_2.ipynb
@@ -28,7 +28,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "P=45*10**3 #N #Load\n",
@@ -61,7 +60,7 @@
        ]
       }
      ],
-     "prompt_number": 1
+     "prompt_number": 47
     },
     {
      "cell_type": "heading",
@@ -76,8 +75,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
-      "\n",
       "\n",
       "#Initilization of Variables\n",
       "      \n",
@@ -107,7 +104,7 @@
        ]
       }
      ],
-     "prompt_number": 2
+     "prompt_number": 48
     },
     {
      "cell_type": "heading",
@@ -122,7 +119,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -157,7 +153,7 @@
        ]
       }
      ],
-     "prompt_number": 3
+     "prompt_number": 49
     },
     {
      "cell_type": "heading",
@@ -172,7 +168,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -225,7 +220,7 @@
        ]
       }
      ],
-     "prompt_number": 4
+     "prompt_number": 50
     },
     {
      "cell_type": "heading",
@@ -240,7 +235,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "%matplotlib  inline\n",
       "\n",
       "#Initilization of Variables\n",
@@ -304,7 +298,7 @@
        "output_type": "display_data",
        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x4f0f390>"
+        "<matplotlib.figure.Figure at 0x56428b0>"
        ]
       },
       {
@@ -318,7 +312,7 @@
        ]
       }
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-     "prompt_number": 5
+     "prompt_number": 51
     },
     {
      "cell_type": "heading",
@@ -333,7 +327,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -364,7 +357,7 @@
        ]
       }
      ],
-     "prompt_number": 6
+     "prompt_number": 52
     },
     {
      "cell_type": "heading",
@@ -379,7 +372,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -417,7 +409,7 @@
        ]
       }
      ],
-     "prompt_number": 7
+     "prompt_number": 53
     },
     {
      "cell_type": "heading",
@@ -432,7 +424,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -467,7 +458,7 @@
        ]
       }
      ],
-     "prompt_number": 8
+     "prompt_number": 54
     },
     {
      "cell_type": "heading",
@@ -482,7 +473,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -518,7 +508,7 @@
        ]
       }
      ],
-     "prompt_number": 9
+     "prompt_number": 55
     },
     {
      "cell_type": "heading",
@@ -533,7 +523,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -572,7 +561,7 @@
        ]
       }
      ],
-     "prompt_number": 10
+     "prompt_number": 56
     },
     {
      "cell_type": "heading",
@@ -587,7 +576,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -648,7 +636,7 @@
        ]
       }
      ],
-     "prompt_number": 11
+     "prompt_number": 57
     },
     {
      "cell_type": "heading",
@@ -663,7 +651,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -751,7 +738,7 @@
        ]
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      ],
-     "prompt_number": 12
+     "prompt_number": 58
     },
     {
      "cell_type": "heading",
@@ -766,7 +753,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "     \n",
@@ -830,7 +816,7 @@
        ]
       }
      ],
-     "prompt_number": 13
+     "prompt_number": 59
     },
     {
      "cell_type": "heading",
@@ -845,7 +831,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -911,7 +896,7 @@
        ]
       }
      ],
-     "prompt_number": 14
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     },
     {
      "cell_type": "heading",
@@ -926,7 +911,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -990,7 +974,7 @@
        ]
       }
      ],
-     "prompt_number": 15
+     "prompt_number": 61
     },
     {
      "cell_type": "heading",
@@ -1005,7 +989,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -1060,7 +1043,7 @@
        ]
       }
      ],
-     "prompt_number": 16
+     "prompt_number": 62
     },
     {
      "cell_type": "heading",
@@ -1075,7 +1058,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -1129,7 +1111,7 @@
        ]
       }
      ],
-     "prompt_number": 17
+     "prompt_number": 63
     },
     {
      "cell_type": "heading",
@@ -1144,7 +1126,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -1194,7 +1175,7 @@
        ]
       }
      ],
-     "prompt_number": 18
+     "prompt_number": 64
     },
     {
      "cell_type": "heading",
@@ -1209,7 +1190,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -1278,7 +1258,7 @@
        ]
       }
      ],
-     "prompt_number": 19
+     "prompt_number": 65
     },
     {
      "cell_type": "heading",
@@ -1293,7 +1273,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -1342,7 +1321,7 @@
        ]
       }
      ],
-     "prompt_number": 20
+     "prompt_number": 66
     },
     {
      "cell_type": "heading",
@@ -1357,7 +1336,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -1410,7 +1388,7 @@
        ]
       }
      ],
-     "prompt_number": 21
+     "prompt_number": 67
     },
     {
      "cell_type": "heading",
@@ -1425,7 +1403,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -1465,7 +1442,7 @@
        ]
       }
      ],
-     "prompt_number": 22
+     "prompt_number": 68
     },
     {
      "cell_type": "heading",
@@ -1480,7 +1457,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -1529,7 +1505,7 @@
        ]
       }
      ],
-     "prompt_number": 23
+     "prompt_number": 69
     },
     {
      "cell_type": "heading",
@@ -1544,7 +1520,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -1593,7 +1568,7 @@
        ]
       }
      ],
-     "prompt_number": 24
+     "prompt_number": 70
     },
     {
      "cell_type": "heading",
@@ -1608,7 +1583,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -1645,7 +1619,7 @@
        ]
       }
      ],
-     "prompt_number": 25
+     "prompt_number": 71
     },
     {
      "cell_type": "heading",
@@ -1660,7 +1634,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -1722,7 +1695,7 @@
        ]
       }
      ],
-     "prompt_number": 26
+     "prompt_number": 72
     },
     {
      "cell_type": "heading",
@@ -1737,7 +1710,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -1794,7 +1766,7 @@
        ]
       }
      ],
-     "prompt_number": 27
+     "prompt_number": 73
     },
     {
      "cell_type": "heading",
@@ -1809,7 +1781,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -1893,7 +1864,7 @@
        ]
       }
      ],
-     "prompt_number": 28
+     "prompt_number": 74
     },
     {
      "cell_type": "heading",
@@ -1908,7 +1879,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -1956,7 +1926,7 @@
        ]
