Added(A)/Deleted(D) following books

A Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter1.ipynb A Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter10.ipynb A Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter11.ipynb A Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter13.ipynb A Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter14.ipynb A Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter15.ipynb A Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter17.ipynb A Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter18.ipynb A Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter19.ipynb A Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter21.ipynb A Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter22.ipynb A Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter23.ipynb A Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter25.ipynb A Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter26.ipynb A Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter3.ipynb A Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter4.ipynb A Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter5.ipynb A Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter6.ipynb A Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter7.ipynb A Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter9.ipynb A Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/screenshots/Ch14PathOfAscent.png A Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/screenshots/Ch14RandomNumberGenerator.png A Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/screenshots/Ch26EulerMethod.png A sample_notebooks/testingtesting/fameetha.ipynb
author: Trupti Kini 2016-05-02 23:30:25 +0600
committer: Trupti Kini 2016-05-02 23:30:25 +0600
commit: 09174527d359bd85404d15d76fabd891c7e5ad6b (patch)
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parent: a50c96a8653eda4256bb1e27242273373ad94732 (diff)
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diff --git a/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter1.ipynb b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter1.ipynb
new file mode 100644
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+++ b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter1.ipynb
@@ -0,0 +1,121 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# CHAPTER 1 : Mathematical Modeling And Engineering Problem Solving"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex : 1.1 Pg : 14"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Time(s) = 0\tv(m/s) = 0.00\n",
+      "Time(s) = 2\tv(m/s) = 16.40\n",
+      "Time(s) = 4\tv(m/s) = 27.77\n",
+      "Time(s) = 6\tv(m/s) = 35.64\n",
+      "Time(s) = 8\tv(m/s) = 41.10\n",
+      "Time(s) = 10\tv(m/s) = 44.87\n",
+      "Time(s) = inf\tv(m/s) = 53.39\n"
+     ]
+    }
+   ],
+   "source": [
+    "from numpy import arange, exp, inf\n",
+    "g=9.8##m/s**2# acceleration due to gravity\n",
+    "m=68.1##kg\n",
+    "c=12.5##kg/sec# drag coefficient\n",
+    "v=[]\n",
+    "j=0\n",
+    "for i in arange(0,12,2):\n",
+    "    v.append(g*m*(1-exp(-c*i/m))/c)\n",
+    "    print \"Time(s) = %d\\t\"%i,\"v(m/s) = %0.2f\"%v[j]\n",
+    "    j+=1\n",
+    "print \"Time(s) = %0.2f\\t\"%inf,\"v(m/s) = %0.2f\"%(g*m/c)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex : 1.2 Pg :17"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Time(s) = 0\tv(m/s) = 0.00\n",
+      "Time(s) = 2\tv(m/s) = 19.60\n",
+      "Time(s) = 4\tv(m/s) = 12.40\n",
+      "Time(s) = 6\tv(m/s) = 34.65\n",
+      "Time(s) = 8\tv(m/s) = 19.29\n",
+      "Time(s) = 10\tv(m/s) = 47.17\n",
+      "Time(s) = 12\tv(m/s) = 21.57\n",
+      "Time(s) = inf\tv(m/s) = 53.39\t\n"
+     ]
+    }
+   ],
+   "source": [
+    "from numpy import arange, exp, inf\n",
+    "g=9.8##m/s**2# acceleration due to gravity\n",
+    "m=68.1##kg\n",
+    "c=12.5##kg/sec# drag coefficient\n",
+    "count=0#\n",
+    "v=[]\n",
+    "v.append(0)\n",
+    "print \"Time(s) = %d\\t\"%(0),\"v(m/s) = %0.2f\"%v[0]\n",
+    "\n",
+    "for i in arange(1,13,2):\n",
+    "    v.append(v[(count-1)]+(g-c*v[(count)]/m)*(2))\n",
+    "    print \"Time(s) = %d\\t\"%(i+1),\"v(m/s) = %0.2f\"%v[(count+1)]\n",
+    "    count=count+1#\n",
+    "\n",
+    "print \"Time(s) = %0.2f\\t\"%inf,\"v(m/s) = %0.2f\\t\"%(g*m/c)\n"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 2",
+   "language": "python",
+   "name": "python2"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.9"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter10.ipynb b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter10.ipynb
new file mode 100644
index 00000000..54d12f92
--- /dev/null
+++ b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter10.ipynb
@@ -0,0 +1,259 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Chapter 10 : LU Decomposition and matrix inverse"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex10.1 Page 277"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "A = [[  3.   -0.1  -0.2]\n",
+      " [  0.1   7.   -0.3]\n",
+      " [  0.3  -0.2  10. ]]\n",
+      "\n",
+      "U = \n",
+      "[[  3.          -0.1         -0.2       ]\n",
+      " [  0.           7.00333333  -0.29333333]\n",
+      " [  0.           0.          10.01204188]]\n",
+      "\n",
+      "L calculated based on gauss elimination method = \n",
+      "[[ 1.          0.          0.        ]\n",
+      " [ 0.03333333  1.          0.        ]\n",
+      " [ 0.1        -0.02712994  1.        ]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "from numpy import mat\n",
+    "from numpy.linalg import det\n",
+    "A = mat([[3,-0.1,-0.2],[0.1,7,-0.3],[0.3,-0.2,10]])\n",
+    "U = A#\n",
+    "print \"A =\",A\n",
+    "m = U[0,0]\n",
+    "n = U[1,0]\n",
+    "a = n/m#\n",
+    "U[1:2] = U[1:2] - U[0:1] / (m/n)#\n",
+    "n = U[2,0]\n",
+    "b = n/m\n",
+    "\n",
+    "U[2:3] = U[2:3] - U[0:1] / (m/n)#\n",
+    "m = U[1,1]\n",
+    "n = U[2,1]\n",
+    "c = n/m#\n",
+    "U[2:3] = U[2:3] - U[1:2] / (m/n)#\n",
+    "print \"\\nU = \\n\",U\n",
+    "L = mat([[1,0,0],[a,1,0],[b,c,1]])\n",
+    "print \"\\nL calculated based on gauss elimination method = \\n\",L"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex10.2 Page 279"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "X = \n",
+      "[[ 3. ]\n",
+      " [-2.5]\n",
+      " [ 7. ]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "from numpy import mat\n",
+    "A = mat([[3,-0.1,-0.2],[0.1,7,-0.3],[0.3,-0.2,10]])\n",
+    "B = mat([[7.85],[-19.3],[71.4]])\n",
+    "X = (A**-1) * B\n",
+    "print \"X = \\n\",X"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex10.3 Page 284"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "B=\n",
+      "[[ 0.33248872  0.00494409  0.00679813]\n",
+      " [-0.00518174  0.14290333  0.00418348]\n",
+      " [-0.01007834  0.00270975  0.09988014]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "from numpy import mat,array\n",
+    "A = mat([[3,-0.1,-0.2],[0.1,7,-0.3],[0.3,-0.2,10]])\n",
+    "B = (A**-1)\n",
+    "L = mat([[1,0,0],[0.033333,1,0],[0.1,-0.02713,1]])\n",
+    "U = mat([[3,-0.1,-0.2],[0,7.0033,-0.293333],[0,0,10.012]])\n",
+    "for i  in range(1,4):\n",
+    "    if i==1:\n",
+    "        m = mat([[1],[0],[0]])\n",
+    "    else:\n",
+    "        if i==2:\n",
+    "            m = mat([[0],[1],[0]])\n",
+    "        else:\n",
+    "            m = mat([[0],[0],[1]])\n",
+    "        \n",
+    "    \n",
+    "    d = (L**-1) * m#\n",
+    "    x = (U**-1) * d#\n",
+    "    B[:,i-1] = x\n",
+    "\n",
+    "print \"B=\\n\",B"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex10.4 Page 291"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "A = \n",
+      "[[ 1.          0.5         0.33333333]\n",
+      " [ 1.          0.66666667  0.5       ]\n",
+      " [ 1.          0.75        0.6       ]]\n",
+      "\n",
+      "Condition number for the matrix =\n",
+      "451.2\n"
+     ]
+    }
+   ],
+   "source": [
+    "from numpy import mat\n",
+    "from __future__ import division\n",
+    "A = mat([[1,1/2,1/3],[1/2,1/3,1/4],[1/3,1/4,1/5]])\n",
+    "n = A[1,0]\n",
+    "A[1,:] = A[1,:]/n\n",
+    "n = A[2,0]\n",
+    "A[2,:] = A[2,:]/n\n",
+    "B = (A**-1)#\n",
+    "print \"A = \\n\",A\n",
+    "\n",
+    "m=range(1,4)\n",
+    "su=range(1,4)\n",
+    "for j in range(1,4):\n",
+    "    a = 0#\n",
+    "    for i in range(1,4):\n",
+    "        m[i-1]= A[j-1,i-1]\n",
+    "        su[j-1] = a + m[i-1]#\n",
+    "        a = su[j-1]#\n",
+    "\n",
+    "\n",
+    "if su[0]< su[1]:\n",
+    "    if su[1]< su[2]:\n",
+    "        z = su[2]\n",
+    "    else:\n",
+    "        z = su[1]\n",
+    "    \n",
+    "else:\n",
+    "     if su[0] < su[2]:\n",
+    "        z = su[2]#\n",
+    "     else:\n",
+    "        z = su[0]#\n",
+    "    \n",
+    "m=range(1,4)\n",
+    "sm=range(1,4)\n",
+    "for j in  range(1,4):\n",
+    "    a = 0#\n",
+    "    for i in range(1,4):\n",
+    "        m[i-1]= B[j-1,i-1]\n",
+    "        sm[j-1]= a + abs(m[i-1])\n",
+    "        a = sm[j-1]#\n",
+    "\n",
+    "\n",
+    "if sm[0]< sm[1]:\n",
+    "    if sm[1]< sm[2] :\n",
+    "        y = sm[2]\n",
+    "    else:\n",
+    "        y = sm[1]\n",
+    "    \n",
+    "else:\n",
+    "     if sm[0]< sm[2]:\n",
+    "        y = sm[2]\n",
+    "     else:\n",
+    "        y = sm[0]#\n",
+    "    \n",
+    "\n",
+    "C = z*y#\n",
+    "print \"\\nCondition number for the matrix =\\n\",C\n",
+    "\n"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 2",
+   "language": "python",
+   "name": "python2"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.9"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter11.ipynb b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter11.ipynb
new file mode 100644
index 00000000..352fdcac
--- /dev/null
+++ b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter11.ipynb
@@ -0,0 +1,303 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Chapter - 11 : Special Matrices and Gauss-Seidel"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:11.1 Pg: 297"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "T1 =  151.165722019\n",
+      "T2 =  267.578072919\n",
+      "T3 =  236.681195836\n",
+      "T4 =  214.451566586\n"
+     ]
+    }
+   ],
+   "source": [
+    "from numpy import mat\n",
+    "A = mat([[2.04,-1,0,0],[-1,2.04,-1,0],[0,-1,2.04,-1],[0,0,-1,2.04]])\n",
+    "B = mat([[40.8],[0.8],[0.8],[200.8]])\n",
+    "g = A[0,1]\n",
+    "f1 =A[0,0]\n",
+    "e2 = A[1,0]\n",
+    "f2 = A[0,0] - e2 * A[1,0]\n",
+    "e3 = A[1,0]/f2\n",
+    "f3 = A[0,0] - e3 * A[1,0]\n",
+    "e4 = A[1,0]/f3#\n",
+    "f4 = A[0,0] - e4 * A[1,0]\n",
+    "M = mat([[f1,g,0,0],[e2,f2,g,0],[0,e3,f3,g],[0,0,e4,f4]])\n",
+    "L = mat([[1,0,0,0],[M[1,0],1,0,0],[0,M[2,1],1,0],[0,0,M[3,2],1]])\n",
+    "U = mat([[M[0,0],g,0,0],[0,M[1,1],g,0],[0,0,M[2,2],g],[0,0,0,M[3,3]]])\n",
+    "r1 = B[0,0]\n",
+    "r2 = B[1,0] - e2*B[0,0]\n",
+    "r3 = B[2,0] - e3*r2#\n",
+    "r4= B[3,0] - e4*r3# \n",
+    "N = mat([[r1],[r2],[r3],[r4]])\n",
+    "T4 = r4/U[3,3]\n",
+    "T3 = (r3 - g*T4)/U[2,2]\n",
+    "T2 = (r2 - g*T3)/U[1,1]\n",
+    "T1 = (r1 - g*T2)/U[0,0]\n",
+    "print \"T1 = \",T1\n",
+    "print \"T2 = \",T2\n",
+    "print \"T3 = \",T3\n",
+    "print \"T4 = \",T4"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:11.2 Pg: 299"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "L = \n",
+      "[[  2.44948974   0.           0.        ]\n",
+      " [  6.12372436   4.18330013   0.        ]\n",
+      " [ 22.45365598  20.91650066   6.11010093]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "from numpy import mat,sqrt\n",
+    "A = mat([[6,15,55],[15,55,225],[55,225,979]])\n",
+    "sl = 0\n",
+    "l11 = sqrt(A[0,0])\n",
+    "#for second row\n",
+    "l21 = (A[1,0])/l11\n",
+    "l22 = (A[1,1] - l21**2)**(0.5)\n",
+    "#for third row\n",
+    "l31 = (A[2,0])/l11#\n",
+    "l32 = (A[2,1] - l21*l31)/l22#\n",
+    "l33 = (A[2,2] - l31**2 - l32**2)**(0.5)#\n",
+    "L = mat([[l11,0,0],[l21,l22,0],[l31,l32,l33]])\n",
+    "print \"\\nL = \\n\",L"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:11.3 Pg: 301"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "x through two iterations = [2.6166666666666667]\n",
+      "y through two iterations = [-2.7945238095238096]\n",
+      "z through two iterations = [7.005609523809525]\n",
+      "error of x =  12.50234999 %\n",
+      "error of y =  -11.7977361365 %\n",
+      "error of z =  -0.075978454143 %\n"
+     ]
+    }
+   ],
+   "source": [
+    "#3x - 0.1y - 0.2z = 7.85\n",
+    "#0.1x + 7y - 0.3z = -19.3\n",
+    "#0.3x - 0.2y + 10z = 71.4\n",
+    "Y = 0# \n",
+    "Z = 0#\n",
+    "x=range(1,3)\n",
+    "y=range(1,3)\n",
+    "z=range(1,3)\n",
+    "for i in range(1,3):\n",
+    "    x[i-1]= (7.85 +0.1*Y+0.2*Z)/3#\n",
+    "    X = x[i-1]\n",
+    "    y[i-1]= (-19.3 - 0.1*X +0.3*Z)/7#\n",
+    "    Y = y[i-1]#\n",
+    "    z[i-1]= (71.4 - 0.3*X+0.2*Y)/10#\n",
+    "    Z = z[i-1]\n",
+    "    if i==2:\n",
+    "        ex = (x[i-1] - x[(i-2)])*100/x[i-1]\n",
+    "        ey = (y[i-1] - y[i-2])*100/y[i-1]\n",
+    "        ez = (z[i-1] - z[i-2])*100/z[i-1]\n",
+    "    \n",
+    "\n",
+    "print \"x through two iterations =\",x[0:1]\n",