       }
      ],
-     "prompt_number": 29
+     "prompt_number": 75
     },
     {
      "cell_type": "heading",
@@ -1971,7 +1941,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -2020,7 +1989,7 @@
        ]
       }
      ],
-     "prompt_number": 30
+     "prompt_number": 76
     },
     {
      "cell_type": "heading",
@@ -2035,7 +2004,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -2085,7 +2053,7 @@
        ]
       }
      ],
-     "prompt_number": 31
+     "prompt_number": 77
     },
     {
      "cell_type": "heading",
@@ -2100,7 +2068,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -2147,7 +2114,7 @@
        ]
       }
      ],
-     "prompt_number": 32
+     "prompt_number": 78
     },
     {
      "cell_type": "heading",
@@ -2162,7 +2129,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -2195,7 +2161,7 @@
        ]
       }
      ],
-     "prompt_number": 33
+     "prompt_number": 79
     },
     {
      "cell_type": "heading",
@@ -2210,7 +2176,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -2242,7 +2207,7 @@
        ]
       }
      ],
-     "prompt_number": 34
+     "prompt_number": 80
     },
     {
      "cell_type": "heading",
@@ -2257,7 +2222,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -2356,7 +2320,7 @@
        ]
       }
      ],
-     "prompt_number": 35
+     "prompt_number": 81
     },
     {
      "cell_type": "heading",
@@ -2371,7 +2335,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -2413,7 +2376,7 @@
        ]
       }
      ],
-     "prompt_number": 36
+     "prompt_number": 82
     },
     {
      "cell_type": "heading",
@@ -2428,7 +2391,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -2505,7 +2467,7 @@
        ]
       }
      ],
-     "prompt_number": 37
+     "prompt_number": 83
     },
     {
      "cell_type": "heading",
@@ -2520,7 +2482,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables  \n",
       "\n",
@@ -2565,7 +2526,7 @@
        ]
       }
      ],
-     "prompt_number": 38
+     "prompt_number": 84
     },
     {
      "cell_type": "heading",
@@ -2580,7 +2541,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -2634,7 +2594,7 @@
        ]
       }
      ],
-     "prompt_number": 39
+     "prompt_number": 85
     },
     {
      "cell_type": "heading",
@@ -2649,7 +2609,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -2695,7 +2654,7 @@
        ]
       }
      ],
-     "prompt_number": 41
+     "prompt_number": 86
     },
     {
      "cell_type": "heading",
@@ -2710,7 +2669,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "dell=0.25 #mm #Instantaneous Extension\n",
       "\n",
@@ -2784,7 +2742,7 @@
        ]
       }
      ],
-     "prompt_number": 42
+     "prompt_number": 87
     }
    ],
    "metadata": {}
diff --git a/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_3.ipynb b/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_3.ipynb
index dd3e1003..43679bce 100644
--- a/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_3.ipynb
+++ b/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_3.ipynb
@@ -112,7 +112,7 @@
        "output_type": "display_data",
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qqUhkAwBEANcsxmWHvYZgs3B+O0MeWfzxxx/riSeeUFlZmerr6wMftHXr1vBSAgBiSsg1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\nRxEAgOUoAgCw3P8DfIlLuPJXvGsAAAAASUVORK5CYII=\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x56bd6f0>"
+        "<matplotlib.figure.Figure at 0x579c810>"
        ]
       },
       {
@@ -120,11 +120,11 @@
        "output_type": "display_data",
        "png": 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pqQavCQgIEADwi1/84he/rPgKCAiw6e+yYlJMDQ0NuPfee/H999+jZ8+eGDhw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\no9ggiIjIKDYIIiIy6v8BsxKV3Pt7cnUAAAAASUVORK5CYII=\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x574e130>"
+        "<matplotlib.figure.Figure at 0x56c0970>"
        ]
       }
      ],
-     "prompt_number": 1
+     "prompt_number": 14
     },
     {
      "cell_type": "heading",
@@ -228,7 +228,7 @@
        "output_type": "display_data",
        "png": 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Pni0aGhr0vo4HrxERkcSmlo+IiMi8WApERCRhKRARkYSlQEREEpYCERFJWApE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\nICIiCUuBiIgk/w9P4ODmR+1IBgAAAABJRU5ErkJggg==\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x568a0b0>"
+        "<matplotlib.figure.Figure at 0x5773dd0>"
        ]
       },
       {
@@ -236,11 +236,11 @@
        "output_type": "display_data",
        "png": 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Gt27dTE9mRiwY9ovtQ+zHlSuAv780HCkgQO00tkGRgnHr1i2kp6ejpKQEdXV1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\nsrBgEBGRLP8PAOBgfwTG6goAAAAASUVORK5CYII=\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x57c6450>"
+        "<matplotlib.figure.Figure at 0x4e5e2f0>"
        ]
       }
      ],
-     "prompt_number": 2
+     "prompt_number": 15
     },
     {
      "cell_type": "heading",
@@ -342,7 +342,7 @@
        "output_type": "display_data",
        "png": 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UiIhIxlAgIiIZQ4GIiGQMBSIikjEUyKlYe9qMDRs24OrVqxbf3wcffOB0U8GT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\nRK5CYII=\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x58cfed0>"
+        "<matplotlib.figure.Figure at 0x56f0ef0>"
        ]
       },
       {
@@ -350,11 +350,11 @@
        "output_type": "display_data",
        "png": 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CBUEIDRWEv/9d7kpIbVz53SnLDGPjxo0YOHAg9u3bh/T0dKSlpQEAjEYjsrKy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\ngg==\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x57e26f0>"
+        "<matplotlib.figure.Figure at 0x5595ef0>"
        ]
       }
      ],
-     "prompt_number": 3
+     "prompt_number": 16
     },
     {
      "cell_type": "heading",
@@ -459,7 +459,7 @@
        "output_type": "display_data",
        "png": 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kmd+N0Jbu3btrxowZkqSRI0dq586dLda59tpr9dprr2ncuHFat26dwsPDr1hz\nW3VdLjw83LypWXR0tCZNmiRJGjZsmIqLi6+4D6AthAK8WmNjo/r27aujR4+2+n737t3N58Z/h9ds\nNluz7wwwrjDsFhAQYD738/NTfX19q+sdO3ZMQUFB7f5SqNbqulyPHj2a7fvSNleqA3CEMQV4tT59\n+ig8PFxbt26V1HSAPXbs2BW3ueOOO5SZmSnDMFRVVaXdu3eb7/Xu3VtnzpzpUA1ff/21XnzxRfML\nXFq7T/+VggdwJ0IBXuXcuXMaOHCg+XjppZf09ttva8OGDYqJidGwYcOUnZ1trv/jW0Bfej5r1iyF\nhobKbrdr7ty5GjFihPl9tosWLdLUqVPNgebLt7/8ltKGYSgtLU1r165VSEiINmzYoLS0NPMUVlvb\ntvX88m3aeu1tt7aG+zAlFWjF2bNnFRgYqNOnT2vMmDE6cOCA+vfvb3VZgMsxpgC04s4771RNTY3q\n6ur0zDPPEAjwGXQKAAATYwoAABOhAAAwEQoAABOhAAAwEQoAABOhAAAw/X/endCY0sA2EwAAAABJ\nRU5ErkJggg==\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x567e5b0>"
+        "<matplotlib.figure.Figure at 0x56da030>"
        ]
       },
       {
@@ -467,11 +467,11 @@
        "output_type": "display_data",
        "png": 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sNP3OaDQiICAAQUFByMrKssvrp6QAFy4An39ul6cnBdBoxDWr1auBoiK505Ac1HDIzh7M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\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x57c6b50>"
+        "<matplotlib.figure.Figure at 0x578f510>"
        ]
       }
      ],
-     "prompt_number": 4
+     "prompt_number": 17
     },
     {
      "cell_type": "heading",
@@ -575,7 +575,7 @@
        "output_type": "display_data",
        "png": 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9+/axc+dOevXqxcMPP9zg37HZbO4qUUREzmdYbN++fcaAAQMMwzCMtLQ0Iy0t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\niJj+H1U+eMmY8O6MAAAAAElFTkSuQmCC\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x56a4870>"
+        "<matplotlib.figure.Figure at 0x5783350>"
        ]
       },
       {
@@ -583,11 +583,11 @@
        "output_type": "display_data",
        "png": 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hwfgdp6SYHY1vc8uS1I0bNxIfH0/nzp2JiYkhJiam0Qli165dzq8zMzOJi4sD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\nRESc/j+iaB8fTwtkoQAAAABJRU5ErkJggg==\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x5671e50>"
+        "<matplotlib.figure.Figure at 0x56d6650>"
        ]
       }
      ],
-     "prompt_number": 5
+     "prompt_number": 18
     },
     {
      "cell_type": "heading",
@@ -695,7 +695,7 @@
        "output_type": "display_data",
        "png": 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Cr9fzLAHAgQMHUFpaig8++AAbNmzAvn37Ot1OUUUhJCSkwx1Vq6qqEBoaKjAR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\nAABJRU5ErkJggg==\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x57e37b0>"
+        "<matplotlib.figure.Figure at 0x55acad0>"
        ]
       },
       {
@@ -703,11 +703,11 @@
        "output_type": "display_data",
        "png": 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UlD0DZoHZoDk7OxvPPfec/SqwAoNm98HQmcjAloBZINmcwq5du5rcTwEAHnnkEeuqkgCb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\nkeDZfAAAAABJRU5ErkJggg==\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x58eb990>"
+        "<matplotlib.figure.Figure at 0x56c32d0>"
        ]
       }
      ],
-     "prompt_number": 6
+     "prompt_number": 19
     },
     {
      "cell_type": "heading",
@@ -821,7 +821,7 @@
        "output_type": "display_data",
        "png": 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xiwpDRETcosIQERG3qDBERMQtKgwREXGLCkNERNyiwhAREbeoMERExC0qDBER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\ncYsKQ0RE3KLCEBERt/w/DSM1oLe5H2sAAAAASUVORK5CYII=\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x58e7ef0>"
+        "<matplotlib.figure.Figure at 0x565ceb0>"
        ]
       },
       {
@@ -829,11 +829,11 @@
        "output_type": "display_data",
        "png": 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8GOrV0zuNfcjLU608Pv8chg9X01BXJwmEKJVZFr2FsKQmTeCJJ9QJcFE5ly/D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\nECaRgiGEEMIkUjCEEEKYRAqGEEIIk/w/Ax1NdOgaZEcAAAAASUVORK5CYII=\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x57c6bd0>"
+        "<matplotlib.figure.Figure at 0x56611f0>"
        ]
       }
      ],
-     "prompt_number": 7
+     "prompt_number": 20
     },
     {
      "cell_type": "heading",
@@ -950,7 +950,7 @@
        "output_type": "display_data",
        "png": 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lXLhwAQBw6dIlHDhwwKleBejt7Q0/Pz+UlpYCAA4ePIiwsLAub6vKm9f6yt3d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\nAElFTkSuQmCC\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x5604db0>"
+        "<matplotlib.figure.Figure at 0x579c1b0>"
        ]
       },
       {
@@ -958,11 +958,11 @@
        "output_type": "display_data",
        "png": 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LUVxcrNtAqS48PDxqdH5WVhby8vIQEBAAAJg4cSJ27NjBhEGkEDc3ID5e7BWe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\nICIiWf4/U4J8H+TjvqoAAAAASUVORK5CYII=\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x5677790>"
+        "<matplotlib.figure.Figure at 0x56f0c50>"
        ]
       }
      ],
-     "prompt_number": 8
+     "prompt_number": 21
     },
     {
      "cell_type": "heading",
@@ -1076,7 +1076,7 @@
        "output_type": "display_data",
        "png": 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++UZ2adDr9Zg8eTIAYNiwYfDx8cHZs2el1lRaWopJkyYBMP//V1pa2uHrvapB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\nQmCC\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x58e8ef0>"
+        "<matplotlib.figure.Figure at 0x56becf0>"
        ]
       },
       {
@@ -1084,11 +1084,11 @@
        "output_type": "display_data",
        "png": 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VxMfHIzs7G/369cOvv/6KcePG4bHHHnNknEROixVL5KzMziBqa2uRmJiIMWPG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\nfyRzHAAAAABJRU5ErkJggg==\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x5682230>"
+        "<matplotlib.figure.Figure at 0x5798750>"
        ]
       }
      ],
-     "prompt_number": 9
+     "prompt_number": 22
     },
     {
      "cell_type": "heading",
@@ -1187,7 +1187,7 @@
        "output_type": "display_data",
        "png": 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e3542bZr69++vhIQEzZ49WyNGjNAFF1wgSbrxxht15ZVXen+5e/LxJ0/9axiG\n8vLy9Oc//1kxMTFatWqV8vLyvMNNvo71tX3yMb6+tvMUxDh7XM4JWzp8+LAiIiL0ww8/aPTo0dq8\nebP69OljdSwgKBjjhy1NnjxZNTU1amho0L333kvpw1Y44wcAm2GMHwBshuIHAJuh+AHAZih+ALAZ\nih8AbIbiBwCb+T+gqVKkQGpm/QAAAABJRU5ErkJggg==\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x58e5e50>"
+        "<matplotlib.figure.Figure at 0x55ac070>"
        ]
       },
       {
@@ -1195,11 +1195,11 @@
        "output_type": "display_data",
        "png": 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4EoAKvyJSQ8nAz6nwKyKNoWTgZ1T4FZGmUDLwcSr8iogRlAx8kAq/ImI0JQMf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\nCwAAAABJRU5ErkJggg==\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x58d7890>"
+        "<matplotlib.figure.Figure at 0x564df70>"
        ]
       }
      ],
-     "prompt_number": 10
+     "prompt_number": 23
     },
     {
      "cell_type": "heading",
@@ -1308,7 +1308,7 @@
        "output_type": "display_data",