+    "print \"y through two iterations =\",y[0:1]\n",
+    "print \"z through two iterations =\",z[0:1]\n",
+    "print \"error of x = \",ex,\"%\"\n",
+    "print \"error of y = \",ey,\"%\"\n",
+    "print \"error of z = \",ez,\"%\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:11.4 Pg: 307"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "x =  0.999991\n",
+      "y =  1.000044\n",
+      "z =  0.99996\n"
+     ]
+    }
+   ],
+   "source": [
+    "from __future__ import division\n",
+    "\n",
+    "from numpy import mat\n",
+    "A = mat([[1,0.5,1/3],[1,2/3,1/2],[1,3/4,3/5]])\n",
+    "B = mat([[1.833333],[2.166667],[2.35]])\n",
+    "U = A**-1\n",
+    "X = U*B#\n",
+    "x = X[0,0]\n",
+    "y = X[1,0]\n",
+    "z = X[2,0]\n",
+    "print \"x = \",x\n",
+    "print \"y = \",y\n",
+    "print \"z = \",z"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:11.5 Pg: 309"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "x =  0.999991\n",
+      "y =  1.000044\n",
+      "z =  0.99996\n"
+     ]
+    }
+   ],
+   "source": [
+    "from __future__ import division\n",
+    "from numpy import mat\n",
+    "A = mat([[1,0.5,1/3],[1,2/3,1/2],[1,3/4,3/5]])\n",
+    "B = mat([[1.833333],[2.166667],[2.35]])\n",
+    "U = A**-1\n",
+    "X = U*B#\n",
+    "x = X[0,0]\n",
+    "y = X[1,0]\n",
+    "z = X[2,0]\n",
+    "print \"x = \",x\n",
+    "print \"y = \",y\n",
+    "print \"z = \",z"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:11.6 Pg: 310"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "x =  0.999999\n",
+      "y =  1.000008\n",
+      "z =  0.99999\n"
+     ]
+    }
+   ],
+   "source": [
+    "from numpy import mat\n",
+    "A = mat([[1,0.5,1/3],[1/2,1/3,1/4],[1/3,1/4,1/5]])\n",
+    "B = mat([[1.833333],[1.083333],[0.783333]])\n",
+    "U = A**-1\n",
+    "X = U*B#\n",
+    "x = X[0,0]\n",
+    "y = X[1,0]\n",
+    "z = X[2,0]\n",
+    "print \"x = \",x\n",
+    "print \"y = \",y\n",
+    "print \"z = \",z"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 2",
+   "language": "python",
+   "name": "python2"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.9"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter13.ipynb b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter13.ipynb
new file mode 100644
index 00000000..c37c77de
--- /dev/null
+++ b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter13.ipynb
@@ -0,0 +1,193 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Chapter - 13 : One-Dimensional Unconstrained Optimization"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:13.1 Pg: 356"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "xl = [0, 0, 0, 0, 0, 0.9442719099991588, 0.9442719099991588, 0.9442719099991588, 0.9442719099991588, 0.9442719099991588, 0.9442719099991588]\n",
+      "\n",
+      "x2 = [1.5278640450004204, 1.5278640450004204, 0.0, 0.9442719099991588, 0.9442719099991588, 0.9442719099991588, 0.9442719099991588, 1.5278640450004206, 1.5278640450004206, 1.5278640450004206]\n",
+      "\n",
+      "x1 = [2.4721359549995796, 2.4721359549995796, 2.4721359549995796, 1.5278640450004208, 1.5278640450004208, 1.5278640450004208, 2.4721359549995796, 1.8885438199983178, 1.8885438199983178, 1.8885438199983178]\n",
+      "\n",
+      "xu = [4, 2.4721359549995796, 2.4721359549995796, 2.4721359549995796, 2.4721359549995796, 2.4721359549995796, 2.4721359549995796, 2.4721359549995796, 2.4721359549995796, 1.8885438199983178, 1.8885438199983178]\n"
+     ]
+    }
+   ],
+   "source": [
+    "from math import sin\n",
+    "#f(x) = 2sinx - x**2/10\n",
+    "xl=[]\n",
+    "xu=[]\n",
+    "xl.append(0)\n",
+    "xu.append(4)\n",
+    "d=[]\n",
+    "x1=[]\n",
+    "x2=[]\n",
+    "m=[]\n",
+    "n=[]\n",
+    "for i in range(0,10):\n",
+    "    d.append(((5)**(0.5) - 1)*(xu[i-1] - xl[i-1])/2)\n",
+    "    x1.append(xl[i-1] + d[i-1])\n",
+    "    x2.append(xu[i-1] - d[i-1])\n",
+    "    m.append(2*sin(x1[i-1]) - (x1[i-1]**2)/10)\n",
+    "    n.append(2*sin(x2[i-1]) - (x2[i-1]**2)/10)\n",
+    "    if n[i-1] > m[i-1]:\n",
+    "        xu.append(x1[(i-1)])\n",
+    "        xl.append(xl[(i-1)])\n",
+    "    else:\n",
+    "        xl.append(x2[i-1])\n",
+    "        xu.append(xu[i-1])\n",
+    "    \n",
+    "\n",
+    "print \"xl =\",xl\n",
+    "print \"\\nx2 =\",x2\n",
+    "print \"\\nx1 =\",x1\n",
+    "print \"\\nxu =\",xu"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:13.2 Pg: 360"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "x0 =  [0, 1, 1, 1.3813008689454946, 1.382057051632978, 1.4273175717149764, 1.4274221422858844]\n",
+      "\n",
+      "x1 =  [1, 1.5921843781407843, 1.3813008689454946, 1.382057051632978, 1.4273175717149764, 1.4274221422858844, 1.4275508501677177]\n",
+      "\n",
+      "x2 =  [4, 4, 1.5921843781407843, 1.5921843781407843, 1.5921843781407843, 1.5921843781407843, 1.5921843781407843]\n"
+     ]
+    }
+   ],
+   "source": [
+    "from math import sin\n",
+    "#f(x) = 2sinx - x**2/10\n",
+    "x0= [0]#\n",
+    "x1= [1]\n",
+    "x2= [4]#\n",
+    "m=[];n=[];r=[];x3=[];s=[]\n",
+    "for i in range(0,6):\n",
+    "    m.append(2*sin(x0[(i)]) - (x0[(i)]**2)/10)\n",
+    "    n.append(2*sin(x1[(i)]) - (x1[(i)]**2)/10)\n",
+    "    r.append(2*sin(x2[(i)]) - (x2[(i)]**2)/10)\n",
+    "    x3.append(((m[(i)]*(x1[(i)]** 2 -x2[(i)] ** 2)) + (n[(i)]*(x2[(i)] ** 2 -x0[(i)] ** 2)) + (r[(i)]*(x0[(i)] ** 2 -x1[(i)] ** 2)))/((2*m[(i)]*(x1[(i)] -x2[(i)]))+(2*n[(i)]*(x2[(i)] -x0[(i)]))+(2*r[(i)]*(x0[(i)] -x1[(i)]))))\n",
+    "    s.append(2*sin(x3[(i)]) - (x3[(i)]**2)/10)\n",
+    "    if x1[(i) ]> x3[(i) ]:\n",
+    "        if n[(i)]<s[(i)]:\n",
+    "            x0.append(x0[(i)])\n",
+    "            x1.append(x3[(i)])\n",
+    "            x2.append(x1[(i)])\n",
+    "        else:\n",
+    "            x0.append(x1[(i)])\n",
+    "            x1.append(x3[(i)])\n",
+    "            x2.append(x2[(i)])\n",
+    "        \n",
+    "    else:\n",
+    "        if n[(i)]>s[(i)]:\n",
+    "            x0.append(x0[(i)])\n",
+    "            x1.append(x3[(i)])\n",
+    "            x2.appedn(x1[(i)])\n",
+    "        else:\n",
+    "            x0.append(x1[(i)])\n",
+    "            x1.append(x3[(i)])\n",
+    "            x2.append(x2[(i)])\n",
+    "        \n",
+    "     \n",
+    "\n",
+    "\n",
+    "print \"x0 = \",x0\n",
+    "print \"\\nx1 = \",x1\n",
+    "print \"\\nx2 = \",x2"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:13.3 Pg: 361"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "x =  [0.5, 2.2261962395657777, 1.1766358162650659, 1.465127166023216, 1.4238568730046828, 1.4279262963228776, 1.427513951598196, 1.427555600748671, 1.4275513926124817, 1.4275518177794067]\n"
+     ]
+    }
+   ],
+   "source": [
+    "from math import sin, cos\n",
+    "#f(x) = 2sinx - x**2/10\n",
+    "x= [.5]\n",
+    "#f'(x) = 2cosx - x/5\n",
+    "#f\"(x) = -2sinx - 1/5\n",
+    "for i in range(1,10):\n",
+    "  x.append(x[(i-1)] - (2*cos(x[(i-1)]) - x[(i-1)]/5)/(-2*sin(x[(i-1)]) - 1/5))\n",
+    "\n",
+    "print \"x = \",x"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 2",
+   "language": "python",
+   "name": "python2"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.9"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter14.ipynb b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter14.ipynb
new file mode 100644
index 00000000..b3607eab
--- /dev/null
+++ b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter14.ipynb
@@ -0,0 +1,260 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Chapter-14 : Multidimensional Unconstrained Optimization"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:14.1 Pg: 368"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Iteration: 1\n",
+      "x: 1.53606983054\n",
+      "y: 1.86168445446\n",
+      "function value: -13.5786300816\n",
+      "------------------------------------------\n",
+      "Iteration: 1001\n",
+      "x: 1.76453990766\n",
+      "y: 1.86004762993\n",
+      "function value: -16.155728181\n",
+      "------------------------------------------\n",
+      "Iteration: 2001\n",
+      "x: -0.735800459375\n",
+      "y: 1.48176151402\n",
+      "function value: 1.11970176233\n",
+      "------------------------------------------\n",
+      "Iteration: 3001\n",
+      "x: -0.493690866305\n",
+      "y: 2.74840585243\n",
+      "function value: -2.08537362139\n",
+      "------------------------------------------\n",
+      "Iteration: 4001\n",
+      "x: 0.191618544017\n",
+      "y: 2.12536130424\n",
+      "function value: -3.47137052343\n",
+      "------------------------------------------\n",
+      "Iteration: 5001\n",
+      "x: 0.556097851317\n",
+      "y: 2.75235702552\n",
+      "function value: -9.05885931809\n",
+      "------------------------------------------\n",
+      "Iteration: 6001\n",
+      "x: -1.3315420382\n",
+      "y: 1.98026194153\n",
+      "function value: 1.11796226726\n",
+      "------------------------------------------\n",
+      "Iteration: 7001\n",
+      "x: -1.30334156994\n",
+      "y: 2.2803362443\n",
+      "function value: 0.930459972575\n",
+      "------------------------------------------\n",
+      "Iteration: 8001\n",
+      "x: -1.42505981694\n",
+      "y: 1.24322307994\n",
+      "function value: 0.604422816099\n",
+      "------------------------------------------\n",
+      "Iteration: 9001\n",
+      "x: -1.04901290775\n",
+      "y: 1.83044616216\n",
+      "function value: 1.16839305819\n",
+      "------------------------------------------\n"
+     ]
+    }
+   ],
+   "source": [
+    "from numpy.random import rand\n",
+    "def f(x,y):\n",
+    "    z=y-x-(2*(x**2))-(2*x*y)-(y**2)\n",
+    "    return z\n",
+    "x1=-2#\n",
+    "x2=2#\n",
+    "y1=1#\n",
+    "y2=3#\n",
+    "fmax=-1*10**(-15)#\n",
+    "n=10000#\n",
+    "for j in range(0,n):\n",
+    "    r=rand(1,2)\n",
+    "    x=x1+(x2-x1)*r[0,0]\n",
+    "    y=y1+(y2-y1)*r[0,1]\n",
+    "    fn=f(x,y)#\n",
+    "    if fn>fmax:\n",
+    "        fmax=fn#\n",
+    "        xmax=x#\n",
+    "        ymax=y#\n",
+    "    \n",
+    "    if j%1000==0:\n",
+    "    \n",
+    "        print \"Iteration:\",(j+1)\n",
+    "        print \"x:\",x\n",
+    "        print \"y:\",y\n",
+    "        print \"function value:\",fn\n",
+    "        print \"------------------------------------------\"\n",
+    "    \n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:14.2 Pg: 374"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Elevation: 8\n",
+      "Theta: 1.107\n",
+      "slope: 8.94\n"
+     ]
+    }
+   ],
+   "source": [
+    "from math import atan\n",
+    "def f(x,y):\n",
+    "    z=x*y*y\n",
+    "    return z\n",
+    "p1=[2, 2]\n",
+    "elevation=f(p1[0],p1[1])\n",
+    "dfx=p1[0]*p1[0]\n",
+    "dfy=2*p1[0]*p1[1]\n",
+    "theta=atan(dfy/dfx)\n",
+    "slope=(dfx**2 + dfy**2)**0.5#\n",
+    "print \"Elevation:\",elevation\n",
+    "print \"Theta: %0.3f\"%theta\n",
+    "print \"slope: %0.2f\"%slope"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:14.3 Pg: 380"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The final equation is= 180*h**2 + 72*h - 7\n"
+     ]
+    }
+   ],
+   "source": [
+    "def f(x,y):\n",
+    "    z=2*x*y + 2*x - x**2 - 2*y**2\n",
+    "    return z\n",
+    "x=-1#\n",
+    "y=1#\n",
+    "dfx=2*y+2-2*x#\n",
+    "dfy=2*x-4*y#\n",
+    "#the function can thus be expressed along h axis as\n",
+    "#f((x+dfx*h),(y+dfy*h))\n",
+    "print \"The final equation is=\",\"180*h**2 + 72*h - 7\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:14.4 Pg: 381"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The final values are: [-1, 1]\n"
+     ]
+    }
+   ],
+   "source": [
+    "def f(x,y):\n",
+    "    z=2*x*y + 2*x - x**2 - 2*y**2\n",
+    "    return z\n",
+    "x=-1#\n",
+    "y=1#\n",
+    "d2fx=-2#\n",
+    "d2fy=-4#\n",
+    "d2fxy=2#\n",
+    "\n",
+    "modH=d2fx*d2fy-(d2fxy)**2#\n",
+    "\n",
+    "for i in range(0,25):\n",
+    "    dfx=2*y+2-2*x#\n",
+    "    dfy=2*x - 4*y#\n",
+    "    #the function can thus be expressed along h axis as\n",
+    "    #f((x+dfx*h),(y+dfy*h))\n",
+    "    def g(h):\n",
+    "        d=2*(x+dfx*h)*(y+dfy*h) + 2*(x+dfx*h) - (x+dfx*h)**2 - 2*(y+dfy*h)**2\n",
+    "        return d\n",
+    "    #2*dfx*(y+dfy*h)+2*dfy*(x+dfx*h)+2*dfx-2*(x+dfx*h)*dfx-4*(y+dfy*h)*dfy=g'(h)=0\n",
+    "    #2*dfx*y + 2*dfx*dfy*h + 2*dfy*x + 2*dfy*dfx*h + 2*dfx - 2*x*dfx - 2*dfx*dfx*h - 4*y*dfy - 4*dfy*dfy*h=0\n",
+    "    #h(2*dfx*dfy+2*dfy*dfx-2*dfx*dfx-4*dfy*dfy)=-(2*dfx*y+2*dfy*x-2*x*dfx-4*y*dfy)\n",
+    "    h=(2*dfx*y+2*dfy*x-2*x*dfx-4*y*dfy+2*dfx)/(-1*(2*dfx*dfy+2*dfy*dfx-2*dfx*dfx-4*dfy*dfy))#\n",
+    "    x=x+dfx*h#\n",
+    "    y=y+dfy*h#\n",
+    "print \"The final values are:\",[x, y]"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 2",
+   "language": "python",
+   "name": "python2"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.9"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter15.ipynb b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter15.ipynb
new file mode 100644
index 00000000..1573bb78
--- /dev/null
+++ b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter15.ipynb