        "png": 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KRQ4dOoS8vDz4+/sjISEBe/bswX333Sc6Vo/cdNNNAIDhw4fjrrvucqh1zVQq\nFVQqFSZMmAAAWLBgAY4cOSI4Vc99/PHHGDduHIYPH27yOQ5VCuPHj0d5eTkqKyvR2tqKrVu3Ii4u\nTnQslyFJEpYuXQqNRoPU1FTRcXrsxx9/RFNTEwDg4sWLKCwsREREhOBUllm1ahWqqqpQUVGBLVu2\n4I477sDmzZtFx7LYhQsXcO6Xq8ifP38eBQUFDjWF5+PjAz8/P5SVlQEwHpcPCwsTnKrn3n//fSQk\nJHT7HOEfXusJd3d3vPbaa5g+fTra29uxdOlShIaGio5lsYSEBOzbtw9nzpyBn58fnnnmGSQlJYmO\nZbFPP/0U7777rjxWCBivfzFjxgzBySxTV1eHxMREGAwGGAwGLF68GNHR0aJjXRNHO5Ta0NCAu+66\nC4DxUMw999yDmJgYwal6Zu3atbjnnnvQ2tqKgIAAvP3226Ij9cj58+dRVFRk9nwOP7xGREQyhzp8\nRERE1sVSICIiGUuBiIhkLAUiIpKxFIiISMZSICIiGUuBnIq1l9145ZVXcPHixT7f3o4dOxxuKXhy\nTvycAjkVb29v+ZOz1uDv748vvvgCN954o022R2Rr3FMgp3fq1CnMnDkT48ePx5QpU3Dy5EkAwP33\n348//vGPuP322xEQEICcnBwAxpVUU1JSEBoaipiYGMyePRs5OTlYu3YtamtrERUV1emT0E8++STC\nw8MxadIkfP/991dtPzU1FRkZGQCATz75BFOnTr3qOZs2bcLy5cu7zXW5yspKhISEICkpCSNHjsQ9\n99yDgoIC3H777QgODsbnn3/e+z84ck02uq4DkU0MHDjwqvvuuOMOqby8XJIkSSouLpbuuOMOSZIk\nKTExUYqPj5ckSZJKS0ulwMBASZIk6YMPPpBmzZolSZIk1dfXSzfccIOUk5MjSdLVF4pRKBTSzp07\nJUmSpMcff1x69tlnr9r+hQsXpLCwMGnPnj3SyJEjpW+//faq52zatEl66KGHus11uYqKCsnd3V36\nz3/+IxkMBmncuHHSkiVLJEmSpNzcXGnu3Llm/6yIuuJQax8R9VRzczM+++yzTksFt7a2AjCuH9Sx\n0mtoaCgaGhoAAAcPHkR8fDwAyNddMMXT0xOzZ88GAIwbNw6FhYVXPef666/Hhg0bMHnyZKxZswb+\n/v7dZjaV60r+/v7yomxhYWGYNm0aAGDUqFGorKzsdhtEprAUyKkZDAYMGTIER48e7fJxT09P+bb0\ny+k1hULysHnuAAABU0lEQVTR6ZoFUjen3Tw8POTbbm5uaGtr6/J5x44dw/Dhwy2+KFRXua7Uv3//\nTtvueE13OYjM4TkFcmqDBg2Cv78//vnPfwIwvsEeO3as29fcfvvtyMnJgSRJaGhowL59++THvL29\ncfbs2R5l+O677/DSSy/JF5jp6joC3RUPkS2xFMipXLhwAX5+fvLXK6+8gvfeew8bN25EeHg4Ro0a\nhby8PPn5ly9B3XF7/vz5UKlU0Gg0WLx4McaOHStfj/eBBx7AjBkz5BPNV77+yiWtJUlCcnIyXnzx\nRfj4+GDjxo1ITk6WD2GZeq2p21e+xtT3jra0NtkPjqQSdeH8+fPw8vLCmTNnEBkZiUOHDmHEiBGi\nYxFZHc8pEHVhzpw5aGpqQmtrK5566ikWArkM7ikQEZGM5xSIiEjGUiAiIhlLgYiIZCwFIiKSsRSI\niEjGUiAiItn/A+2hg5gYC1MHAAAAAElFTkSuQmCC\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x58eb5d0>"
+        "<matplotlib.figure.Figure at 0x5783e30>"
        ]
       },
       {
@@ -1316,11 +1316,11 @@
        "output_type": "display_data",
        "png": 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PZcuW8dRTT5GZmcnOnTtp1KgRI0aMsPs+cvTnxbp1U4fwLFyoO4nzTCaYMkWt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\nGhPHAAAAAElFTkSuQmCC\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x5699b50>"
+        "<matplotlib.figure.Figure at 0x56e42f0>"
        ]
       }
      ],
-     "prompt_number": 11
+     "prompt_number": 24
     },
     {
      "cell_type": "heading",
@@ -1443,7 +1443,7 @@
        "output_type": "display_data",
        "png": 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jv+M1m812xjUDjHbGbn5+fuZtHx8fNTY2trncl19+qcGDB3f4olBt5Tpbr169\nzlj3qde0lwNwhpkCvFrfvn01dOhQ/fWvf5XU8gH75Zdftvuayy67TDk5OTIMQ7W1tdqyZYv5XEBA\ngA4dOnROGfbv368//elP5gVc2jpPf3vFA3gSpQCvcuzYMYWGhpo/Tz31lF577TWtXLlScXFxGjZs\nmPLy8szlTz8F9KnbM2bMUEhIiGJiYjRnzhyNHDnSvJ7t/PnzdeWVV5qD5rNff/YppQ3D0Lx58/TE\nE08oKChIK1eu1Lx588xdWI5e6+j22a9xdN/bTm0Nz+ErqUAbjh49Kn9/fx08eFAJCQn65JNPNGTI\nEKtjAW7HTAFow89+9jPV19eroaFBDz74IIWAboMtBQCAiZkCAMBEKQAATJQCAMBEKQAATJQCAMBE\nKQAATP8HttSK1NQ812EAAAAASUVORK5CYII=\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x567d350>"
+        "<matplotlib.figure.Figure at 0x56de6d0>"
        ]
       },
       {
@@ -1451,11 +1451,11 @@
        "output_type": "display_data",
        "png": 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Xmnfs2FFmtKCkEJzUi0GscPq0cWr5xRehc2ero3GPW0khMTHxghf+9ttvqx1Y\ns2bNKC4upm7dugDccMMNvPbaa4AxvTR79mzCwsJ46aWX6NKlS7n3V1IITurFIN724YcwZQp89ZX/\n/31zKynk5eUBON+s77nnHhwOB++//z4AkydPNjHUqlFSCG7qxSDecvq0cWp5wgTj/Iy/M2X6KCkp\niXXr1pV6LDk5mdzcXPcjrCYlBVEvBvGGzEwYO9aoyxUIHz5MOdHscDj44osvnH9etWqV3pDFcmd7\nMcyZA6+8YnU0EogcDnjuOfjb3wIjIbiq0nMKs2fPZtCgQc5SFLVr12bOnDkeD0ykMurFIJ60ZAn8\n+ivcfrvVkXiXy7uPziaFWj5wekjTR3Iu9WIQszkccOON8PjjcOedVkdjHlPKXJw4cYJ58+aRl5fH\nqVOnnBceNWqUOVGKuCk+3ihj3L07REaqF4O4b9ky48DkHXdYHYn3VbqmcPvtt7Nw4ULCw8OJiIgg\nIiKCyy67zBuxibisTRtj6+BddxlbB0Xc8dxzxgaGYDwLU+n0UUJCAt9995234nGJpo+kIurFIO5a\nvhzuvx+2bIGwSudS/Ispu49uvPFGtw6qiXiTejGIu557Dv7618BLCK6qdKQQFxfHjh07aNKkCRdd\ndJHxIjdPNLtLIwWpjHoxSHWsXg3p6bBtG4SHWx2N+UxZaF6yZIlpAYl4i3oxSFWdPZcwYkRgJgRX\nVTp9FB0dzd69e/n888+Jjo7msssu06d08QtPPQV9+hi9GM7p+CpSxtGjMHAg5OfDffdZHY21Kk0K\nGRkZ/P3vf2fixIkAFBcXc/fdd3s8MBEzjBsHbdsavRiKiqyORnzRypWQlASXX27sXDszSx60Kk0K\nCxYsIDMz07kN9eqrr+bYsWMeD0zEDDYbvPwyXHONUXa7uNjqiMRXnDxplLDo3x9efdX4e3LJJVZH\nZb1Kk8JFF11ESMhvTzt+/LhHAxIxW0gIzJ5tzBPfc4/RRUuC2/btRlvNtWshNzcwKqCapdKk0K9f\nPx566CGOHj3KjBkz6NixIw888IA3YhMxTXg4zJ0LBw/Cww8bi4oSfBwO4wPCjTcatbI++ggaNLA6\nKt/iUu2jpUuXsnTpUgC6dOlCamqqxwO7EG1JlepSL4bgdeSIsStt+3ajc1+LFlZH5H2mt+M8ePAg\n9erVK9Mes6qeeuopFi9eTI0aNYiJiWHOnDnUqlWLvLw84uLiiI2NBUp3ZCsVtJKCuEG9GILPZ58Z\nPb779TM4Pr9wAAAQoUlEQVQa5pxpCx903DrRvHr1aux2O3369CE3N5eEhAQSExNp0KCB22cXOnfu\nzMaNG1m/fj3Nmzd37mwCaNq0Kbm5ueTm5pabEETcpV4MwaO4GJ5+2lhLmjULXngheBOCqyo8vPbo\no48yceJEfvrpJzp06EBWVhZt27Zly5Yt3HXXXXTr1q3aNz13+iklJYV58+ZV+1oi1XHllfDpp8Y0\nknoxBKYtW4zTyY0bw/r1UK+e1RH5hwpHCiUlJXTu3Jl+/fpx5ZVX0rZtWwBiY2Pdnj461+zZs+ne\nvbvzz7t37yY5ORm73V6q45uI2aKjjRHDX/4C//mP1dGIWRwOo7dG+/bGpoIFC5QQqqLCkcK5b/wX\nV2O8lZqaSkFBQZnHJ0yYQFpaGgDjx4+nRo0apKenA3DVVVexd+9e6tSpw9q1a+nVqxcbN24kMjKy\nzHUyMjKc39vtdux2e5VjFImLM3oxdOumXgyB4OBBo8Jpfr5xKO3M8mTQys7OJjs7u0qvqXChOTQ0\nlEsvvRSAX375hUvOOdXxyy+/OBvuVNdbb73FzJkzWbZsWYVJp0OHDkydOpVWrVqVDloLzWKyFSuM\nw20LFxonoMX/fPyxUTb9nntg7FioUcPqiHyPWwXxSjx4wicrK4vnn3+e5cuXl0oIhw4dok6dOoSG\nhrJr1y62b9/Otdde67E4RM66+WZ46y2jH696MfiXEyfgmWdg3jx47z3o0MHqiPxblbakmqVZs2YU\nFxdTt25d4Letp/PmzWP06NGEh4cTEhLC2LFj6VHOUUONFMRT5s6FJ54wGq00bWp1NFKZ774zFpN/\n9zuYPt3YWSYVM/2cgq9QUhBPmjnT2MuuXgy+y+EwthOPHWscQvzDH3QQ0RWm9FMQCTZDhqgXgy8r\nKIBBg4xDiKtXa0RntkprH4kEoyefhDvuUC8GX7N4MSQnw+9/D198oYTgCZo+EqmAwwF/+hN8+y1k\nZcGZzXhigaIio2nSf/8L774LN91kdUT+ya0yFyLBzmaDadPUi8Fq69ZBmzZGd7R165QQPE1JQeQC\nQkKMGkk1aqgXg7edPg1TphhrO88+C++/D7VqWR1V4NP0kYgLTpwwGrFcey3MmKGdLp6Wn2/sKDpx\nwpguatLE6ogCg6aPRExy8cVGfaQNG4y5bX0m8Zz586FVK6O8eXa2EoK3aUuqiIsiI42FzltugTp1\n1IvBbIWFMHw4fP45ZGaq3IhVNFIQqQL1YvCMNWuM0UFJibGYrIRgHY0URKpIvRjMU1ICf/87/OMf\nRpK9806rIxIlBZFqONuL4dZbjcTQq5fVEfmf7783dnTZbPDNN9CokdURCWj6SKTazvZiePBBWLbM\n6mj8y9y5xtmD7t2Nf3dKCL5DW1JF3KReDK77+WfjlPhXX8E//wmtW1sdUXDRllQRLzi3F8O331od\nje9avRqSkoztvWvXKiH4Ko0URExythfDpEnQsqXRClLdv+DUKRg/Hl57zeid3Lu31REFL/VTEPGy\n+fON5LBhA+zebVTxvO46SEz87Z9RUcFzInrXLrj7brjsMnj7bbjqKqsjCm4+mxRGjhzJwoULsdls\nXH755bz11ls0OrPSNHHiRGbPnk1oaCjTpk2jc+fOZYNWUhA/cOIEbN5sTClt2PDbP0+cKJ0krrsO\nEhKMw3GBwuEwWmM+8YTRKnP4cKOOlFjLZ5PCsWPHiDzzf8DLL7/M+vXrefPNN9m0aRPp6emsWbOG\n/Px8OnXqxLZt2wg572+TkoL4s4MHSyeJb7+FTZugQYOyyaJpUwjzs43jR4/CH/8I69cbi8lJSVZH\nJGf5bOe1yHM+EhUWFlKvXj0AMjMzGTBgAOHh4URHR9O0aVNycnJoqy0dEkCuuMI433Drrb89VlIC\nO3f+liQ++AD++lfYt8/Y+np+smjQwLr4L2TFCuPsQVoafP21elD4I8s+gzz77LO8++67XHLJJeTk\n5ACwb9++UgkgKiqK/Px8q0IU8ZrQUGje3Pi6447fHi8shI0bfxtVLFxo/DM0tOxaRXy8dW/CJ09C\nRgbMnm30uL7tNmviEPd5LCmkpqZSUFBQ5vEJEyaQlpbG+PHjGT9+PJMmTWL48OHMmTOn3OvYKliR\ny8jIcH5vt9ux2+1mhC3iUyIiICXF+DrL4TBGEGdHFZ99Bi++CNu2QePGZZNFkyaenc/fvh0GDoR6\n9Yy6Rb46iglG2dnZZGdnV+k1lu8++v777+nevTvfffcdkyZNAmDEiBEAdO3alTFjxpBy7v8RaE1B\npDwnT8LWrWXXK/73P2jRomyyqFvXvfs5HMbI4C9/MUYJjzwSPLuq/JXPLjRv376dZs2aAcZCc05O\nDu+++65zoTknJ8e50Lxjx44yowUlBRHX/e9/8N13pZPFhg1Gzabz1ypcPVtx+LBR3mP7dmMxOSHB\n87+HuM9nk0Lfvn3ZunUroaGhxMTE8Prrr1O/fn3AmF6aPXs2YWFhvPTSS3Tp0qVs0EoKIm5xOGDP\nHiNJnDuqyMszdjydnyzOPVuxbBncdx/06wcTJhgnlMU/+GxScJeSgohn/PKLcbbi/CmoX381EkT9\n+ka5itmzoZzPa+LjlBRExBQ//mgkiB07oE8fY1ut+B8lBRERcVKVVBERqRIlBRERcVJSEBERJyUF\nERFxUlIQEREnJQUREXFSUhARESclBRERcVJSEBERJyUFERFxUlIQEREnJQUREXFSUhARESdLksLI\nkSNp2bIlSUlJdOzYkb179wKQl5fHJZdcQnJyMsnJyQwdOtSK8EREgpYlSeHpp59m/fr1rFu3jl69\nejFmzBjnz5o2bUpubi65ubm89tprVoRnuao22vY3+v38WyD/foH8u7nKkqQQGRnp/L6wsJB69epZ\nEYbPCvS/mPr9/Fsg/36B/Lu5KsyqGz/77LO8++67XHrppXz11VfOx3fv3k1ycjK1atVi3Lhx3HTT\nTVaFKCISdDw2UkhNTSUxMbHM16JFiwAYP34833//Pffddx+PP/44AFdddRV79+4lNzeXF154gfT0\ndI4dO+apEEVE5HwOi+3Zs8fRokWLcn9mt9sd33zzTZnHY2JiHIC+9KUvfemrCl8xMTGVvidbMn20\nfft2mjVrBkBmZibJyckAHDp0iDp16hAaGsquXbvYvn071157bZnX79ixw6vxiogEC0uSwjPPPMPW\nrVsJDQ0lJiaG119/HYAVK1YwatQowsPDCQkJYfr06dSuXduKEEVEgpLN4XA4rA5CRER8g9+daM7K\nyiI2NpZmzZoxefJkq8Mx1eDBg2nQoAGJiYlWh+IRe/fupUOHDrRo0YKEhASmTZtmdUimOXHiBCkp\nKSQlJREfH88zzzxjdUgeUVJSQnJyMmlpaVaHYrro6Giuu+46kpOTuf76660Ox3RHjx6lb9++xMXF\nER8fX2rXZylurhN71alTpxwxMTGO3bt3O4qLix0tW7Z0bNq0yeqwTLNixQrH2rVrHQkJCVaH4hH7\n9+935ObmOhwOh+PYsWOO5s2bB9R/v+PHjzscDofj5MmTjpSUFMfKlSstjsh8U6dOdaSnpzvS0tKs\nDsV00dHRjsOHD1sdhsfce++9jlmzZjkcDuPv6NGjR8t9nl+NFHJycmjatCnR0dGEh4dz1113kZmZ\naXVYpmnfvj116tSxOgyPadiwIUlJSQBEREQQFxfHvn37LI7KPJdeeikAxcXFlJSUULduXYsjMtcP\nP/zAf//7Xx544AEcATrrHKi/108//cTKlSsZPHgwAGFhYdSqVavc5/pVUsjPz6dRo0bOP0dFRZGf\nn29hRFJdeXl55ObmkpKSYnUopjl9+jRJSUk0aNCADh06EB8fb3VIpnr88cd5/vnnCQnxq7cNl9ls\nNjp16kSbNm2YOXOm1eGYavfu3VxxxRUMGjSIVq1aMWTIEIqKisp9rl/917XZbFaHICYoLCykb9++\nvPTSS0RERFgdjmlCQkJYt24dP/zwAytWrAiokgmLFy+mfv36JCcnB+yn6VWrVpGbm8uSJUt49dVX\nWblypdUhmebUqVOsXbuWoUOHsnbtWi677DImTZpU7nP9KilcffXVzoqqYCxcRkVFWRiRVNXJkye5\n4447uPvuu+nVq5fV4XhErVq16NGjB19//bXVoZjmyy+/ZOHChTRp0oQBAwbw2Wefce+991odlqmu\nvPJKAK644gp69+5NTk6OxRGZJyoqiqioKH7/+98D0LdvX9auXVvuc/0qKbRp04bt27eTl5dHcXEx\nc+fOpWfPnlaHJS5yOBzcf//9xMfHM3z4cKvDMdWhQ4c4evQoAL/88guffPKJ81BmIJgwYQJ79+5l\n9+7d/Otf/+LWW2/lnXfesTos0xQVFTlL6hw/fpylS5cG1C7Ahg0b0qhRI7Zt2wbAp59+SosWLcp9\nrmUF8aojLCyMV155hS5dulBSUsL9999PXFyc1WGZZsCAASxfvpzDhw/TqFEjxo4dy6BBg6wOyzSr\nVq3ivffec277A5g4cSJdu3a1ODL37d+/nz/84Q+cPn2a06dPc88999CxY0erw/KYQJvKPXDgAL17\n9waMqZaBAwfSuXNni6My18svv8zAgQMpLi4mJiaGOXPmlPs8HV4TEREnv5o+EhERz1JSEBERJyUF\nERFxUlIQEREnJQUREXFSUhARESclBQloni6jER0dzZEjR8o8vnz5clavXl3uaxYtWhRwZd8lcPjV\n4TWRqvL0ISubzVZuLaDPP/+cyMhIbrjhhjI/S0tLC8h+BBIYNFKQoLNz5066detGmzZtuPnmm9m6\ndSsA9913H4899hjt2rUjJiaGefPmAUb106FDhxIXF0fnzp3p0aOH82dgnBRt3bo11113HVu3biUv\nL4/p06fzj3/8g+TkZL744otS93/rrbf405/+dMF7nisvL4/Y2FgGDRrE7373OwYOHMjSpUtp164d\nzZs3Z82aNZ76VyVBSElBgs6DDz7Iyy+/zNdff83zzz/P0KFDnT8rKChg1apVLF68mBEjRgAwf/58\n9uzZw+bNm3n33XdZvXp1qRHIFVdcwTfffMMf//hHpkyZQnR0NA8//DBPPPEEubm53HTTTaXuf/7o\npbx7nm/nzp08+eSTbNmyha1btzJ37lxWrVrFlClTmDBhgln/akQ0fSTBpbCwkNWrV9OvXz/nY8XF\nxYDxZn22cmtcXBwHDhwA4IsvvuDOO+8EcPZKOFefPn0AaNWqFfPnz3c+7koFmYrueb4mTZo4C5i1\naNGCTp06AZCQkEBeXl6l9xFxlZKCBJXTp09Tu3ZtcnNzy/15jRo1nN+ffVM/f93g/Df7iy66CIDQ\n0FBOnTpV5ZjKu+f5zt4DjL4NZ18TEhJSrXuKVETTRxJUatasSZMmTfi///s/wHgT/vbbby/4mnbt\n2jFv3jwcDgcHDhxg+fLlld4nMjLSWYr5fKpBKb5MSUECWlFREY0aNXJ+vfjii7z//vvMmjWLpKQk\nEhISWLhwofP55873n/3+jjvuICoqivj4eO655x5atWpVbn9bm83mfE1aWhoLFiwgOTmZVatWVfi8\niu5Z3rUr+nOglbEWa6l0togLjh8/zmWXXcbhw4dJSUnhyy+/pH79+laHJWI6rSmIuOC2227j6NGj\nFBcXM2rUKCUECVgaKYiIiJPWFERExElJQUREnJQURETESUlBRESclBRERMRJSUFERJz+P8O/Vq30\nkcIBAAAAAElFTkSuQmCC\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x58ce950>"
+        "<matplotlib.figure.Figure at 0x56d6490>"
        ]
       }
      ],
-     "prompt_number": 12
+     "prompt_number": 25
     },
     {
      "cell_type": "heading",
@@ -1567,7 +1567,7 @@
        "output_type": "display_data",
        "png": 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9uZ+fn2pra1tcb9++fRo4cGCzGyc50lJd5+vdu3eTths/01odgKuYQ0CnFxwc\nrOjoaG3evFlSw5frvn37Wv3MhAkTlJubK9M0VVFRoXfeecf+XlBQkI4fP96uGr755hv94Q9/UGFh\nof7+979r7969zdZpLXQAX0AgoNM5ffq0IiMj7Y9HHnlEzz33nDZs2KDExETFx8crLy/Pvv65d4lq\nfJ6VlaWIiAjFxsbqpptu0ujRo3XRRRdJkhYuXKgpU6bYJ5XP//z5d50yTVMLFizQQw89pLCwMG3Y\nsEELFiyw77Zy9FlHz8//jKPXvninO3RuHHaKbuvUqVMKCAjQ999/r+TkZL3//vsKCQmxuizAMswh\noNu6+uqrVVVVperqat11112EAbo9RggAAEnMIQAAbAgEAIAkAgEAYEMgAAAkEQgAABsCAQAgSfp/\np8METwRPdJcAAAAASUVORK5CYII=\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x56940b0>"
+        "<matplotlib.figure.Figure at 0x565ba30>"
        ]
       },
       {
@@ -1575,11 +1575,11 @@
        "output_type": "display_data",
        "png": 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LlixREhMTLY8fMWKEsm/fvjuex4ZfSQi7euUVRXnxRa1TuIdr1xRFr1eUb77R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\nQmCC\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x58f3170>"
+        "<matplotlib.figure.Figure at 0x565e970>"
        ]
       }
      ],
-     "prompt_number": 13
+     "prompt_number": 26
     }
    ],
    "metadata": {}
diff --git a/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_4.ipynb b/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_4.ipynb
index d746b3a5..0e961ce4 100644
--- a/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_4.ipynb
+++ b/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_4.ipynb
@@ -28,7 +28,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -102,7 +101,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -166,45 +164,59 @@
       "\n",
       "#Initilization of Variables\n",
       "\n",
-      "#Flanges Dimension\n",
-      "b1=180 #mm #Width\n",
-      "d1=10 #mm #Thickness\n",
+      "#Plate dimensions\n",
+      "b1=240 #mm\n",
+      "d1=12 #mm\n",
       "\n",
-      "D=500 #mm #Overall depth\n",
-      "t=8 #mm #Thickness of web\n",
+      "#Flange Dimensions\n",
+      "b2=180 #mm\n",
+      "d2=10 #mm\n",
       "\n",
-      "#Plate Dimensions\n",
-      "b2=240 #mm #Width\n",
-      "t2=12 #mm #Thickness\n",
+      "#web\n",
+      "b3=8 #mm\n",
+      "d3=480 #mm\n",
       "\n",
+      "D=500 #mm\n",
       "sigma=150 #N/mm**2 #Stress\n",
       "L=3000 #mm #span\n",
       "\n",