@@ -0,0 +1,358 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Chapter-15 : Constrained Optimization"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:15.1 Pg: 388"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Maximize z=150*x1+175*x2\n",
+      "subject to\n",
+      "7*x1+11*x2<=77 (Material constraint)\n",
+      "10*x1+8*x2<=80 (Time constraint)\n",
+      "x1<=9 (Regular storage constraint)\n",
+      "x2<=6 (Premium storage constraint)\n",
+      "x1,x2>=0 (Positivity constraint)\n"
+     ]
+    }
+   ],
+   "source": [
+    "regular=[7, 10, 9 ,150]#\n",
+    "premium=[11, 8, 6, 175]#\n",
+    "res_avail=[77, 80]#\n",
+    "#total profit(to be maximized)=z=150*x1+175*x2\n",
+    "#total gas used=7*x1+11*x2 (has to be less than 77 m**3/week)\n",
+    "#similarly other constraints are developed\n",
+    "print \"Maximize z=150*x1+175*x2\"\n",
+    "print \"subject to\"\n",
+    "print \"7*x1+11*x2<=77 (Material constraint)\"\n",
+    "print \"10*x1+8*x2<=80 (Time constraint)\"\n",
+    "print \"x1<=9 (Regular storage constraint)\"\n",
+    "print \"x2<=6 (Premium storage constraint)\"\n",
+    "print \"x1,x2>=0 (Positivity constraint)\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:15.2 Pg: 389"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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c6e6/zNXmn+rECVi3LjgjqKyEMWOSdw8pUyBhavEWdhzakRgIautqWTpjKWUl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\nv4hIHvr/jNG1VBcwIEMAAAAASUVORK5CYII=\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7fa838951c50>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "%matplotlib inline\n",
+    "from matplotlib.pyplot import plot,xlabel,ylabel,title ,show\n",
+    "x21=[];x22=[];x23=[];x24=[];x25=[];x26=[]\n",
+    "\n",
+    "for x1 in range(0,9):\n",
+    "    x21.append(-(7/11)*x1+7)\n",
+    "    x22.append((80-10*x1)/8)\n",
+    "    x23.append(6)\n",
+    "    x24.append(-150*x1/175)\n",
+    "    x25.append((600-150*x1)/175)\n",
+    "    x26.append((1400-150*x1)/175)\n",
+    "\n",
+    "x1=range(0,9)\n",
+    "\n",
+    "plot(x1,x24)\n",
+    "plot(x1,x25)\n",
+    "plot(x1,x26)\n",
+    "#h1=legend(['Z=0'#'Z=600'#'Z=1400'])\n",
+    "plot(x1,x21)#\n",
+    "plot(x1,x22)#\n",
+    "plot(x1,x23)#\n",
+    "title('x2 vs x1')\n",
+    "xlabel('x1 (tonnes)')\n",
+    "ylabel('x2 (tonnes)')\n",
+    "show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:15.3 Pg: 399"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The maximized profit is= 1413.888925\n"
+     ]
+    }
+   ],
+   "source": [
+    "x1=[0,4.888889, 3.888889]\n",
+    "x2=[0,7, 11]#\n",
+    "x3=[0,10, 8]#\n",
+    "x4=[0,150, 175]#\n",
+    "x5=[0,77, 80, 9, 6]\n",
+    "profit=[0,x1[(1)]*x4[(1)], x1[(2)]*x4[(2)]]#\n",
+    "total=[0,x1[(1)]*x3[(1)]+x1[(2)]*x3[(2)], x1[(1)]*x3[(1)]+x1[(2)]*x3[(2)], x1[(1)], x1[(2)], profit[(1)]+profit[(2)]]\n",
+    "e=1000#\n",
+    "\n",
+    "while e>total[(5)]:\n",
+    "    if total[(1)]<=x5[(1)]:\n",
+    "        if total[(2)]<=x5[(2)]:\n",
+    "            if total[(3)]<=x5[(3)]:\n",
+    "                if total[(4)]<=x5[(4)]:\n",
+    "                    l=1#\n",
+    "                \n",
+    "            \n",
+    "        \n",
+    "    \n",
+    "    if l==1:\n",
+    "        x1[(1)]=x1[(1)]+4.888889\n",
+    "        x1[(2)]=x1[(2)]+3.888889#    \n",
+    "        profit=[0,x1[(1)]*x4[(1)], x1[(2)]*x4[(2)]]\n",
+    "        total[(5)]=profit[(1)]+profit[(2)]\n",
+    "    \n",
+    "\n",
+    "print \"The maximized profit is=\",total[(5)]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:15.4 Pg: 401"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The final value of velocity=19.980\n",
+      "6 The final no. of load parcels= 6\n",
+      "The chute radius=2.944 m\n",
+      "The minimum cost = 4377.264 $\n"
+     ]
+    }
+   ],
+   "source": [
+    "from math import pi,exp\n",
+    "\n",
+    "Mt=2000##kg\n",
+    "g=9.8##m/s**2\n",
+    "c0=200##$\n",
+    "c1=56##$/m\n",
+    "c2=0.1##$/m**2\n",
+    "vc=20##m/s\n",
+    "kc=3##kg/(s*m**2)\n",
+    "z0=500##m\n",
+    "t=27#\n",
+    "r=2.943652#\n",
+    "n=6#\n",
+    "A=2*pi*r*r#\n",
+    "l=(2**0.5)*r#\n",
+    "c=3*A#\n",
+    "m=Mt/n#\n",
+    "def f(t):\n",
+    "    y=(z0+g*m*m/(c*c)*(1-exp(-c*t/m)))*c/(g*m)#\n",
+    "    return y\n",
+    "\n",
+    "while abs(f(t)-t)>0.00001:\n",
+    "        t=t+0.00001\n",
+    "    \n",
+    "v=g*m*(1-exp(-c*t/m))/c#\n",
+    "print \"The final value of velocity=%0.3f\"%v\n",
+    "print n,\"The final no. of load parcels=\",n\n",
+    "print \"The chute radius=%0.3f m\"%r\n",
+    "print \"The minimum cost = %0.3f $\"%((c0+c1*l+c2*A*A)*n)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:15.5 Pg: 406"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Optimization terminated successfully.\n",
+      "         Current function value: -1.775726\n",
+      "         Iterations: 26\n",
+      "         Function evaluations: 52\n",
+      "After maximization:\n",
+      "x= [ 1.4275625]\n",
+      "f(x)= [-1.77572565]\n"
+     ]
+    }
+   ],
+   "source": [
+    "from scipy.optimize import fmin\n",
+    "from math import sin\n",
+    "def fx(x):\n",
+    "    y=-(2*sin(x))+x**2/10\n",
+    "    return y\n",
+    "x=fmin(fx,0)\n",
+    "print \"After maximization:\"\n",
+    "print \"x=\",x\n",
+    "print \"f(x)=\",fx(x)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:15.6 Pg: 407"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Optimization terminated successfully.\n",
+      "         Current function value: -2.000000\n",
+      "         Iterations: 45\n",
+      "         Function evaluations: 86\n",
+      "After maximization:\n",
+      "x= [ 1.99993372  0.99996476]\n",
+      "f(x)= -1.99999999779\n"
+     ]
+    }
+   ],
+   "source": [
+    "from scipy.optimize import fmin\n",
+    "def fx(x):\n",
+    "    f=-(2*x[0]*x[1]+2*x[0]-x[0]**2-2*x[1]**2)\n",
+    "    return f\n",
+    "x=fmin(fx,[-1, 1])\n",
+    "print \"After maximization:\"\n",
+    "print \"x=\",x\n",
+    "print \"f(x)=\",fx(x)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:15.7 Pg: 408"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Optimization terminated successfully.\n",
+      "         Current function value: -1.775726\n",
+      "         Iterations: 26\n",
+      "         Function evaluations: 52\n",
+      "After maximization:\n",
+      "x= [ 1.4275625]\n",
+      "f(x)= [-1.77572565]\n"
+     ]
+    }
+   ],
+   "source": [
+    "from scipy.optimize import fmin\n",
+    "from math import sin\n",
+    "\n",
+    "def fx(x):\n",
+    "    y=-(2*sin(x)-x**2/10)\n",
+    "    return y\n",
+    "x=fmin(fx,0)\n",
+    "print \"After maximization:\"\n",
+    "print \"x=\",x\n",
+    "print \"f(x)=\",fx(x)"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 2",
+   "language": "python",
+   "name": "python2"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.9"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter17.ipynb b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter17.ipynb
new file mode 100644
index 00000000..14e89b11
--- /dev/null
+++ b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter17.ipynb
@@ -0,0 +1,607 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Chapter-17 : Least-squares Regression"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:17.1 Pg: 458"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "sum of product of x and y = 119.5\n",
+      "sum of square of x =  140\n",
+      "sum of all the x =  28\n",
+      "sum of all the y =  24.0\n",
+      "a1 =  0.839285714286\n",
+      "a0 =  0.0714285714286\n",
+      "The equation of the line obtained is y = a0 + a1*x\n"
+     ]
+    }
+   ],
+   "source": [
+    "x = [1,2,3,4,5,6,7]#\n",
+    "y = [0.5,2.5,2,4,3.5,6,5.5]#\n",
+    "n = 7#\n",
+    "s = 0#\n",
+    "xsq = 0#\n",
+    "xsum = 0#\n",
+    "ysum = 0#\n",
+    "\n",
+    "for i in range(0,7):\n",
+    "    s = s + (x[i])*y[i]\n",
+    "    xsq = xsq + x[i]**2\n",
+    "    xsum = xsum + x[i]\n",
+    "    ysum = ysum + y[i]\n",
+    "\n",
+    "print \"sum of product of x and y =\",s\n",
+    "print \"sum of square of x = \",xsq\n",
+    "print \"sum of all the x = \",xsum\n",
+    "print \"sum of all the y = \",ysum\n",
+    "a = xsum/n#\n",
+    "b = ysum/n#\n",
+    "a1 = (n*s - xsum*ysum)/(n*xsq -xsum**2)#\n",
+    "a0 = b - a*a1#\n",
+    "print \"a1 = \",a1\n",
+    "print \"a0 = \",a0\n",
+    "print \"The equation of the line obtained is y = a0 + a1*x\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:17.2 Pg: 462"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "sum of all y = 24.0\n",
+      "\n",
+      "(yi - yavg)**2 =  [0.010204081632653073, 2.010204081632653, 1.510204081632653, 3.510204081632653, 3.010204081632653, 5.510204081632653, 5.010204081632653]\n",
+      "\n",
+      "total (yi - yavg)**2 =  20.5714285714\n",
+      "\n",
+      "(yi - a0 - a1*x)**2 =  [-0.4107142857142855, -0.9285714285714284, -5.625, -9.5, -17.55357142857143, -24.285714285714285, -35.69642857142857]\n",
+      "\n",
+      "total (yi - a0 - a1*x)**2 =  -94.0\n",
+      "\n",
+      "sy =  1.85164019955\n",
+      "r =  2.35996704308\n",
+      "The result indicate that 86.8 percent of the original uncertainty has been explained by linear model\n"
+     ]
+    }
+   ],
+   "source": [
+    "x = [1,2,3,4,5,6,7]#\n",
+    "y = [0.5,2.5,2,4,3.5,6,5.5]#\n",
+    "n = 7#\n",
+    "s = 0#\n",
+    "ssum = 0#\n",
+    "xsq = 0#\n",
+    "xsum = 0#\n",
+    "ysum = 0#\n",
+    "msum = 0#\n",
+    "for i in range(0,7):\n",
+    "    s = s + x[i]*y[i]\n",
+    "    xsq = xsq + x[i]**2\n",
+    "    xsum = xsum + x[i]\n",
+    "    ysum = ysum + y[i]\n",
+    "\n",
+    "a = xsum/n#\n",
+    "b = ysum/n#\n",
+    "a1 = (n*s - xsum*ysum)/(n*xsq -xsum**2)#\n",
+    "a0 = b - a*a1#\n",
+    "m=[];si=[]\n",
+    "for i in range(0,7):\n",
+    "    m.append(y[i] - ysum/7**2)\n",
+    "    msum = msum +m[i]#\n",
+    "    si.append(y[i] - a0 - a1*x[i]**2)\n",
+    "    ssum = ssum + si[i]\n",
+    "\n",
+    "print \"sum of all y =\",ysum\n",
+    "print \"\\n(yi - yavg)**2 = \",m\n",
+    "print \"\\ntotal (yi - yavg)**2 = \",msum\n",
+    "print \"\\n(yi - a0 - a1*x)**2 = \",si\n",
+    "print \"\\ntotal (yi - a0 - a1*x)**2 = \",ssum\n",
+    "sy = (msum / (n-1))**(0.5)#\n",
+    "#sxy = (ssum/(n-2))**(0.5)#\n",
+    "print \"\\nsy = \",sy\n",
+    "#print \"sxy = \",sxy\n",
+    "r2 = (msum - ssum)/(msum)#\n",
+    "r = r2**0.5#\n",
+    "print \"r = \",r\n",
+    "print \"The result indicate that 86.8 percent of the original uncertainty has been explained by linear model\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:17.3 Pg: 463"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "time =  [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]\n",
+      "\n",
+      "measured v = [10, 16.3, 23, 27.5, 31, 35.6, 39, 41.5, 42.9, 45, 46, 45.5, 46, 49, 50]\n",
+      "\n",
+      "using equation(1.10) v1 =  [8.953182207901257, 16.404980802870615, 22.607166909502304, 27.769291463870154, 32.06576523242002, 35.641751563129084, 38.61807096510561, 41.09528322582064, 43.15708498693595, 44.87313757134839, 46.30142060418256, 47.490190948641704, 48.479613142547706, 49.30311642251821, 49.988524185047744]\n",
+      "\n",
+      "using equation((17.3)) v2 =  [11.240084210526316, 18.57057391304348, 23.729066666666665, 27.556335483870967, 30.5088, 32.855630769230764, 34.765841860465116, 36.35091063829787, 37.68734117647059, 38.82938181818182, 39.81656949152543, 40.678399999999996, 41.43732537313433, 42.11073802816901, 42.712320000000005]\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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ILsXaEzCzB4EjgbaE8f8/AI8BY4FO1DFF1Mz8zDOdV1+F++8P9wCIiEjdUnVh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\nAyM6fhLOY0unAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f2a3c39d2d0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "%matplotlib inline\n",
+    "from matplotlib.pyplot import plot, title,xlabel,ylabel,show\n",
+    "from math import exp\n",
+    "s = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]#\n",
+    "v = [10,16.3,23,27.5,31,35.6,39,41.5,42.9,45,46,45.5,46,49,50]#\n",
+    "g = 9.8#m/s**2\n",
+    "m = 68.1##kg\n",
+    "c = 12.5#kg/s\n",
+    "v1=[]\n",
+    "v2=[]\n",
+    "for i in range(0,15):\n",
+    "    v1.append(g*m*(1 - exp(-c*s[(i)]/m))/c)\n",
+    "    v2.append(g*m*s[(i)]/(c*(3.75+s[(i)])))\n",
+    "\n",
+    "print \"time = \",s\n",
+    "print \"\\nmeasured v =\",v\n",
+    "print \"\\nusing equation(1.10) v1 = \",v1\n",
+    "print \"\\nusing equation((17.3)) v2 = \",v2\n",
+    "plot(v,v1)#\n",
+    "title('v vs v1')\n",
+    "xlabel('v')\n",
+    "ylabel('v1')#\n",
+    "show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:17.4 Pg: 468"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "a= 0.501187233627\n",
+      "x= [1, 2, 3, 4, 5]\n",
+      "y= [0.5011872336272722, 1.6857861925123965, 3.4273795077270295, 5.670286264671531, 8.379102586654781]\n",
+      "m= [0.0, 0.3010299956639812, 0.47712125471966244, 0.6020599913279624, 0.6989700043360189]\n",
+      "n= [-0.30000000000000004, 0.226802492411967, 0.5349621957594092, 0.7536049848239341, 0.9231975075880328]\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f7763106d50>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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XWhUVeYxjF+CQiDg5Ik4G3kYyAzkCmJP3B5rVia9ea/0oy0UO94+ITS3bz6b3PS9pS0F1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\nzMwsl38FAoe+bnMSv0IAAAAASUVORK5CYII=\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f7762cd79d0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "from math import log10\n",
+    "%matplotlib inline\n",
+    "from matplotlib.pyplot import plot, title,xlabel,ylabel,show\n",
+    "\n",
+    "#y = a*x**b\n",
+    "a1 = -0.3000#\n",
+    "a = 10**(a1)#\n",
+    "b = 1.75#\n",
+    "print \"a=\",a\n",
+    "x=[];y=[];m=[];n=[];\n",
+    "for i in range(0,5):\n",
+    "    x.append(i+1)\n",
+    "    y.append(a*x[(i)]**b)\n",
+    "    m.append(log10(x[(i)]))\n",
+    "    n.append(log10(y[(i)]))\n",
+    "\n",
+    "print \"x=\",x\n",
+    "print \"y=\",y\n",
+    "print \"m=\",m\n",
+    "print \"n=\",n\n",
+    "plot(x,y)\n",
+    "title('y vs x')\n",
+    "xlabel('x')\n",
+    "ylabel('y')\n",
+    "show()\n",
+    "plot(m,n)\n",
+    "title('log y vs log x')\n",
+    "xlabel('log x')\n",
+    "ylabel('log y')\n",
+    "show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:17.5 Pg: 471"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "sum y = 152.6\n",
+      "sum x = 15\n",
+      "xavg =  2\n",
+      "yavg =  25.4333333333\n",
+      "sum x**2 = 55\n",
+      "sum x**3 = 225\n",
+      "sum x**4 = 979\n",
+      "sum x*y = 585.6\n",
+      "sum x**2 * y = 2488.8\n",
+      "(yi - yavg)**2 =  [4.41, 41.173611111111114, 60.58027777777777, 60.580277777777745, 33.446944444444505, 1332.2500000000005]\n",
+      "(yi - a0 - a1*x - a2*x**2)**2 =  [0.14331632653056853, 1.0028591836732743, 1.0816000000005044, 0.80486530612177265, 0.61959387755180939, 0.094336734693502053]\n",
+      "The standard error of the estimate based on regression polynomial = 1.11752277062\n",
+      "Percentage of original uncertainty that has been explained by the model =  99.7555161238 %\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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EJGcU/CIiOaPgFxHJGQW/SCOZ2b5mNsvM2pjZxslNYXaLXZdIU+nKXZEmMLPL\ngA2BtsACd786ckkiTabgF2mCZJXQacDnwIGuf0BShjTqEWmarYCNgU0IXb9I2VHHL9IEZjYCGAps\nD3R09/MilyTSZK1iFyBSLszsVOAf7v6QmbUAnjezgrsXI5cm0iTq+EVEckYzfhGRnFHwi4jkjIJf\nRCRnFPwiIjmj4BcRyRkFv4hIzij4RURyRsEvIpIz/wdyyqrOJ80ArAAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f777c4e0a90>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "%matplotlib inline\n",
+    "from matplotlib.pyplot import plot, title,xlabel,ylabel,show\n",
+    "from numpy import mat\n",
+    "x = [0,1,2,3,4,5]#\n",
+    "y = [2.1,7.7,13.6,27.2,40.9,61.1]#\n",
+    "sumy = 0#\n",
+    "sumx = 0#\n",
+    "m = 2#\n",
+    "n = 6#\n",
+    "xsqsum = 0#\n",
+    "xcsum = 0#\n",
+    "x4sum = 0#\n",
+    "xysum = 0#\n",
+    "x2ysum = 0#\n",
+    "rsum = 0#\n",
+    "usum = 0#\n",
+    "r=[];s=0\n",
+    "for i in range(0,6):\n",
+    "    s = s + x[i]*y[i]\n",
+    "    sumy = sumy+y[(i)]\n",
+    "    sumx = sumx+x[(i)]\n",
+    "    r.append((y[(i)] - s/n)**2)\n",
+    "    xsqsum = xsqsum + x[(i)]**2\n",
+    "    xcsum = xcsum +x[(i)]**3\n",
+    "    x4sum = x4sum + x[(i)]**4\n",
+    "    xysum = xysum + x[(i)]*y[(i)]\n",
+    "    x2ysum = x2ysum + y[(i)]*x[(i)]**2\n",
+    "    rsum = r[(i)] + rsum\n",
+    "\n",
+    "print \"sum y =\",sumy\n",
+    "print \"sum x =\",sumx\n",
+    "xavg = sumx/n#\n",
+    "yavg = sumy/n#\n",
+    "print \"xavg = \",xavg\n",
+    "print \"yavg = \",yavg\n",
+    "print \"sum x**2 =\",xsqsum\n",
+    "print \"sum x**3 =\",xcsum\n",
+    "print \"sum x**4 =\",x4sum\n",
+    "print \"sum x*y =\",xysum\n",
+    "print \"sum x**2 * y =\",x2ysum\n",
+    "J = mat([[n,sumx,xsqsum],[sumx,xsqsum,xcsum],[xsqsum,xcsum,x4sum]])\n",
+    "I = mat([[sumy],[xysum],[x2ysum]])\n",
+    "X = (J**-1)* I\n",
+    "a0 = X[0,0]\n",
+    "a1 = X[1,0]\n",
+    "a2 = X[2,0]\n",
+    "u=[]\n",
+    "for i in range(0,6):\n",
+    "    u.append((y[(i) ]- a0 - a1*x[(i)] - a2*x[(i)]**2)**2)\n",
+    "    usum = usum + u[i]\n",
+    "\n",
+    "print \"(yi - yavg)**2 = \",r\n",
+    "print \"(yi - a0 - a1*x - a2*x**2)**2 = \",u\n",
+    "plot(x,y)#\n",
+    "title('x vs y')\n",
+    "xlabel('x')\n",
+    "ylabel('y')  \n",
+    "syx = (usum/(n-3))**0.5#\n",
+    "print \"The standard error of the estimate based on regression polynomial =\",syx\n",
+    "R2 = (rsum - usum)/(rsum)#\n",
+    "print \"Percentage of original uncertainty that has been explained by the model = \",R2*100,'%'"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:17.6 Pg: 475"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "a0= -0.850183257587\n",
+      "a1= 7.17727605923\n",
+      "a2= 2.80543175487\n",
+      "Thus, y = a0 + a1*x1 + a2*x2\n"
+     ]
+    }
+   ],
+   "source": [
+    "from numpy import mat\n",
+    "x1 = [0,2,2.5,1,4,7]\n",
+    "x2 = [0,1,2,3,6,2]\n",
+    "x1sum = 0#\n",
+    "x2sum = 0#\n",
+    "ysum = 0#\n",
+    "x12sum = 0#\n",
+    "x22sum = 0#\n",
+    "x1ysum = 0#\n",
+    "x2ysum = 0#\n",
+    "x1x2sum = 0#\n",
+    "n = 6#\n",
+    "x12=[];x22=[];x1x2=[];x1y=[];x2y=[]\n",
+    "for i in range(0,6):\n",
+    "    y.append(5 + 4*x1[(i)] - 3*x2[(i)])\n",
+    "    x12.append(x1[(i)]**2)\n",
+    "    x22.append(x2[(i)]**2)\n",
+    "    x1x2.append(x1[(i)] * x2[(i)])\n",
+    "    x1y.append(x1[(i)] * y[(i)])\n",
+    "    x2y.append(x2[(i)] * y[(i)])\n",
+    "    x1sum = x1sum + x1[(i)]\n",
+    "    x2sum = x2sum + x2[(i)]\n",
+    "    ysum = ysum + y[(i)]\n",
+    "    x1ysum = x1ysum + x1y[(i)]#\n",
+    "    x2ysum = x2ysum + x2y[(i)]#\n",
+    "    x1x2sum = x1x2sum + x1x2[(i)]#\n",
+    "    x12sum = x12sum + x12[(i)]#\n",
+    "    x22sum = x22sum + x22[(i)]#\n",
+    "\n",
+    "X = mat([[n,x1sum,x2sum],[x1sum,x12sum,x1x2sum],[x2sum,x1x2sum,x22sum]])\n",
+    "Y = mat([[ysum],[x1ysum],[x2ysum]])\n",
+    "Z = (X**-1)*Y\n",
+    "a0 = Z[0,0]\n",
+    "a1 = Z[1,0]\n",
+    "a2 = Z[2,0]\n",
+    "print \"a0=\",a0\n",
+    "print \"a1=\",a1\n",
+    "print \"a2=\",a2\n",
+    "print \"Thus, y = a0 + a1*x1 + a2*x2\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:17.7 Pg: 479"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "a0= -0.858655686175\n",
+      "a1= 1.03160389481\n",
+      "standard error of co efficient a0 =  0.716371758333\n",
+      "standard error of co efficient a1 =  0.0186248847544\n",
+      "interval of a0 =  [-2.4062823089821084, 0.68897093663270859]\n",
+      "interval of a1 =  [0.99136728978321009, 1.0718404998372961]\n"
+     ]
+    }
+   ],
+   "source": [
+    "from numpy import mat,exp,transpose,shape,array\n",
+    "#y = -0.859 + 1.032*x\n",
+    "Z = mat([[1,10],[1,16.3],[1,23],[1,27.5],[1,31],[1,35.6],[1,39],[1,41.5],[1,42.9],[1,45],[1,46],[1,45.5],[1,46],[1,49],[1,50]])\n",
+    "Y=[]\n",
+    "for i in range(0,15):\n",
+    "    Y.append(9.8*68.1*(1-exp(-12.5*(i+1)/68.1))/12.5)\n",
+    "Y=array(Y)\n",
+    "Y=Y.reshape(15,1)\n",
+    "M = transpose(Z)\n",
+    "R = M*Z#\n",
+    "S = M*Y#\n",
+    "P = (R**-1)#\n",
+    "X = (R**-1)*S#\n",
+    "a0 = X[0,0]\n",
+    "a1 = X[1,0]\n",
+    "print \"a0=\",a0\n",
+    "print \"a1=\",a1\n",
+    "sxy = 0.863403#\n",
+    "sa0 = ((P[0,0]) * sxy**2)**0.5\n",
+    "sa1 = (P[1,1] * sxy**2)**0.5\n",
+    "print \"standard error of co efficient a0 = \",sa0\n",
+    "print \"standard error of co efficient a1 = \",sa1\n",
+    "TINV = 2.160368#\n",
+    "a0 = [a0 - TINV*(sa0),a0 + TINV*(sa0)]#\n",
+    "a1 = [a1 - TINV*(sa1),a1 + TINV*(sa1)]#\n",
+    "print \"interval of a0 = \",a0\n",
+    "print \"interval of a1 = \",a1"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:17.8 Pg: 481"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Z0 =  [[ 0.22119922  0.1947002 ]\n",
+      " [ 0.52763345  0.35427491]\n",
+      " [ 0.7134952   0.358131  ]\n",
+      " [ 0.82622606  0.3041044 ]\n",
+      " [ 0.89460078  0.23714826]]\n",
+      "D =  [[ 0.05880078]\n",
+      " [ 0.04236655]\n",
+      " [-0.0334952 ]\n",
+      " [-0.08622606]\n",
+      " [-0.10460078]]\n",
+      "X =  [[-0.27147736]\n",
+      " [ 0.50193087]]\n",
+      "The value of a0 after 1st iteration =  0.728522640015\n",
+      "The value of a1 after 1st iteration =  1.5019308677\n"
+     ]
+    }
+   ],
+   "source": [
+    "from math import exp\n",
+    "from numpy import array,transpose,mat\n",
+    "x = [0.25,0.75,1.25,1.75,2.25]#\n",
+    "y = [0.28,0.57,0.68,0.74,0.79]#\n",
+    "a0 = 1#\n",
+    "a1 = 1#\n",
+    "sr = 0.0248#\n",
+    "pda0=[];pda1=[]\n",
+    "for i in range(0,5):\n",
+    "    pda0.append(1 - exp(-a1 * x[(i)]))\n",
+    "    pda1.append(a0 * x[(i)]*exp(-a1*x[(i)]))\n",
+    "\n",
+    "Z0 = mat([[pda0[0],pda1[0]],[pda0[1],pda1[1]],[pda0[2],pda1[2]],[pda0[3],pda1[3]],[pda0[4],pda1[4]]])\n",
+    "print \"Z0 = \",Z0\n",
+    "R = transpose(Z0)*Z0\n",
+    "S = (R**-1)\n",
+    "y1=[];D=[]\n",
+    "for i in range(0,5):\n",
+    "    y1.append(a0 * (1-exp(-a1*x[(i)])))\n",
+    "    D.append(y[(i)] - y1[(i)])\n",
+    "D=array(D)    \n",
+    "D=D.reshape(5,1)\n",
+    "print \"D = \",D\n",
+    "M = transpose(Z0)*D\n",
+    "X = S *M#\n",
+    "print \"X = \",X\n",
+    "a0 = a0 + X[0,0]\n",
+    "a1 = a1 + X[1,0]\n",
+    "print \"The value of a0 after 1st iteration = \",a0\n",
+    "print \"The value of a1 after 1st iteration = \",a1"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 2",
+   "language": "python",
+   "name": "python2"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.9"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter18.ipynb b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter18.ipynb
new file mode 100644
index 00000000..e44e3a7b
--- /dev/null
+++ b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter18.ipynb
@@ -0,0 +1,268 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Chapter-18 : Interpolation"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:18.1 Pg: 490"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "value of ln2 for interpolation region 1 to 6 = 0.3583518\n",
+      "error by interpolation for interval[1,6] = 48.3007635246 %\n",
+      "value of ln2 for interpolation region 1 to 6 = 0.462098\n",
+      "error by interpolation for interval[1,6] = 33.3333506995 %\n"
+     ]
+    }
+   ],
+   "source": [
+    "from math import log\n",
+    "#f1(x) = f0(x) +(f(x1) - f(x0) *(x - x0)/ (x1 - x0)\n",
+    "x = 2#\n",
+    "x0 = 1#\n",
+    "x1 = 6#\n",
+    "m = 1.791759#\n",
+    "n = 0#\n",
+    "r = log(2)#\n",
+    "f = 0 + (m - n) * (x - x0) / (x1 - x0)#\n",
+    "print \"value of ln2 for interpolation region 1 to 6 =\",f\n",
+    "e = (r - f) * 100/r#\n",
+    "print \"error by interpolation for interval[1,6] =\",e,\"%\"\n",
+    "x2 = 4#\n",
+    "p = 1.386294#\n",
+    "f = 0 + (p - n) * (x - x0) / (x2 - x0)#\n",
+    "print \"value of ln2 for interpolation region 1 to 6 =\",f\n",
+    "e = (r - f) * 100/r#\n",
+    "print \"error by interpolation for interval[1,6] =\",e,\"%\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:18.2 Pg: 492"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "b0 =  0\n",
+      "b1 =  0.462098\n",
+      "b2 =  -0.0518731\n",
+      "f(2) =  0.5658442\n",
+      "error =  18.3659378744 %\n"
+     ]
+    }
+   ],
+   "source": [
+    "from math import log\n",
+    "x = 2#\n",
+    "x0 = 1#\n",
+    "m = 0#\n",
+    "x1 = 4#\n",
+    "n = 1.386294#\n",
+    "x2 = 6#\n",
+    "p = 1.791759#\n",
+    "b0 = m#\n",
+    "b1 = (n - m)/(x1 - x0)#\n",
+    "b2 = ((p - n)/(x2 - x1) - (n - m)/(x1 - x0))/(x2 - x0)#\n",
+    "print \"b0 = \",b0\n",
+    "print \"b1 = \",b1\n",
+    "print \"b2 = \",b2\n",
+    "f = b0 + b1*(x - x0) + b2*(x - x0)*(x - x1)#\n",
+    "print \"f(2) = \",f\n",
+    "r = log(2)#\n",
+    "e = (r -f)*100/r#\n",
+    "print \"error = \",e,\"%\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:18.3 Pg: 494"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "b0 =  0\n",
+      "b1 =  0.462098\n",
+      "b2 =  -0.0518731\n",
+      "b3 =  0.0078654\n",
+      "f(2) =  0.6287674\n",
+      "error =  9.28803901474 %\n"
+     ]
+    }
+   ],
+   "source": [
+    "from math import log\n",
+    "x = 2#\n",
+    "x0 = 1#\n",
+    "m = 0#\n",
+    "x1 = 4#\n",
+    "n = 1.386294#\n",
+    "x3 = 5#\n",
+    "p = 1.609438#\n",
+    "x2 = 6#\n",
+    "o = 1.791759#\n",
+    "f01 = (m - n)/(x0 - x1)#\n",
+    "f12 = (n - o)/(x1 - x2)#\n",
+    "f23 = (p - o)/(x3 - x2)#\n",
+    "f210 =  (f12 - f01)/(x2 - x0)#\n",
+    "f321 = (f23 - f12)/(x3 - x1)#\n",
+    "f0123 = (f321 - f210) / (x3 - x0)#\n",
+    "b0 = m#\n",
+    "b1 = f01#\n",
+    "b2 = f210#\n",
+    "b3 = f0123#\n",
+    "print \"b0 = \",b0\n",
+    "print \"b1 = \",b1\n",
+    "print \"b2 = \",b2\n",
+    "print \"b3 = \",b3\n",
+    "f = b0 + b1*(x - x0) + b2*(x - x0)*(x - x1) + b3*(x - x0)*(x - x1)*(x - x2)#\n",
+    "print \"f(2) = \",f\n",
+    "r = log(2)#\n",
+    "e = (r -f)*100/r#\n",
+    "print \"error = \",e,\"%\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:18.4 Pg: 496"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "error R2 =  0.0629232\n"