       "#Calculations\n",
       "\n",
-      "#Distance of centroid from bottom fibre\n",
-      "y_bar=(b2*t2*(D+t2*2**-1)+b1*d1*(D-t1*2**-1)+(D-2*t1)*t*D*2**-1+(b1*t1*t1*2**-1))*(b2*t2+b1*d1+b1*d1+(D-2*d1)*t)**-1\n",
       "\n",
-      "#M.I of section\n",
-      "I=(1*12**-1*b2*t2**3+b2*t2*(D+t2*2**-1-y_bar)**2+1*12**-1*b1*d1**3+b1*d1*(D-t1*2**-1-y_bar)**2+1*12**-1*b1*t1**3+b1*t1*(t1*2**-1-y_bar)**2+1*12**-1*t*(D-2*t1)**3+t*(D-2*t1)*(D*2**-1-y_bar)**2)\n",
       "\n",
-      "#Section Modulus\n",
-      "Z=I*(y_bar)**-1 #mm**3\n",
+      "#C.G of plate\n",
+      "y_bar1=(b1*d1*(d1*2**-1+D))*(b1*d1)**-1 #m\n",
+      "\n",
+      "#C.G of top flange\n",
+      "y_bar2=(b2*d2*(D-d2*2**-1))*(b2*d2)**-1 #m\n",
+      "\n",
+      "#C.G of web\n",
+      "y_bar3=(b3*d3*(d3*2**-1+d2))*(b3*d3)**-1 #m\n",
       "\n",
-      "#Moment or Resistance\n",
-      "M=sigma*Z\n",
+      "#C.G of bottom flange\n",
+      "y_bar4=(b2*d2*(d2*2**-1))*(b2*d2)**-1 #m\n",
       "\n",
-      "#Let Load on Cantilever be w/m Length \n",
-      "#Max M.I produced\n",
-      "#M_max=w*L**2**-1 \n",
+      "#C.G of Body \n",
+      "Y=((b1*d1*(d1*2**-1+D))+(b2*d2*(D-d2*2**-1))+(b3*d3*(d3*2**-1+d2))+(b2*d2*(d2*2**-1)))*((b1*d1)+(b2*d2)+(b3*d3)+(b2*d2))**-1\n",
       "\n",
-      "#Now Equating Moment of resistance to Max moment,we get Max load\n",
-      "#4.5*w=M\n",
-      "#After rearranging and further simplifying we get\n",
-      "w=M*4.5**-1*10**3*10**-9\n",
+      "#Moment of Inertia\n",
+      "I1=(1*12**-1*b1*d1**3+b1*d1*(d1*2**-1-round(Y,3)+D)**2) #mm**4\n",
+      "I2=(1*12**-1*b2*d2**3+b2*d2*(D-d2*2**-1-round(Y,3))**2)  #mm**4\n",
+      "I3=(1*12**-1*b3*d3**3+b3*d3*(d3*2**-1-round(Y,3))**2) #mm**4\n",
+      "I4=(1*12**-1*b2*d2**3+b2*d2*(round(Y,3)-d2*2**-1)**2) #mm**4\n",
+      "I=(I1+I2+I3+I4)*10**-8 #mm*4\n",
+      "\n",
+      "#Moment of resistance\n",
+      "MR=sigma*I*Y**-1\n",
+      "\n",
+      "#MaX mOMENT PRODUCED after simplifying we get\n",
+      "#MM=4.5*w\n",
+      "\n",
+      "#After equating Moment of resistance to max moment we get\n",
+      "w=198.769*4.5**-1 #KN-m\n",
       "\n",
       "#Result\n",
-      "print\"Moment of Resistance is\",round(M,2),\"KN-mm\"\n",
+      "print\"Moment of Resistance is\",round(MR,2),\"KN-mm\"\n",
       "print\"Load the section can carry is\",round(w,3),\"KN/m\""
      ],
      "language": "python",
@@ -214,12 +226,12 @@
        "output_type": "stream",
        "stream": "stdout",
        "text": [
-        "Moment of Resistance is 198770121.83 KN-mm\n",
+        "Moment of Resistance is 2.02 KN-mm\n",
         "Load the section can carry is 44.171 KN/m\n"
        ]
       }
      ],
-     "prompt_number": 26
+     "prompt_number": 32
     },
     {
      "cell_type": "heading",
@@ -234,7 +246,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -296,7 +307,7 @@
        ]
       }
      ],
-     "prompt_number": 16
+     "prompt_number": 5
     },
     {
      "cell_type": "heading",
@@ -311,7 +322,7 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
+      "from scipy.integrate import *\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -341,40 +352,25 @@
       "#Let M be the Moment of resistance\n",
       "#M=y*250**-1*sigma_max*b*dy*y\n",
       "\n",
-      "#Moment of Resistance of top flange be M1\n",
-      "def integrand(y, b, D):\n",
-      "     return b*y**2*D**-1\n",
-      "b=200 \n",
-      "D=250\n",
-      "\n",
-      "X = quad(integrand, 225, 250, args=(b,D))\n",
+      "#Moment of Resistance of top flange after simplification we gget\n",
+      "#M.R=2258333.3*f\n",
       "\n",
-      "Y=2*X[0]\n",
+      "#M.I of I section\n",
+      "I=1*12**-1*(b*D1**3-180*d**3)*10**-8\n",
       "\n",
-      "#M1=Y*sigma\n",
+      "#Moment acting on section \n",
+      "#After simplifying we get\n",
+      "#M=2865833.3*f\n",
       "\n",
-      "#Now Moment of Inertia I section is\n",
-      "X=b*D1**3\n",
-      "Y=(b-t2)*d**3\n",
-      "I=(X-Y)*12**-1*10**-8\n",
+      "#Percentage moment resistance\n",
+      "M1=2258333.3*2865833.3**-1*100\n",
       "\n",
-      "#Moment acting on the entire section\n",
-      "#since sigmais the value at y=250\n",
-      "y_max=250\n",
-      "Z=I*10**8*y_max**-1\n",
-      "#M=sigma*Z   \n",
-      "#After Simplifying Further we get\n",
-      "#M2=Z*sigma\n",
-      "\n",
-      "#Percentage Moment resisted by Flanges\n",
-      "P1=2258333.3*(2865833.3)**-1*100\n",
-      "\n",
-      "#Percentage Moment resisted by web\n",
-      "P2=100-P1\n",
+      "#Percentage moment resisted by web\n",
+      "M2=100-M1\n",
       "\n",
       "#Result\n",
-      "print\"Percentage Moment resisted by Flanges\",round(P1,2),\"%\"\n",
-      "print\"Percentage Moment resisted by web\",round(P2,2),\"%\""
+      "print\"Percentage Moment resisted by Flanges\",round(M1,2),\"%\"\n",
+      "print\"Percentage Moment resisted by web\",round(M2,2),\"%\""
      ],
      "language": "python",
      "metadata": {},
@@ -388,7 +384,7 @@
        ]
       }
      ],
-     "prompt_number": 38
+     "prompt_number": 26
     },
     {
      "cell_type": "heading",
@@ -403,7 +399,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -479,7 +474,7 @@
        ]
       }
      ],
-     "prompt_number": 25
+     "prompt_number": 7
     },
     {
      "cell_type": "heading",
@@ -494,7 +489,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -544,7 +538,7 @@
        ]
       }
      ],
-     "prompt_number": 30
+     "prompt_number": 8
     },
     {
      "cell_type": "heading",
@@ -559,7 +553,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -636,7 +629,7 @@
        ]
       }
      ],
-     "prompt_number": 26
+     "prompt_number": 9
     },
     {
      "cell_type": "heading",
@@ -651,7 +644,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -710,7 +702,7 @@
        ]
       }
      ],
-     "prompt_number": 28
+     "prompt_number": 10
     },
     {
      "cell_type": "heading",
@@ -725,7 +717,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "H=10 #mm #Height\n",
@@ -790,7 +781,7 @@
        ]
       }
      ],
-     "prompt_number": 4
+     "prompt_number": 11
     },
     {
      "cell_type": "heading",
@@ -805,7 +796,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -858,7 +848,7 @@
        ]
       }
      ],
-     "prompt_number": 23
+     "prompt_number": 12
     },
     {
      "cell_type": "heading",
@@ -873,7 +863,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -925,7 +914,7 @@
        ]
       }
      ],
-     "prompt_number": 17
+     "prompt_number": 13