+     ]
+    }
+   ],
+   "source": [
+    "x = 2#\n",
+    "x0 = 1#\n",
+    "m = 0#\n",
+    "x1 = 4#\n",
+    "n = 1.386294#\n",
+    "x3 = 5#\n",
+    "p = 1.609438#\n",
+    "x2 = 6#\n",
+    "o = 1.791759#\n",
+    "f01 = (m - n)/(x0 - x1)#\n",
+    "f12 = (n - o)/(x1 - x2)#\n",
+    "f23 = (p - o)/(x3 - x2)#\n",
+    "f210 =  (f12 - f01)/(x2 - x0)#\n",
+    "f321 = (f23 - f12)/(x3 - x1)#\n",
+    "f0123 = (f321 - f210) / (x3 - x0)#\n",
+    "b0 = m#\n",
+    "b1 = f01#\n",
+    "b2 = f210#\n",
+    "b3 = f0123#\n",
+    "R2 = b3 * (x - x0) * (x - x1)*(x-x2)#\n",
+    "print \"error R2 = \",R2"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:18.6 Pg: 501"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "first order polynomial f1(2) =  0.462098\n",
+      "second order polynomial f2(2) =  0.5658442\n"
+     ]
+    }
+   ],
+   "source": [
+    "x = 2#\n",
+    "x0 = 1#\n",
+    "m = 0#\n",
+    "x1 = 4#\n",
+    "n = 1.386294#\n",
+    "x2 = 6#\n",
+    "p = 1.791759#\n",
+    "f1 = (x - x1)*m/((x0 - x)) + (x- x0) * n/(x1 - x0)#\n",
+    "print \"first order polynomial f1(2) = \",f1\n",
+    "f2 = (x - x1)*(x - x2)*m/((x0 - x1)*(x0 - x2)) + (x - x0)*(x - x2)*n/((x1-x0)*(x1-x2)) + (x - x0)*(x - x1)*p/((x2 - x0)*(x2 - x1))#\n",
+    "print \"second order polynomial f2(2) = \",f2"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 2",
+   "language": "python",
+   "name": "python2"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.9"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter19.ipynb b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter19.ipynb
new file mode 100644
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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "collapsed": true
+   },
+   "source": [
+    "# Chapter-19 : Fourier Approximation"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:19.1 Pg: 529"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The least square fit is y=A0+A1*cos(w0*t)+A2*sin(w0*t), where\n",
+      "A0= 1.70003783298\n",
+      "A1= 0.500211429839\n",
+      "B1= -0.866058310862\n",
+      "Alternatively, the least square fit can be expressed as\n",
+      "y=A0+C1*cos(w0*t + theta), where\n",
+      "A0= 1.70003783298\n",
+      "Theta= 1.04703092349\n",
+      "C1= 1.00013422717\n",
+      "Or\n",
+      "y=A0+C1*sin(w0*t + theta + pi/2), where\n",
+      "A0= 1.70003783298\n",
+      "Theta= 1.04703092349\n",
+      "C1= 1.00013422717\n"
+     ]
+    }
+   ],
+   "source": [
+    "from math import sin,cos,atan\n",
+    "def f(t):\n",
+    "    y=1.7+cos(4.189*t+1.0472)\n",
+    "    return y\n",
+    "deltat=0.15#\n",
+    "t1=0#\n",
+    "t2=1.35#\n",
+    "omega=4.189#\n",
+    "Del=(t2-t1)/9#\n",
+    "t=[]\n",
+    "for i in range(1,11):\n",
+    "    t.append(t1+Del*(i-1))\n",
+    "\n",
+    "sumy=0#\n",
+    "suma=0#\n",
+    "sumb=0#\n",
+    "y=[];a=[];b=[]\n",
+    "for i in range(1,11):\n",
+    "    y.append(f(t[i-1]))\n",
+    "    a.append(y[(i-1)]*cos(omega*t[(i-1)]))\n",
+    "    b.append(y[i-1]*sin(omega*t[i-1]))\n",
+    "    sumy=sumy+y[i-1]\n",
+    "    suma=suma+a[i-1]\n",
+    "    sumb=sumb+b[i-1]\n",
+    "\n",
+    "A0=sumy/10#\n",
+    "A1=2*suma/10#\n",
+    "B1=2*sumb/10#\n",
+    "print \"The least square fit is y=A0+A1*cos(w0*t)+A2*sin(w0*t), where\"\n",
+    "print \"A0=\",A0\n",
+    "print \"A1=\",A1\n",
+    "print \"B1=\",B1\n",
+    "theta=atan(-B1/A1)#\n",
+    "C1=(A1**2 + B1**2)**0.5#\n",
+    "print \"Alternatively, the least square fit can be expressed as\"\n",
+    "print \"y=A0+C1*cos(w0*t + theta), where\"\n",
+    "print \"A0=\",A0\n",
+    "print \"Theta=\",theta\n",
+    "print \"C1=\",C1\n",
+    "print \"Or\"\n",
+    "print \"y=A0+C1*sin(w0*t + theta + pi/2), where\"\n",
+    "print \"A0=\",A0\n",
+    "print \"Theta=\",theta\n",
+    "print \"C1=\",C1\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:19.2 Pg: 532"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The fourier approximtion is:\n",
+      "4/(pi)*cos(w)*t) - 4/(3*pi)*cos(3*(w)*t) + 4/(5*pi)*cos(5*(w)*t) - 4/(7*pi)*cos(7*(w)*t) + .....\n"
+     ]
+    }
+   ],
+   "source": [
+    "a0=0#\n",
+    "#f(t)=-1 for -T/2 to -T/4\n",
+    "#f(t)=1 for -T/4 to T/4\n",
+    "#f(t)=-1 for T/4 to T/2\n",
+    "#ak=2/T* (integration of f(t)*cos(w0*t) from -T/2 to T/2)\n",
+    "#ak=2/T*((integration of f(t)*cos(w0*t) from -T/2 to -T/4) + (integration of f(t)*cos(w0*t) from -T/4 to T/4) + (integration of f(t)*cos(w0*t) from T/4 to T/2))\n",
+    "#Therefore, \n",
+    "#ak=4/(k*pi) for k=1,5,9,.....\n",
+    "#ak=-4/(k*pi) for k=3,7,11,.....\n",
+    "#ak=0 for k=even integers\n",
+    "#similarly we find the b's.\n",
+    "#all the b's=0\n",
+    "print \"The fourier approximtion is:\"\n",
+    "print \"4/(pi)*cos(w)*t) - 4/(3*pi)*cos(3*(w)*t) + 4/(5*pi)*cos(5*(w)*t) - 4/(7*pi)*cos(7*(w)*t) + .....\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:19.3 Pg: 550"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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mTgz7/ohIcVN3kLTY6tVhv5/KSpg6FXr2jF2RiDSWQkBaZNGisMlb586h+2eLLWJXJCJN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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f1a75daff90>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "from numpy import arange,log\n",
+    "%matplotlib inline\n",
+    "from matplotlib.pyplot import plot, title,xlabel,ylabel,show\n",
+    "x=arange(0.5,5.6,0.5)\n",
+    "y=[]\n",
+    "for i in range(1,12):\n",
+    "    y.append(0.9846*log(x[i-1])+1.0004)\n",
+    "\n",
+    "plot(x,y)\n",
+    "title(\"y vs x\")\n",
+    "xlabel(\"x\")\n",
+    "ylabel(\"y\")\n",
+    "show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:19.6 Pg: 555"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The cubic polynomial is y=a0 + a1*x + a2*x**2 + a3*x**3, where a0, a1, a2 and a3 are\n",
+      "[[ 1.67644593  0.76697402  0.5511316   0.46451844]\n",
+      " [ 2.56065822  1.84003582  1.55086475  1.40157818]\n",
+      " [ 3.36495108  2.83613174  2.5631251   2.40990305]\n",
+      " [ 3.94388659  3.56424723  3.35117872  3.23471752]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "from numpy import nditer,mat,divide\n",
+    "x=[0.05, 0.12, 0.15, 0.3, 0.45 ,0.7 ,0.84 ,1.05]\n",
+    "y=[0.957, 0.851, 0.832, 0.72 ,0.583, 0.378, 0.295, 0.156]\n",
+    "sx=sum(x)#\n",
+    "sxx=0\n",
+    "for xx in x:\n",
+    "    sxx+=xx*xx\n",
+    "sx3=0\n",
+    "for xx in x:\n",
+    "    sx3+=xx*xx*xx\n",
+    "sx4=0\n",
+    "for xx in x:\n",
+    "    sx4+=xx*xx*xx*xx\n",
+    "\n",
+    "sx5=0\n",
+    "for xx in x:\n",
+    "    sx5+=xx*xx*xx*xx*xx\n",
+    "    \n",
+    "sx6=0\n",
+    "for xx in x:\n",
+    "    sx6+=xx*xx*xx*xx*xx*xx\n",
+    "\n",
+    "n=8#\n",
+    "sy=sum(y)#\n",
+    "sxy=0\n",
+    "for xx,yy in nditer([x,y]):\n",
+    "    sxy+=xx*yy\n",
+    "    \n",
+    "    \n",
+    "sx2y=0\n",
+    "for xx,yy in nditer([x,y]):\n",
+    "    sx2y+=xx*xx*yy\n",
+    "\n",
+    "sx3y=0\n",
+    "for xx,yy in nditer([x,y]):\n",
+    "    sx3y+=xx*xx*xx*yy\n",
+    "\n",
+    "m=mat([[n, sx, sxx ,sx3],[sx, sxx, sx3, sx4],[sxx, sx3, sx4, sx5],[sx3, sx4, sx5, sx6]])\n",
+    "p=mat([[sy],[sxy],[sx2y],[sx3y]])\n",
+    "a=divide(m,p)\n",
+    "print \"The cubic polynomial is y=a0 + a1*x + a2*x**2 + a3*x**3, where a0, a1, a2 and a3 are\"\n",
+    "print a"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 2",
+   "language": "python",
+   "name": "python2"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.9"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter21.ipynb b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter21.ipynb
new file mode 100644
index 00000000..507735ab
--- /dev/null
+++ b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter21.ipynb
@@ -0,0 +1,725 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Chapter 21 Newtin-cotes integration formula"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex : 21.1   Pg : 612"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The Error Et= 1.468\n",
+      "The percent relative error et= 89.467 %\n",
+      "The approximate error estimate without using the true value= 2.56\n"
+     ]
+    }
+   ],
+   "source": [
+    "from __future__ import division\n",
+    "def f(x):\n",
+    "    y=(0.2+25*x-200*x**2+675*x**3-900*x**4+400*x**5)\n",
+    "    return y\n",
+    "tval=1.640533#\n",
+    "a=0#\n",
+    "b=0.8#\n",
+    "fa=f(a)#\n",
+    "fb=f(b)#\n",
+    "l=(b-a)*((fa+fb)/2)#\n",
+    "Et=tval-l##error\n",
+    "et=Et*100/tval##percent relative error\n",
+    "\n",
+    "#by using approximate error estimate\n",
+    "\n",
+    "#the second derivative of f\n",
+    "def g(x):\n",
+    "    y=-400+4050*x-10800*x**2+8000*x**3\n",
+    "    return y\n",
+    "\n",
+    "from sympy.mpmath import quad\n",
+    "f2x=quad(g,[0,0.8])/(b-a)##average value of second derivative\n",
+    "Ea=-(1/12)*(f2x)*(b-a)**3#\n",
+    "print \"The Error Et=\",round(Et,3)\n",
+    "print \"The percent relative error et=\",round(et,3),\"%\"\n",
+    "print \"The approximate error estimate without using the true value=\",Ea"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex : 21.2   Pg : 613"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The Error Et= 0.572\n",
+      "The percent relative error et= 34.85 %\n",
+      "The approximate error estimate without using the true value= 0.64\n"
+     ]
+    }
+   ],
+   "source": [
+    "def f(x):\n",
+    "    y=(0.2+25*x-200*x**2+675*x**3-900*x**4+400*x**5)\n",
+    "    return y\n",
+    "a=0#\n",
+    "b=0.8#\n",
+    "tval=1.640533#\n",
+    "n=2#\n",
+    "h=(b-a)/n#\n",
+    "fa=f(a)#\n",
+    "fb=f(b)#\n",
+    "fh=f(h)#\n",
+    "l=(b-a)*(fa+2*fh+fb)/(2*n)#\n",
+    "Et=tval-l##error\n",
+    "et=Et*100/tval##percent relative error\n",
+    "\n",
+    "#by using approximate error estimate\n",
+    "\n",
+    "#the second derivative of f\n",
+    "def g(x):\n",
+    "    y=-400+4050*x-10800*x**2+8000*x**3\n",
+    "    return y\n",
+    "f2x=quad(g,[0,0.8])/(b-a)##average value of second derivative\n",
+    "Ea=-(1/12)*(f2x)*(b-a)**3/(n**2)#\n",
+    "print \"The Error Et=\",round(Et,3)\n",
+    "print \"The percent relative error et=\",round(et,3),\"%\"\n",
+    "print \"The approximate error estimate without using the true value=\",Ea"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex :21.3    Pg : 614"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "No. of segments= 10\n",
+      "Segment size= 1.0\n",
+      "Estimated d= 288.749146143 m\n",
+      "0.237014701487 et(%)\n",
+      "---------------------------------------------------------\n",
+      "No. of segments= 20\n",
+      "Segment size= 0.5\n",
+      "Estimated d= 289.263574224 m\n",
+      "0.0592795228803 et(%)\n",
+      "---------------------------------------------------------\n",
+      "No. of segments= 50\n",
+      "Segment size= 0.2\n",
+      "Estimated d= 298.382319223 m\n",
+      "et(%) -3.09125177877\n",
+      "---------------------------------------------------------\n",
+      "No. of segments= 100\n",
+      "Segment size= 0.1\n",
+      "Estimated d= 293.915596452 m\n",
+      "et(%) -1.54799665905\n",
+      "---------------------------------------------------------\n",
+      "No. of segments= 100\n",
+      "Segment size= 0.1\n",
+      "Estimated d= 293.915596452 m\n",
+      "et(%) -1.54799665905\n",
+      "---------------------------------------------------------\n",
+      "No. of segments= 200\n",
+      "Segment size= 0.05\n",
+      "Estimated d= 289.43343055 m\n",
+      "et(%) 0.000594070904571\n",
+      "---------------------------------------------------------\n",
+      "No. of segments= 200\n",
+      "Segment size= 0.05\n",
+      "Estimated d= 289.43343055 m\n",
+      "et(%) 0.000594070904571\n",
+      "---------------------------------------------------------\n",
+      "No. of segments= 500\n",
+      "Segment size= 0.02\n",
+      "Estimated d= 290.332334709 m\n",
+      "et(%) -0.309977799375\n",
+      "---------------------------------------------------------\n",
+      "No. of segments= 1000\n",
+      "Segment size= 0.01\n",
+      "Estimated d= 289.883809248 m\n",
+      "et(%) -0.155012011658\n",
+      "---------------------------------------------------------\n",
+      "No. of segments= 2000\n",
+      "Segment size= 0.005\n",
+      "Estimated d= 289.435129352 m\n",
+      "et(%) 7.13401428866e-06\n",
+      "---------------------------------------------------------\n",
+      "No. of segments= 2000\n",
+      "Segment size= 0.005\n",
+      "Estimated d= 289.435129352 m\n",
+      "et(%) 7.13401428866e-06\n",
+      "---------------------------------------------------------\n",
+      "No. of segments= 5000\n",
+      "Segment size= 0.002\n",
+      "Estimated d= 289.435143766 m\n",
+      "et(%) 2.15393877364e-06\n",
+      "---------------------------------------------------------\n",
+      "No. of segments= 5000\n",
+      "Segment size= 0.002\n",
+      "Estimated d= 289.435143766 m\n",
+      "et(%) 2.15393877364e-06\n",
+      "---------------------------------------------------------\n",
+      "No. of segments= 10000\n",
+      "Segment size= 0.001\n",
+      "Estimated d= 289.480018962 m\n",
+      "et(%) -0.0155022506708\n",
+      "---------------------------------------------------------\n"
+     ]
+    }
+   ],
+   "source": [
+    "g=9.8##m/s**2# acceleration due to gravity\n",
+    "m=68.1##kg\n",
+    "c=12.5##kg/sec# drag coefficient\n",
+    "def f(t):\n",
+    "    from numpy import exp\n",
+    "    v=g*m*(1-exp(-c*t/m))/c\n",
+    "    return v\n",
+    "tval=289.43515##m\n",
+    "a=0#\n",
+    "b=10#\n",
+    "fa=f(a)#\n",
+    "fb=f(b)#\n",
+    "from numpy import arange, exp\n",
+    "for i in arange(10,21,10):\n",
+    "    n=i#\n",
+    "    h=(b-a)/n#\n",
+    "    print \"No. of segments=\",i\n",
+    "    print \"Segment size=\",h\n",
+    "    j=a+h#\n",
+    "    s=0#\n",
+    "    while j<b:\n",
+    "        s=s+f(j)#\n",
+    "        j=j+h#\n",
+    "    \n",
+    "    l=(b-a)*(fa+2*s+fb)/(2*n)#\n",
+    "    Et=tval-l##error\n",
+    "    et=Et*100/tval##percent relative error\n",
+    "    print \"Estimated d=\",l,\"m\"\n",
+    "    print et,\"et(%)\"\n",
+    "    print \"---------------------------------------------------------\"\n",
+    "\n",
+    "for i in arange(50,101,50):\n",
+    "    n=i#\n",
+    "    h=(b-a)/n#\n",
+    "    print \"No. of segments=\",i\n",
+    "    print \"Segment size=\",h\n",
+    "    j=a+h#\n",
+    "    s=0#\n",
+    "    while j<b:\n",
+    "        s=s+f(j)#\n",
+    "        j=j+h#\n",
+    "    \n",
+    "    l=(b-a)*(fa+2*s+fb)/(2*n)#\n",
+    "    Et=tval-l##error\n",
+    "    et=Et*100/tval##percent relative error\n",
+    "    print \"Estimated d=\",l,\"m\"\n",
+    "    print \"et(%)\",et\n",
+    "    print \"---------------------------------------------------------\"\n",
+    "\n",
+    "for i in arange(100,201,100):\n",
+    "    n=i#\n",
+    "    h=(b-a)/n#\n",
+    "    print \"No. of segments=\",i\n",
+    "    print \"Segment size=\",h\n",
+    "    j=a+h#\n",
+    "    s=0#\n",
+    "    while j<b:\n",
+    "        s=s+f(j)#\n",
+    "        j=j+h#\n",
+    "    \n",
+    "    l=(b-a)*(fa+2*s+fb)/(2*n)#\n",
+    "    Et=tval-l##error\n",
+    "    et=Et*100/tval##percent relative error\n",
+    "    print \"Estimated d=\",l,\"m\"\n",
+    "    print \"et(%)\",et\n",
+    "    print \"---------------------------------------------------------\"\n",
+    "\n",
+    "for i in arange(200,501,300):\n",
+    "    n=i#\n",
+    "    h=(b-a)/n#\n",
+    "    print \"No. of segments=\",i\n",
+    "    print \"Segment size=\",h\n",
+    "    j=a+h#\n",
+    "    s=0#\n",
+    "    while j<b:\n",
+    "        s=s+f(j)#\n",
+    "        j=j+h#\n",
+    "    \n",
+    "    l=(b-a)*(fa+2*s+fb)/(2*n)#\n",
+    "    Et=tval-l##error\n",
+    "    et=Et*100/tval##percent relative error\n",
+    "    print \"Estimated d=\",l,\"m\"\n",
+    "    print \"et(%)\",et\n",
+    "    print \"---------------------------------------------------------\"\n",
+    "\n",
+    "for i in arange(1000,2001,1000):\n",
+    "    n=i#\n",
+    "    h=(b-a)/n#\n",
+    "    print \"No. of segments=\",i\n",
+    "    print \"Segment size=\",h\n",
+    "    j=a+h#\n",
+    "    s=0#\n",
+    "    while j<b:\n",
+    "        s=s+f(j)#\n",
+    "        j=j+h#\n",
+    "    \n",
+    "    l=(b-a)*(fa+2*s+fb)/(2*n)#\n",
+    "    Et=tval-l##error\n",
+    "    et=Et*100/tval##percent relative error\n",
+    "    print \"Estimated d=\",l,\"m\"\n",
+    "    print \"et(%)\",et\n",
+    "    print \"---------------------------------------------------------\"\n",
+    "\n",
+    "for i in arange(2000,5001,3000):\n",
+    "    n=i#\n",
+    "    h=(b-a)/n#\n",
+    "    print \"No. of segments=\",i\n",
+    "    print \"Segment size=\",h\n",
+    "    j=a+h#\n",
+    "    s=0#\n",
+    "    while j<b:\n",
+    "        s=s+f(j)#\n",
+    "        j=j+h#\n",
+    "    \n",
+    "    l=(b-a)*(fa+2*s+fb)/(2*n)#\n",
+    "    Et=tval-l##error\n",
+    "    et=Et*100/tval##percent relative error\n",
+    "    print \"Estimated d=\",l,\"m\"\n",
+    "    print \"et(%)\",et\n",
+    "    print \"---------------------------------------------------------\"\n",
+    "\n",
+    "for i in arange(5000,10001,5000):\n",
+    "    n=i#\n",
+    "    h=(b-a)/n#\n",
+    "    print \"No. of segments=\",i\n",
+    "    print \"Segment size=\",h\n",
+    "    j=a+h#\n",
+    "    s=0#\n",
+    "    while j<b:\n",
+    "        s=s+f(j)#\n",
+    "        j=j+h#\n",
+    "    \n",
+    "    l=(b-a)*(fa+2*s+fb)/(2*n)#\n",
+    "    Et=tval-l##error\n",
+    "    et=Et*100/tval##percent relative error\n",
+    "    print \"Estimated d=\",l,\"m\"\n",
+    "    print \"et(%)\",et\n",
+    "    print \"---------------------------------------------------------\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex : 21.4   Pg : 618"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "l= 1.37\n",
+      "The Error Et= 0.27\n",
+      "The percent relative error et= 16.645 %\n",
+      "The approximate error estimate without using the true value= 0.273\n"
+     ]
+    }
+   ],
+   "source": [
+    "def f(x):\n",
+    "    y=(0.2+25*x-200*x**2+675*x**3-900*x**4+400*x**5)\n",
+    "    return y\n",
+    "a=0#\n",
+    "b=0.8#\n",
+    "tval=1.640533#\n",
+    "n=2#\n",
+    "h=(b-a)/n#\n",
+    "fa=f(a)#\n",
+    "fb=f(b)#\n",
+    "fh=f(h)#\n",
+    "l=(b-a)*(fa+4*fh+fb)/(3*n)#\n",
+    "print\"l=\", round(l,2)\n",
+    "Et=tval-l##error\n",
+    "et=Et*100/tval##percent relative error\n",
+    "\n",
+    "#by using approximate error estimate\n",
+    "\n",
+    "#the fourth derivative of f\n",
+    "def g(x):\n",
+    "    y=-21600+48000*x\n",
+    "    return y\n",
+    "\n",
+    "f4x=quad(g,[0,0.8])/(b-a)##average value of fourth derivative\n",
+    "Ea=-(1/2880)*(f4x)*(b-a)**5#\n",
+    "print \"The Error Et=\",round(Et,2)\n",
+    "print \"The percent relative error et=\",round(et,3),\"%\"\n",
+    "print \"The approximate error estimate without using the true value=\",round(Ea,3)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex : 23.5   Pg : 620"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "l= 1.62\n",
+      "The Error Et= 0.02\n",
+      "The percent relative error et= 1.04 %\n",
+      "The approximate error estimate without using the true value= 0.017\n"
+     ]
+    }
+   ],
+   "source": [
+    "def f(x):\n",
+    "    y=(0.2+25*x-200*x**2+675*x**3-900*x**4+400*x**5)\n",
+    "    return y\n",
+    "a=0#\n",
+    "b=0.8#\n",
+    "tval=1.640533#\n",
+    "n=4#\n",
+    "h=(b-a)/n#\n",
+    "fa=f(a)#\n",
+    "fb=f(b)#\n",
+    "j=a+h#\n",
+    "s=0#\n",
+    "count=1#\n",
+    "while j<b:\n",
+    "    if (-1)**count==-1:\n",
+    "        s=s+4*f(j)#\n",
+    "    else:\n",
+    "        s=s+2*f(j)#\n",
+    "    \n",
+    "    count=count+1#\n",
+    "    j=j+h#\n",
+    "\n",
+    "l=(b-a)*(fa+s+fb)/(3*n)#\n",
+    "print\"l=\", round(l,2)\n",
+    "Et=tval-l##error\n",
+    "et=Et*100/tval##percent relative error\n",
+    "\n",
+    "#by using approximate error estimate\n",
+    "\n",
+    "#the fou:rth derivative of f\n",
+    "def g(x):\n",
+    "    y=-21600+48000*x\n",
+    "    return y\n",
+    "f4x=quad(g,[0,0.8])/(b-a)##average value of fourth derivative\n",
+    "Ea=-(1/(180*4**4))*(f4x)*(b-a)**5#\n",
+    "print \"The Error Et=\",round(Et,2)\n",
+    "print \"The percent relative error et=\",round(et,3),\"%\"\n",
+    "print \"The approximate error estimate without using the true value=\",round(Ea,3)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex :23.6    Pg : 625"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Part A:\n",
+      "l= 1.519\n",
+      "The Error Et= 0.12\n",
+      "The percent relative error et= 7.398 %\n",
+      "The approximate error estimate without using the true value= 0.121\n",
+      "---------------------------------------------------\n",
+      "Part B:\n",
+      "l= 1.645\n",
+      "The Error Et= -0.005\n",
+      "The percent relative error et= -0.277 %\n"
+     ]
+    }
+   ],
+   "source": [
+    "def f(x):\n",
+    "    y=(0.2+25*x-200*x**2+675*x**3-900*x**4+400*x**5)\n",
+    "    return y\n",
+    "a=0#\n",
+    "b=0.8#\n",
+    "tval=1.640533#\n",
+    "#part a\n",
+    "n=3#\n",
+    "h=(b-a)/n#\n",
+    "fa=f(a)#\n",
+    "fb=f(b)#\n",
+    "j=a+h#\n",
+    "s=0#\n",
+    "count=1#\n",
+    "while j<b:\n",
+    "    s=s+3*f(j)#\n",
+    "    count=count+1#\n",
+    "    j=j+h#\n",
+    "\n",
+    "l=(b-a)*(fa+s+fb)/(8)#\n",
+    "print \"Part A:\"\n",
+    "print \"l=\",round(l,3)\n",
+    "Et=tval-l##error\n",
+    "et=Et*100/tval##percent relative error\n",
+    "\n",
+    "#by using approximate error estimate\n",
+    "\n",
+    "#the fourth derivative of f\n",
+    "def g(x):\n",
+    "    y=-21600+48000*x\n",
+    "    return y\n",
+    "f4x=quad(g,[0,0.8])/(b-a)##average value of fourth derivative\n",
+    "Ea=-(1/6480)*(f4x)*(b-a)**5#\n",
+    "print \"The Error Et=\",round(Et,2)\n",
+    "print \"The percent relative error et=\",round(et,3),\"%\"\n",
+    "print \"The approximate error estimate without using the true value=\",round(Ea,3)\n",
+    "#part b\n",
+    "n=5#\n",
+    "h=(b-a)/n#\n",
+    "l1=(a+2*h-a)*(fa+4*f(a+h)+f(a+2*h))/6#\n",
+    "l2=(a+5*h-a-2*h)*(f(a+2*h)+3*(f(a+3*h)+f(a+4*h))+fb)/8#\n",
+    "l=l1+l2#\n",
+    "print \"---------------------------------------------------\"\n",
+    "print \"Part B:\"\n",
+    "print \"l=\", round(l,3)\n",
+    "Et=tval-l##error\n",
+    "et=Et*100/tval##percent relative error\n",
+    "print \"The Error Et=\", round(Et,3)\n",
+    "print \"The percent relative error et=\", round(et,3), \"%\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex : 23.7   Pg : 626"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "l= 1.59480096\n",
+      "The Error Et= 0.04573204\n",
+      "The percent relative error et= 2.78763304365 %\n"
+     ]
+    }
+   ],
+   "source": [
+    "def f(x):\n",
+    "    y=(0.2+25*x-200*x**2+675*x**3-900*x**4+400*x**5)\n",
+    "    return y\n",
+    "tval=1.640533#\n",
+    "x=[0, 0.12, 0.22, 0.32, 0.36, 0.4 ,0.44 ,0.54 ,0.64 ,0.7 ,0.8]\n",
+    "func=[]\n",
+    "for i in range(0,11):\n",
+    "    func.append(f(x[i]))#\n",
+    "\n",
+    "l=0#\n",
+    "for i in range(0,10):\n",
+    "    l=l+(x[i+1]-x[i])*(func[i]+func[i+1])/2#\n",
+    "\n",
+    "print \"l=\",l\n",
+    "Et=tval-l##error\n",
+    "et=Et*100/tval##percent relative error\n",
+    "print \"The Error Et=\",Et\n",
+    "print \"The percent relative error et=\",et,\"%\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex : 23.8   Pg : 230"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "l= 1.60364091733\n",
+      "The Error Et= 0.0368920826667\n",
+      "The percent relative error et= 2.2487863802 %\n"
+     ]
+    }
+   ],
+   "source": [
+    "def f(x):\n",
+    "    y=(0.2+25*x-200*x**2+675*x**3-900*x**4+400*x**5)\n",
+    "    return y\n",
+    "tval=1.640533#\n",
+    "x=[0, 0.12, 0.22, 0.32, 0.36, 0.4 ,0.44 ,0.54, 0.64, 0.7, 0.8]\n",
+    "func =[]\n",
+    "for i in range(0,11):\n",
+    "    func.append(f(x[i]))\n",
+    "\n",
+    "l1=(x[1]-x[0])*((f(x[0])+f(x[1]))/2)#\n",
+    "l2=(x[3]-x[1])*(f(x[3])+4*f(x[2])+f(x[1]))/6#\n",
+    "l3=(x[6]-x[3])*(f(x[3])+3*(f(x[4])+f(x[5]))+f(x[6]))/8#\n",
+    "l4=(x[8]-x[6])*(f(x[6])+4*f(x[7])+f(x[8]))/6\n",
+    "l5=(x[9]-x[8])*((f(x[9])+f(x[8]))/2)#\n",
+    "l6=(x[10]-x[9])*((f(x[10])+f(x[9]))/2)#\n",
+    "l=l1+l2+l3+l4+l5+l6#\n",
+    "print \"l=\",l\n",
+    "Et=tval-l##error\n",
+    "et=Et*100/tval##percent relative error\n",
+    "print \"The Error Et=\",Et\n",
+    "print \"The percent relative error et=\",et,\"%\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex : 23.9   Pg : 629"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The average termperature is= 53.0\n"
+     ]
+    }
+   ],
+   "source": [
+    "def f(x,y):\n",
+    "    t=2*x*y+2*x-x**2-2*y**2+72\n",
+    "    return t\n",
+    "Len=8##m,length\n",
+    "wid=6##m,width\n",
+    "a=0#\n",
+    "b=Len#\n",
+    "n=2#\n",
+    "h=(b-a)/n#\n",
+    "a1=0#\n",
+    "b1=wid#\n",
+    "h1=(b1-a1)/n#\n",
+    "\n",
+    "fa=f(a,0)#\n",
+    "fb=f(b,0)#\n",
+    "fh=f(h,0)#\n",
+    "lx1=(b-a)*(fa+2*fh+fb)/(2*n)#\n",
+    "\n",
+    "fa=f(a,h1)#\n",
+    "fb=f(b,h1)#\n",
+    "fh=f(h,h1)#\n",
+    "lx2=(b-a)*(fa+2*fh+fb)/(2*n)#\n",
+    "\n",
+    "fa=f(a,b1)#\n",
+    "fb=f(b,b1)#\n",
+    "fh=f(h,b1)#\n",
+    "lx3=(b-a)*(fa+2*fh+fb)/(2*n)#\n",
+    "\n",
+    "l=(b1-a1)*(lx1+2*lx2+lx3)/(2*n)#\n",
+    "\n",
+    "avg_temp=l/(Len*wid)#\n",
+    "print\"The average termperature is=\", avg_temp"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 2",
+   "language": "python",
+   "name": "python2"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.9"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter22.ipynb b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter22.ipynb
new file mode 100644
index 00000000..50a8dfb0
--- /dev/null
+++ b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter22.ipynb
@@ -0,0 +1,334 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Chapter-22 : Integration of Equations"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:22.1 Pg: 624"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Error of the improved integral for segment 1 and 2 =  16.6449765615 %\n",