     },
     {
      "cell_type": "heading",
@@ -940,7 +929,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -1005,7 +993,7 @@
        ]
       }
      ],
-     "prompt_number": 4
+     "prompt_number": 14
     },
     {
      "cell_type": "heading",
@@ -1020,7 +1008,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -1066,7 +1053,7 @@
        ]
       }
      ],
-     "prompt_number": 6
+     "prompt_number": 15
     },
     {
      "cell_type": "heading",
@@ -1158,11 +1145,11 @@
        "output_type": "display_data",
        "png": 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dSnJyMjt37sThcBAcHMycOXPKfHwRTxYRARs3mgK29HRT2awCNrFTsS2E/v37s3r1aoKC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\niIgIoIQgIiLnKCGIiAighCAiIuf8f5wqyy9KzUKHAAAAAElFTkSuQmCC\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x4e02350>"
+        "<matplotlib.figure.Figure at 0x5020390>"
        ]
       }
      ],
-     "prompt_number": 5
+     "prompt_number": 16
     },
     {
      "cell_type": "heading",
@@ -1177,7 +1164,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "%matplotlib  inline\n",
       "\n",
       "#Initilization of Variables\n",
@@ -1256,11 +1242,11 @@
        "output_type": "display_data",
        "png": 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2vPfee7Ro0cKdZYiIyEXcPmq/YsWKLFy4kD59+pCXl8e4ceMUBCIiNvPIGcgi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\n/w/qZz1xEBCKMwAAAABJRU5ErkJggg==\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x55ed710>"
+        "<matplotlib.figure.Figure at 0x5857ff0>"
        ]
       }
      ],
-     "prompt_number": 6
+     "prompt_number": 17
     },
     {
      "cell_type": "heading",
@@ -1275,7 +1261,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -1323,7 +1308,7 @@
        ]
       }
      ],
-     "prompt_number": 7
+     "prompt_number": 18
     },
     {
      "cell_type": "heading",
@@ -1338,7 +1323,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -1379,7 +1363,7 @@
        ]
       }
      ],
-     "prompt_number": 8
+     "prompt_number": 19
     },
     {
      "cell_type": "heading",
@@ -1394,7 +1378,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -1454,7 +1437,7 @@
        ]
       }
      ],
-     "prompt_number": 9
+     "prompt_number": 20
     },
     {
      "cell_type": "heading",
@@ -1469,7 +1452,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -1521,7 +1503,7 @@
        ]
       }
      ],
-     "prompt_number": 10
+     "prompt_number": 21
     },
     {
      "cell_type": "heading",
@@ -1536,7 +1518,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -1585,7 +1566,7 @@
        ]
       }
      ],
-     "prompt_number": 11
+     "prompt_number": 22
     },
     {
      "cell_type": "heading",
@@ -1600,7 +1581,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -1651,7 +1631,7 @@
        ]
       }
      ],
-     "prompt_number": 12
+     "prompt_number": 23
     }
    ],
    "metadata": {}
diff --git a/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_5.ipynb b/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_5.ipynb
index ef53a555..93998543 100644
--- a/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_5.ipynb
+++ b/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_5.ipynb
@@ -28,7 +28,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -79,7 +78,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "\n",
       "#Initilization of Variables\n",
@@ -131,7 +129,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "\n",
       "#Initilization of Variables\n",
@@ -236,7 +233,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "\n",
       "#Initilization of Variables\n",
@@ -316,7 +312,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "\n",
       "#Initilization of Variables\n",
@@ -428,7 +423,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -537,7 +531,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -722,7 +715,7 @@
        "output_type": "display_data",
        "png": 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8yjGZmZkkJSWRmZlJSkoKM2bMoLKy8pxilcZbsQJGj4Y//QkWL1aSEWnvaq3R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\nL+mlAAAAAElFTkSuQmCC\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x4f23390>"
+        "<matplotlib.figure.Figure at 0x4f06390>"
        ]
       }
      ],
@@ -741,7 +734,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -825,7 +817,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -925,7 +916,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
diff --git a/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_6.ipynb b/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_6.ipynb
index 8f1678ce..6ece5381 100644
--- a/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_6.ipynb
+++ b/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_6.ipynb
@@ -28,7 +28,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -79,7 +78,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -130,7 +128,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -183,7 +180,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -236,7 +232,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -288,7 +283,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -344,7 +338,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -403,7 +396,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -494,7 +486,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -568,7 +559,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "d=100 #mm #Diameter of solid shaft\n",
@@ -637,7 +627,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "T=8 #KN-m #Torque \n",
@@ -699,7 +688,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -764,7 +752,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -845,7 +832,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -923,7 +909,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -995,7 +980,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -1059,7 +1043,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -1120,7 +1103,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -1176,7 +1158,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -1231,7 +1212,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -1291,7 +1271,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -1353,7 +1332,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -1408,7 +1386,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -1460,7 +1437,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
diff --git a/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_7.ipynb b/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_7.ipynb