+      "Error of the improved integral for segment 4 and 2 =  1.04029198641 %\n"
+     ]
+    }
+   ],
+   "source": [
+    "h = [0,0.8,0.4,0.2]#\n",
+    "I = [0,0.1728,1.0688,1.4848]#\n",
+    "E = [0,89.5,34.9,9.5]#\n",
+    "I1 = 4 * I[(2)] / 3 - I[(1)] / 3#\n",
+    "t = 1.640533#\n",
+    "et1 = t - I1 #\n",
+    "Et1 = et1 * 100/t#\n",
+    "print \"Error of the improved integral for segment 1 and 2 = \",Et1,\"%\"\n",
+    "I2 = 4 * I[(3)] / 3 - I[(2)] / 3#\n",
+    "et2 = t - I2 #\n",
+    "Et2 = et2 * 100/t#\n",
+    "print \"Error of the improved integral for segment 4 and 2 = \",Et2,\"%\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:22.2 Pg: 645"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Obtained integral which is the correct answer till the seventh decimal 1.64053366667\n"
+     ]
+    }
+   ],
+   "source": [
+    "I1 = 1.367467#\n",
+    "I2 = 1.623467#\n",
+    "I = 16 * I2 /15 - I1 / 15#\n",
+    "print \"Obtained integral which is the correct answer till the seventh decimal\",I"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:22.3 Pg: 645"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Integral obtained using gauss legendre formulae = 1.9648\n",
+      "error =  -19.7659541137 %\n"
+     ]
+    }
+   ],
+   "source": [
+    "#f(x) = 0.2 + 25*x - 200*x**2 + 675*x**3 - 900*x**4 + 400*x**5\n",
+    "# for using two point gauss legendre formulae, the intervals have to be changed to -1 and 1\n",
+    "#therefore, x = 0.4 + 0.4 * xd\n",
+    "#thus the integral is transferred to \n",
+    "#(0.2 + 25*(0.4+0.4*x) - 200*(0.4 + 0.4*x)**2 + 675*(0.4 + 0.4*x)**3 - 900*(0.4 + 0.4*x)**4 + 400*(0.4 + 0.4*x)**5)*0.4\n",
+    "#for three point gauss legendre formulae\n",
+    "x1 = -(1/3) ** 0.5#\n",
+    "x2 = (1/3) ** 0.5#\n",
+    "I1 = (0.2 + 25*(0.4+0.4*x1) - 200*(0.4 + 0.4*x1)**2 + 675*(0.4 + 0.4*x1)**3 - 900*(0.4 + 0.4*x1)**4 + 400*(0.4 + 0.4*x1)**5)*0.4#\n",
+    "I2 = (0.2 + 25*(0.4+0.4*x2) - 200*(0.4 + 0.4*x2)**2 + 675*(0.4 + 0.4*x2)**3 - 900*(0.4 + 0.4*x2)**4 + 400*(0.4 + 0.4*x2)**5)*0.4#\n",
+    "I = I1 + I2#\n",
+    "print \"Integral obtained using gauss legendre formulae =\",I\n",
+    "t = 1.640533#\n",
+    "e = (t - I)*100/t#\n",
+    "print \"error = \",e,\"%\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Ex:22.4 Pg: 647"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "integral obtained using three point gauss legendre formulae =  1.64053334735\n"
+     ]
+    }
+   ],
+   "source": [
+    "# f(x) = 0.2 + 25*x - 200*x**2 + 675*x**3 - 900*x**4 + 400*x**5\n",
+    "# for using three point gauss legendre formulae, the intervals have to be changed to -1 and 1\n",
+    "#therefore, x = 0.4 + 0.4 * xd\n",
+    "#thus the integral is transferred to \n",
+    "#(0.2 + 25*(0.4+0.4*x) - 200*(0.4 + 0.4*x)**2 + 675*(0.4 + 0.4*x)**3 - 900*(0.4 + 0.4*x)**4 + 400*(0.4 + 0.4*x)**5)*0.4\n",
+    "#for three point gauss legendre formulae\n",
+    "x1 = -0.7745967#\n",
+    "x2 = 0#\n",
+    "x3 = 0.7745967#\n",
+    "c0 = 0.5555556#\n",
+    "c1 = 0.8888889#\n",
+    "c2 = 0.5555556#\n",
+    "I1 = (0.2 + 25*(0.4+0.4*x1) - 200*(0.4 + 0.4*x1)**2 + 675*(0.4 + 0.4*x1)**3 - 900*(0.4 + 0.4*x1)**4 + 400*(0.4 + 0.4*x1)**5)*0.4#\n",
+    "I2 = (0.2 + 25*(0.4+0.4*x2) - 200*(0.4 + 0.4*x2)**2 + 675*(0.4 + 0.4*x2)**3 - 900*(0.4 + 0.4*x2)**4 + 400*(0.4 + 0.4*x2)**5)*0.4#\n",
+    "I3 = (0.2 + 25*(0.4+0.4*x3) - 200*(0.4 + 0.4*x3)**2 + 675*(0.4 + 0.4*x3)**3 - 900*(0.4 + 0.4*x3)**4 + 400*(0.4 + 0.4*x3)**5)*0.4#\n",
+    "I = c0 * I1 + c1 * I2 + c2 * I3#\n",
+    "print \"integral obtained using three point gauss legendre formulae = \",I"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:22.5 Pg: 647"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "integral by two point method =  320.657652324\n",
+      "integral by three point method = 289.439308244\n",
+      "integral by four point method = 289.435164941\n",
+      "integral by five point method = 289.435160633\n"
+     ]
+    }
+   ],
+   "source": [
+    "from math import exp\n",
+    "#f(t) = g*m*(int(0,10,(1-exp(-c*t/m))))/c\n",
+    "#for using gauss quadrature method, limits are changed to -1 to 1 by replcing x = 5 + 5*xd\n",
+    "#the new integral obtained is\n",
+    "#(1 - exp(-c*(5 + 5*x)/m ))*5\n",
+    "g = 9.8#\n",
+    "c = 12.5#\n",
+    "m = 68.1#\n",
+    "#for two point method\n",
+    "x1 = -(1/3)**0.5#\n",
+    "x2 = (1/3)**0.5#\n",
+    "I1 = g*m*(1 - exp(-c*(5 + 5*x1)/m ))*5 / c#\n",
+    "I2 = g*m*(1 - exp(-c*(5 + 5*x2)/m ))*5 / c#\n",
+    "I = I1 + I2#\n",
+    "print \"integral by two point method = \",I\n",
+    "x1 = -0.7745967#\n",
+    "x2 = 0#\n",
+    "x3 = 0.7745967#\n",
+    "c0 = 0.5555556#\n",
+    "c1 = 0.8888889#\n",
+    "c2 = 0.5555556#\n",
+    "I1 = g*m*(1 - exp(-c*(5 + 5*x1)/m ))*5 / c#\n",
+    "I2 = g*m*(1 - exp(-c*(5 + 5*x2)/m ))*5 / c#\n",
+    "I3 = g*m*(1 - exp(-c*(5 + 5*x3)/m ))*5 / c#\n",
+    "I = c0*I1 + c1 * I2 + c2 * I3#\n",
+    "print \"integral by three point method =\",I\n",
+    "x1 = -0.861136312#\n",
+    "x2 = -0.339981044#\n",
+    "x3 = 0.339981044#\n",
+    "x4 = 0.861136312#\n",
+    "c1 = 0.3478548#\n",
+    "c2 = 0.6521452#\n",
+    "c3 = 0.6521452#\n",
+    "c4 = 0.3478548#\n",
+    "I1 = g*m*(1 - exp(-c*(5 + 5*x1)/m ))*5 / c#\n",
+    "I2 = g*m*(1 - exp(-c*(5 + 5*x2)/m ))*5 / c#\n",
+    "I3 = g*m*(1 - exp(-c*(5 + 5*x3)/m ))*5 / c#\n",
+    "I4 = g*m*(1 - exp(-c*(5 + 5*x4)/m ))*5 / c#\n",
+    "I = c1*I1 + c2 * I2 + c3 * I3 + c4 * I4#\n",
+    "print \"integral by four point method =\",I\n",
+    "x1 = -0.906179846#\n",
+    "x2 = -0.538469310#\n",
+    "x3 = 0#\n",
+    "x4 = 0.538469310#\n",
+    "x5 = 0.906179846\n",
+    "c1 = 0.2369269#\n",
+    "c2 = 0.4786287#\n",
+    "c3 = 0.5688889#\n",
+    "c4 = 0.4786287#\n",
+    "c5 = 0.2369269# \n",
+    "I1 = g*m*(1 - exp(-c*(5 + 5*x1)/m ))*5 / c#\n",
+    "I2 = g*m*(1 - exp(-c*(5 + 5*x2)/m ))*5 / c#\n",
+    "I3 = g*m*(1 - exp(-c*(5 + 5*x3)/m ))*5 / c#\n",
+    "I4 = g*m*(1 - exp(-c*(5 + 5*x4)/m ))*5 / c#\n",
+    "I5 = g*m*(1 - exp(-c*(5 + 5*x5)/m ))*5 / c#\n",
+    "I = c1*I1 + c2 * I2 + c3 * I3 + c4 * I4 + c5 * I5#\n",
+    "print \"integral by five point method =\",I"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:22.6 Pg: 649"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "the value of first integral =  0.0\n",
+      "The value of second integral =  1.93292644948\n",
+      "Therefore the final result can be computed as : 0.771126085603\n",
+      "error =  8.34112853886 %\n"
+     ]
+    }
+   ],
+   "source": [
+    "from math import exp,pi\n",
+    "#N(x) = (int(-infinity,-2,exp(-(x**2)/2)) + int(-2,1,exp(-(x**2)/2)))/(2*pi)**0.5\n",
+    "#first integral can be solved as\n",
+    "#int(-infinity,-2,exp(-(x**2)/2)) = int(-0.5,0,exp(-1/(2*t**2))/t**2)\n",
+    "h = 1/8#\n",
+    "#int(-0.5,0,exp(-1/(2*t**2))/t**2) = h*(f(x-7/16) + f(x-5/16) + f(x-3/16) + f(x-1/16)) \n",
+    "t1 = -7/16#\n",
+    "t2 = -5/16#\n",
+    "t3 = -3/16#\n",
+    "t4 = -1/16#\n",
+    "m1 = exp(-1/(2*t1**2))/t1**2#\n",
+    "m2 = exp(-1/(2*t2**2))/t2**2#\n",
+    "m3 = exp(-1/(2*t3**2))/t3**2#\n",
+    "m4 = exp(-1/(2*t4**2))/t4**2#\n",
+    "I1 = h*(m1 + m2 + m3 + m4)#\n",
+    "print \"the value of first integral = \",I1\n",
+    "#simpsons 1/3rd sule is applied for the second integral\n",
+    "h1 = 0.5#\n",
+    "x1 = -2#\n",
+    "x2 = -1.5#\n",
+    "x3 = -1#\n",
+    "x4 = -0.5#\n",
+    "x5 = 0#\n",
+    "x6 = 0.5#\n",
+    "x7 = 1#\n",
+    "n1 = exp(-(x1**2)/2)#\n",
+    "n2 = exp(-(x2**2)/2)#\n",
+    "n3 = exp(-(x3**2)/2)#\n",
+    "n4 = exp(-(x4**2)/2)#\n",
+    "n5 = exp(-(x5**2)/2)#\n",
+    "n6 = exp(-(x6**2)/2)#\n",
+    "n7 = exp(-(x7**2)/2)#\n",
+    "I2 =(1-(-2)) * (n1 + 4 *(n2 + n4 + n6) + 2*(n3 + n5) + n7)/(18)#\n",
+    "print \"The value of second integral = \",I2\n",
+    "f = (I1 + I2)/(2 * pi)**0.5#\n",
+    "print \"Therefore the final result can be computed as :\",f\n",
+    "N = 0.8413#\n",
+    "e = (N - f) * 100 / N#\n",
+    "print \"error = \",e,\"%\""
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 2",
+   "language": "python",
+   "name": "python2"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.9"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter23.ipynb b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter23.ipynb
new file mode 100644
index 00000000..fd068f1e
--- /dev/null
+++ b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter23.ipynb
@@ -0,0 +1,271 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Chapter-23  : Numerical Differentiation"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:23.1 Pg: 656"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "x =  [ 0.    0.25  0.5   0.75  1.  ]\n",
+      "f(x) =  [0, 1.2, 1.103515625, 0.92499999999999993, 0.63632812499999991, 0.19999999999999996]\n",
+      "by forward difference :  -0.859375\n",
+      "error in forward difference method =  5.82191780822 %\n",
+      "by backward difference -0.878125\n",
+      "error in backward difference method =  3.76712328767 %\n",
+      "by central difference :  -0.9125\n",
+      "error in central difference method =  -2.43336553343e-14 %\n"
+     ]
+    }
+   ],
+   "source": [
+    "from numpy import arange\n",
+    "#f(x) = -0.1*x**4 - 0.15*x**3 - 0.5 * x**2 - 0.25 *x + 1.2\n",
+    "h = 0.25#\n",
+    "t = -0.9125#\n",
+    "x = arange(0,1.1,h)\n",
+    "print \"x = \",x\n",
+    "fx=[0]\n",
+    "for xx in x:\n",
+    "    fx.append(-0.1*xx**4 - 0.15*xx**3 - 0.5 * xx**2 - 0.25 *xx + 1.2)\n",
+    "print \"f(x) = \",fx\n",
+    "fd = (- fx[(5)] + 4*fx[(4)] - 3 * fx[(3)])/(2 * h)\n",
+    "efd = (t - fd) * 100 / t#\n",
+    "print \"by forward difference : \",fd\n",
+    "print \"error in forward difference method = \",efd,\"%\"\n",
+    "bd = (3 * fx[(3)] - 4 * fx[(2)] + fx[(1)])/ (2*h)\n",
+    "ebd = (t - bd) * 100 / t#\n",
+    "print \"by backward difference\",bd\n",
+    "print \"error in backward difference method = \",ebd,\"%\"\n",
+    "cdm = (-fx[(5)] + 8*(fx[(4)]) -8*fx[(2)] + fx[(1)] ) / (12*h)\n",
+    "ecdm = (t - cdm) * 100 / t\n",
+    "print \"by central difference : \",cdm\n",
+    "print \"error in central difference method = \",ecdm,\"%\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:23.2 Pg: 657"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "x with h = 0.5 is [ 0.   0.5  1. ]\n",
+      "f(x) with h = 0.5 is [0, 1.2, 0.92499999999999993, 0.19999999999999996]\n",
+      "by central difference ( h = 0.5 )  -1.0\n",
+      "error in central difference method ( h = 0.5 ) =  -9.58904109589 %\n",
+      "x with h = 0.25 is [ 0.    0.25  0.5   0.75  1.  ]\n",
+      "fx with h = 0.25 is [0, 1.2, 1.103515625, 0.92499999999999993, 0.63632812499999991, 0.19999999999999996]\n",
+      "by central difference ( h = 0.25 )  =  -0.934375 error in central difference method ( h = 0.25 ) =  -2.39726027397 %\n",
+      "improved estimate = -0.9125\n"
+     ]
+    }
+   ],
+   "source": [
+    "from numpy import arange\n",
+    "#f(x) = -0.1*x**4 - 0.15*x**3 - 0.5 * x**2 - 0.25 *x + 1.2\n",
+    "h = 0.5#\n",
+    "t = -0.9125#\n",
+    "x = arange(0,1.1,h)\n",
+    "print \"x with h = 0.5 is\",x\n",
+    "fx=[0]\n",
+    "for xx in x:\n",
+    "    fx.append(-0.1*xx**4 - 0.15*xx**3 - 0.5 * xx**2 - 0.25 *xx + 1.2)\n",
+    "print \"f(x) with h = 0.5 is\",fx\n",
+    "cdm = (fx[(3)] - fx[(1)])/ 1#\n",
+    "ecdm = (t - cdm) * 100 / t#\n",
+    "print \"by central difference ( h = 0.5 ) \",cdm\n",
+    "print \"error in central difference method ( h = 0.5 ) = \",ecdm,\"%\"\n",
+    "h1 = 0.25#\n",
+    "x1 = arange(0,1.1,h1)\n",
+    "print \"x with h = 0.25 is\",x1\n",
+    "fx1=[0]\n",
+    "for xx in x1:\n",
+    "    fx1.append(-0.1*xx**4 - 0.15*xx**3 - 0.5 * xx**2 - 0.25 *xx + 1.2)\n",
+    "print \"fx with h = 0.25 is\",fx1\n",
+    "cdm1 = (fx1[(4)] - fx1[(2)])/ (2*h1)\n",
+    "ecdm1 = (t - cdm1) * 100 / t#\n",
+    "print \"by central difference ( h = 0.25 )  = \",cdm1,\n",
+    "print \"error in central difference method ( h = 0.25 ) = \",ecdm1,\"%\"\n",
+    "D = 4 * cdm1 /3 - cdm / 3#\n",
+    "print \"improved estimate =\",D"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:23.3 Pg: 658"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(dT/dz) =  -1.33333333333 C/cm\n",
+      "q(z = 0) = 70.56 W/m**2\n"
+     ]
+    }
+   ],
+   "source": [
+    "#q(z = 0) = -k*p*C*(dT/dz)/(z = 0)\n",
+    "k = 3.5 * 10** - 7##m**2/s\n",
+    "p = 1800##kg/m**3\n",
+    "C = 840# #(J/(kg.C))\n",
+    "x = 0#\n",
+    "fx0 = 13.5#\n",
+    "fx1 = 12#\n",
+    "fx2 = 10#\n",
+    "x0 = 0#\n",
+    "x1 = 1.25#\n",
+    "x2 = 3.75#\n",
+    "dfx = fx0 *(2*x - x1 - x2)/((x0 - x1)*(x0 - x2)) + fx1 *(2*x - x0 - x2)/((x1 - x0)*(x1 - x2)) + fx2 *(2*x - x1 - x0)/((x2 - x1)*(x2 - x0))#\n",
+    "print \"(dT/dz) = \",dfx,\"C/cm\"\n",
+    "q = - k * p *C * dfx*100#\n",
+    "print \"q(z = 0) =\",q,\"W/m**2\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:23.4 Pg: 662"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Q= 1.64053333333333\n",
+      "intergral= -1.40920096\n",
+      "diff(x)= [ 0.12  0.1   0.1   0.04  0.04  0.04  0.1   0.1   0.06  0.1 ]\n",
+      "d= [  9.247744  -0.04488    4.38152    8.287744   9.527424   9.674624\n",