index 40900c17..16a15154 100644
--- a/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_7.ipynb
+++ b/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_7.ipynb
@@ -28,7 +28,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -89,7 +88,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -145,7 +143,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -205,7 +202,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -259,7 +255,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -316,7 +311,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -374,7 +368,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -432,7 +425,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -499,7 +491,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -556,7 +547,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -613,7 +603,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -678,7 +667,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -808,7 +796,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -889,7 +876,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -941,7 +927,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -1035,7 +1020,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -1110,7 +1094,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -1197,7 +1180,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -1262,7 +1244,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
diff --git a/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_8.ipynb b/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_8.ipynb
index 69c4471a..2cf267c6 100644
--- a/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_8.ipynb
+++ b/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_8.ipynb
@@ -28,7 +28,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -106,7 +105,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -197,7 +195,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -245,7 +242,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -296,7 +292,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -344,7 +339,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -423,7 +417,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -479,7 +472,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -522,7 +514,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -585,7 +576,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "%matplotlib  inline\n",
       "\n",
       "#Initilization of Variables\n",
@@ -690,7 +680,7 @@
        "output_type": "display_data",
        "png": 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psPpzP4zq6moEBwfj999/N6pCuTGRkD7V1UBaWt0zXZyc6p7p8ucyJqJ2Q9YFiQEBAdJ0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\nRERkEiYSIiIyCRMJERGZhImEiIhM8v8BOmQpuVllnG0AAAAASUVORK5CYII=\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x4e17390>"
+        "<matplotlib.figure.Figure at 0x4fa1390>"
        ]
       }
      ],
@@ -709,7 +699,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "%matplotlib  inline\n",
       "\n",
       "#Initilization of Variables\n",
@@ -800,7 +789,7 @@
        "output_type": "display_data",
        "png": 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29vaQJAknTpx4bAP379/HiBEjMGzYMMycOdNwT41GA1dXV2RkZGDgwIEcMiIi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\nSUVORK5CYII=\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x563ec90>"
+        "<matplotlib.figure.Figure at 0x57bea30>"
        ]
       }
      ],
@@ -819,7 +808,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -888,7 +876,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -955,7 +942,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -1054,7 +1040,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "%matplotlib  inline\n",
       "\n",
       "#Initilization of Variables\n",
@@ -1199,7 +1184,7 @@
        "output_type": "display_data",
        "png": 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MHz4cr7zyCmbPno1///vf1fIBnZeXp/l+8+bNmhVR0dHR+P7771FYWIjMzExcvHgRnTp1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\nEenEREFERDoxURARkU7/H21GIMqBrUIbAAAAAElFTkSuQmCC\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x5576590>"
+        "<matplotlib.figure.Figure at 0x57dbb10>"
        ]
       },
       {
@@ -1207,7 +1192,7 @@
        "output_type": "display_data",
        "png": 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HAHzwwQdYvnw51qxZg6amJgQHB5usgkREZF5aexQtuyiHDh3C9OnT1SdY6b1R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\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x566a330>"
+        "<matplotlib.figure.Figure at 0x57dc090>"
        ]
       }
      ],
@@ -1226,7 +1211,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -1313,7 +1297,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -1431,7 +1414,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "%matplotlib  inline\n",
       "\n",
       "#Initilization of Variables\n",
@@ -1518,7 +1500,7 @@
        "output_type": "display_data",
        "png": 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w3g2UlJRgzJgxCAsLw3vvvQcA8PT0hFqthpOTE7KyshAYGIhLly7VLIxzCERE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\nBgIREQEA/h+bezx5xlsz+QAAAABJRU5ErkJggg==\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x58d75b0>"
+        "<matplotlib.figure.Figure at 0x5912830>"
        ]
       }
      ],
diff --git a/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_9.ipynb b/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_9.ipynb
index cd67d50b..4f1ca0ff 100644
--- a/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_9.ipynb
+++ b/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_9.ipynb
@@ -28,7 +28,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "L=5000 #mm #Length of strut\n",
@@ -76,7 +75,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -156,7 +154,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -218,7 +215,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -285,7 +281,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -352,7 +347,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -437,7 +431,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -529,7 +522,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -598,7 +590,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -653,7 +644,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",
@@ -729,7 +719,6 @@
      "collapsed": false,
      "input": [
       "import math\n",
-      "import numpy as np\n",
       "\n",
       "#Initilization of Variables\n",
       "\n",