+      "   6.64312   -3.25368  -13.648816 -21.31    ]\n"
+     ]
+    }
+   ],
+   "source": [
+    "from sympy.mpmath import quad\n",
+    "from numpy import trapz,diff\n",
+    "def f(x):\n",
+    "    y=0.2+25*x-200*x**2+675*x**3-900*x**4+400*x**5\n",
+    "    return y\n",
+    "a=0#\n",
+    "b=0.8#\n",
+    "Q=quad(f,[0,0.8])\n",
+    "print \"Q=\",Q\n",
+    "x=[0, 0.12 ,0.22 ,0.32 ,0.36 ,0.4 ,0.44 ,0.54 ,0.64, 0.7 ,0.8]\n",
+    "y=[]\n",
+    "for xx in x:\n",
+    "    y.append(f(xx))\n",
+    "integral=trapz(x,y)\n",
+    "print \"intergral=\",integral\n",
+    "print \"diff(x)=\",diff(x)\n",
+    "d=diff(y)/diff(x)#\n",
+    "print \"d=\",d"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:23.5 Pg: 664"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Computed= 1.64053333333333\n",
+      "Error estimate= 2.03185997099678e-5\n"
+     ]
+    }
+   ],
+   "source": [
+    "from __future__ import division\n",
+    "from sympy.mpmath import quad\n",
+    "def f(x):\n",
+    "    y=0.2+25*x-200*x**2+675*x**3-900*x**4+400*x**5\n",
+    "    return y\n",
+    "a=0#\n",
+    "b=0.8#\n",
+    "Qt=1.640533#\n",
+    "Q=quad(f,[0,0.8])\n",
+    "print \"Computed=\",Q\n",
+    "Er=abs(Q-Qt)*100/Qt\n",
+    "print \"Error estimate=\",Er"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 2",
+   "language": "python",
+   "name": "python2"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.9"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter25.ipynb b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter25.ipynb
new file mode 100644
index 00000000..e4e7a3f4
--- /dev/null
+++ b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter25.ipynb
@@ -0,0 +1,178 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Chapter-25 : Runge-Kutta Methods"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:25.1 Pg: 708"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "x =  [ 0.   0.5  1.   1.5  2.   2.5  3.   3.5  4. ]\n",
+      "\n",
+      "true values of y =  [1.0, 3.21875, 3.0, 2.21875, 2.0, 2.71875, 4.0, 4.71875, 3.0]\n",
+      "\n",
+      "y by euler method = [1.0, 5.25, 5.875, 5.125, 4.5, 4.75, 5.875, 7.125, 7.0]\n",
+      "\n",
+      "error = [0.0, -63.106796116504853, -95.833333333333329, -130.98591549295776, -125.0, -74.712643678160916, -46.875, -50.993377483443709, -133.33333333333334]\n"
+     ]
+    }
+   ],
+   "source": [
+    "from numpy import arange\n",
+    "#dy/dx = -2*x**3 + 12*x**2 - 20*x + 8.5\n",
+    "#therefore, y = -0.5*x**4 + 4*x**3 - 10*x**2 + 8.5 + c\n",
+    "x1 = 0#\n",
+    "y1 = 1#\n",
+    "h = 0.5#\n",
+    "c =-(-0.5*x1**4 + 4*x1**3 - 10*x1**2 + 8.5*x1 - y1)#\n",
+    "x = arange(0,4.1,0.5)\n",
+    "print \"x = \",x\n",
+    "y=[]\n",
+    "for xx in x:\n",
+    "    y.append(-0.5*xx**4 + 4*xx**3 - 10*xx**2 + 8.5*xx + c)\n",
+    "print \"\\ntrue values of y = \",y\n",
+    "fxy=[]\n",
+    "for xx in x:\n",
+    "    fxy.append(-2*xx**3 + 12*xx**2 - 20*xx + 8.5)\n",
+    "y2=[y[0]]\n",
+    "e = [(y[0] - y2[0]) * 100 / y[0]]\n",
+    "for i in range(1,9):\n",
+    "    y2.append(y2[(i-1)] + fxy[(i-1)]*h)\n",
+    "    e.append((y[(i)] - y2[(i)])*100/y[(i)])\n",
+    "\n",
+    "print \"\\ny by euler method =\",y2\n",
+    "print \"\\nerror =\",e"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:25.2 Pg: 712"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Total truncation error = -2.03125\n"
+     ]
+    }
+   ],
+   "source": [
+    "#f(x,y) = dy/dx = -2*x**3 + 12*x**2 - 20*x + 8.5\n",
+    "#f'(x,y) = -6*x**2 + 24*x - 20\n",
+    "#f\"(x,y) = -12*x + 24\n",
+    "#f\"'(x,y) = -12\n",
+    "x = 0#\n",
+    "Et2 = (-6*x**2 + 24*x - 20) * 0.5**2 / 2\n",
+    "Et3 = (-12*x + 24) * (0.5)**3 / 6#\n",
+    "Et4 = (-12) *(0.5 ** 4) / 24#\n",
+    "Et = Et2 + Et3 + Et4#\n",
+    "print \"Total truncation error =\",Et"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:25.3 Pg: 713"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "x =  [ 0.    0.25  0.5   0.75  1.    1.25  1.5   1.75  2.    2.25  2.5   2.75\n",
+      "  3.    3.25  3.5   3.75  4.  ]\n",
+      "\n",
+      "true values of y =  [1.0, 2.560546875, 3.21875, 3.279296875, 3.0, 2.591796875, 2.21875, 1.998046875, 2.0, 2.248046875, 2.71875, 3.341796875, 4.0, 4.529296875, 4.71875, 4.310546875, 3.0]\n",
+      "\n",
+      "y by euler method = [1.0, 3.125, 4.1796875, 4.4921875, 4.34375, 3.96875, 3.5546875, 3.2421875, 3.125, 3.25, 3.6171875, 4.1796875, 4.84375, 5.46875, 5.8671875, 5.8046875, 5.0]\n",
+      "\n",
+      "error = [0.0, -22.04424103737605, -29.854368932038835, -36.986301369863014, -44.791666666666664, -53.127354935945739, -60.2112676056338, -62.267839687194524, -56.25, -44.569939183318851, -33.045977011494251, -25.073056691992985, -21.09375, -20.741699008193187, -24.337748344370862, -34.662437698232893, -66.666666666666671]\n"
+     ]
+    }
+   ],
+   "source": [
+    "from numpy import arange\n",
+    "#dy/dx = -2*x**3 + 12*x**2 - 20*x + 8.5\n",
+    "#therefore, y = -0.5*x**4 + 4*x**3 - 10*x**2 + 8.5 + c\n",
+    "x1 = 0#\n",
+    "y1 = 1#\n",
+    "h = 0.25#\n",
+    "c =-(-0.5*x1**4 + 4*x1**3 - 10*x1**2 + 8.5*x1 - y1)#\n",
+    "xx = arange(0,4.1,h)\n",
+    "print \"x = \",xx\n",
+    "y=[]\n",
+    "for x in xx:\n",
+    "    y.append(-0.5*x**4 + 4*x**3 - 10*x**2 + 8.5*x + c)\n",
+    "print \"\\ntrue values of y = \",y\n",
+    "fxy=[]\n",
+    "for x in xx:\n",
+    "    fxy.append(-2*x**3 + 12*x**2 - 20*x + 8.5)\n",
+    "y2= [y[0]]\n",
+    "e = [(y[0] - y2[0]) * 100 / y[0]]\n",
+    "for i in range(1,17):\n",
+    "    y2.append(y2[(i-1)] + fxy[(i-1)]*h)\n",
+    "    e.append((y[(i)] - y2[(i)])*100/y[(i)])\n",
+    "\n",
+    "print \"\\ny by euler method =\",y2\n",
+    "print \"\\nerror =\",e"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 2",
+   "language": "python",
+   "name": "python2"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.9"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter26.ipynb b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter26.ipynb
new file mode 100644
index 00000000..b52f1078
--- /dev/null
+++ b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter26.ipynb
@@ -0,0 +1,401 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Chapter-26 : Stiffness & Multi step Methods"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:26.1 Pg: 754"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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cwSvrX6HxxUYaGhpoaGgAkgHj618fxFKLiERUU1MTTU1NgeVv7sX8Xh9AxmYf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\ngCEiIkX5P35bsBSB1IexAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7fbf23e04950>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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P58MOS7tCEal3ComEHToEzzwTbsIzfz4cfjh885thGztWE88iUls0cZ2AAwfCBW0PPxzm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\nSAoJERGJpJAQEZFICgkREYn0P5bbRGIvXNRJAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7fbf23882f10>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "%matplotlib inline\n",
+    "from matplotlib.pyplot import plot,xlabel,ylabel,show,title,legend\n",
+    "from numpy import arange,exp\n",
+    "def f(t,y):\n",
+    "    yp=-1000*y+3000-2000*exp(-t)\n",
+    "    return yp\n",
+    "y0=0#\n",
+    "#explicit euler\n",
+    "h1=0.0005#\n",
+    "y1 =[y0]\n",
+    "count=1#\n",
+    "t=arange(0,0.0061,0.0001)\n",
+    "for i in arange(0,0.00591,0.0001):\n",
+    "    y1.append(y1[(count-1)]+f(i,y1[(count-1)])*h1)\n",
+    "    count=count+1#\n",
+    "\n",
+    "plot(t,y1)\n",
+    "h2=0.0015#\n",
+    "y2=[y0]#\n",
+    "count=1#\n",
+    "t=arange(0,0.0061,0.0001)\n",
+    "for i in arange(0,0.00591,0.0001):\n",
+    "    y2.append(y2[(count-1)]+f(i,y2[(count-1)])*h2)\n",
+    "    count=count+1#\n",
+    "\n",
+    "plot(t,y2)\n",
+    "title(\"y vs t\")\n",
+    "xlabel(\"t\")\n",
+    "ylabel(\"y\")\n",
+    "h=legend([\"h-0.0005\",\"h=0.0015\"])\n",
+    "show()\n",
+    "#implicit order\n",
+    "h3=0.05#\n",
+    "y3=[y0]#\n",
+    "count=1#\n",
+    "t=arange(0,0.401,0.01)\n",
+    "for j in arange(0,0.40,0.01):\n",
+    "    y3.append((y3[(count-1)]+3000*h3-2000*h3*exp(-(j+0.01)))/(1+1000*h3))\n",
+    "    count=count+1#\n",
+    "\n",
+    "plot(t,y3)\n",
+    "title(\"y vs t\")\n",
+    "xlabel(\"t\")\n",
+    "ylabel(\"y\")\n",
+    "show()\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:26.2 Pg: 758"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "f(x,y) = 4*exp(0.8*x) - 0.5*y\n",
+      "the first corrector yields y =  15.7669298488\n",
+      "error =  -6.21810039929 %\n"
+     ]
+    }
+   ],
+   "source": [
+    "from math import exp\n",
+    "print \"f(x,y) = 4*exp(0.8*x) - 0.5*y\"\n",
+    "#f'(x,y) = 4*exp(0.8*x) - 0.5*y\n",
+    "h = 1#\n",
+    "x=range(0,5)\n",
+    "y = [2]\n",
+    "x1 = -1#\n",
+    "y1 = -0.3929953#\n",
+    "y10 = y1 + (4*exp(0.8*x[0]) - 0.5*y[0])*2\n",
+    "y11 = y[0] + (4*exp(0.8*x[0]) - 0.5*y[0] + 4*exp(0.8*x[0]) - 0.5*y10)*h/2\n",
+    "y12 = y[0] + (3 + 4*exp(0.8*x[1]) - 0.5*y11)*h/2#\n",
+    "t = 6.360865#\n",
+    "y20 = y[0] + (4*exp(0.8*x[1]) - 0.5*t) *2\n",
+    "y21 = t + (4*exp(0.8*x[1]) - 0.5*t + 4*exp(0.8*x[2]) - 0.5*y20)*h/2\n",
+    "print \"the first corrector yields y = \",y21\n",
+    "t = 14.84392\n",
+    "e = (t - y21)*100/t#\n",
+    "print \"error = \",e,\"%\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:26.3 Pg: 762"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Ec (x = 1) =  -0.150772\n",
+      "true error (x = 1) =  -0.166234\n",
+      "Ec (x = 2) =  -0.371756\n",
+      "true error (x = 2) =  -0.45832\n"
+     ]
+    }
+   ],
+   "source": [
+    "x1 = 1#\n",
+    "x2 = 2#\n",
+    "y1 = 6.194631#\n",
+    "y2 = 14.84392#\n",
+    "y10 = 5.607005#\n",
+    "y11 = 6.360865#\n",
+    "y20 = 13.44346#\n",
+    "y21 = 15.30224#\n",
+    "Ec1 = -(y11 - y10)/5#\n",
+    "print \"Ec (x = 1) = \",Ec1\n",
+    "e1 = y1 - y11#\n",
+    "print \"true error (x = 1) = \",e1\n",
+    "Ec2 = -(y21 - y20)/5#\n",
+    "print \"Ec (x = 2) = \",Ec2\n",
+    "e2 = y2 - y21#\n",
+    "print \"true error (x = 2) = \",e2"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:26.4 Pg: 763"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ym = 6.210093\n",
+      "error =  -0.249603245133 %\n",
+      "y20 =  13.5942344279\n",
+      "error =  8.41883796235 %\n",
+      "y20 =  14.1973224279\n",
+      "error =  4.35597586123 %\n",
+      "y2 =  14.8882708856\n",
+      "error =  -0.2987814916 %\n"
+     ]
+    }
+   ],
+   "source": [
+    "x0 = 0#\n",
+    "x1 = 1#\n",
+    "x2 = 2#\n",
+    "y1 = 6.194631#\n",
+    "y2 = 14.84392#\n",
+    "y10 = 5.607005#\n",
+    "y11 = 6.360865#\n",
+    "y1m = y11 - (y11 - y10)/5#\n",
+    "e = (y1 - y1m)*100/y1#\n",
+    "print \"ym =\",y1m\n",
+    "print \"error = \",e,\"%\"\n",
+    "y20 =2+(4*exp(0.8*x1) - 0.5*y1m)*2#\n",
+    "e2 = (y2 - y20)*100/y2#\n",
+    "print \"y20 = \",y20\n",
+    "print \"error = \",e2,\"%\"\n",
+    "y2o = y20 + 4* (y11 - y10)/5#\n",
+    "e2 = (y2 - y2o)*100/y2#\n",
+    "print \"y20 = \",y2o\n",
+    "print \"error = \",e2,\"%\"\n",
+    "y21 = 15.21178#\n",
+    "y23 = y21 - (y21 - y20)/5#\n",
+    "print \"y2 = \",y23\n",
+    "e3 = (y2 - y23)*100/y2#\n",
+    "print \"error = \",e3,\"%\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:26.5 Pg: 773"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "f(x,y) = 4*exp(0.8*x) - 0.5*y\n",
+      "x =  [ 1.  2.  3.  4.]\n",
+      "y0 =  [2, 6.0227228499844756, 20.083112587836688, 41.872835141608761]\n",
+      "corrected y1 =  [6.9056637734795867, 19.136474376155903, 38.385462010990274, 82.755745651588995]\n"
+     ]
+    }
+   ],
+   "source": [
+    "from numpy import arange,exp\n",
+    "print \"f(x,y) = 4*exp(0.8*x) - 0.5*y\"\n",
+    "#f'(x,y) = 4*exp(0.8*x) - 0.5*y\n",
+    "h = 1#\n",
+    "x = arange(-3,4.1,h)\n",
+    "y=[-4.547302,-2.306160,-0.3929953,2,2]\n",
+    "y1=[0,0,0,0]\n",
+    "for  i in range(3,7):\n",
+    "    y.append(y[(i-3)] + 4*h*(2*(4*exp(0.8*x[(i)]) - 0.5*y[(i)]) - 4*exp(0.8*x[(i-1)]) + 0.5*y[(i-1)] + 2*(4*exp(0.8*x[(i-2)]) - 0.5*y[(i-2)]))/3)\n",
+    "    y1.append(y[(i-1)] + h*(4*exp(0.8*x[(i-1)]) - 0.5*y[(i-1)] +4 * (4*exp(0.8*x[(i)]) - 0.5*y[(i)]) + 4*exp(0.8*x[(i+1)]) - 0.5*y[(i+1)])/3)\n",
+    "\n",
+    "print \"x = \",x[4:8]\n",
+    "print \"y0 = \",y[4:8]\n",
+    "print \"corrected y1 = \",y1[4:8]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:26.6 Pg: 774"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "f(x,y) = 4*exp(0.8*x) - 0.5*y\n",
+      "x =  [ 1.  2.  3.  4.]\n",
+      "y0 =  [2, 6.0075392692969114, 6.2532143855636217, 14.488238413222703]\n",
+      "y1 =  [6.0075392692969114, 6.2532143855636217, 14.488238413222703, 16.39224775082873]\n"
+     ]
+    }
+   ],
+   "source": [
+    "print \"f(x,y) = 4*exp(0.8*x) - 0.5*y\"\n",
+    "#f'(x,y) = 4*exp(0.8*x) - 0.5*y\n",
+    "h = 1#\n",
+    "x = arange(-3,4.1,h)\n",
+    "y = [-4.547302,-2.306160,-0.3929953,2]\n",
+    "m= [0,0,0,0,y[3]]\n",
+    "for i in range(3,7):\n",
+    "    y.append(y[(i)] + h *(55* (4*exp(0.8*x[(i)]) - 0.5*y[(i)]) / 24 - 59 * (4*exp(0.8*x[(i-1)]) - 0.5*y[(i-1)]) / 24 + 37*(4*exp(0.8*x[(i-2)]) - 0.5*y[(i-2)])/24 - 9*(4*exp(0.8*x[(i-3)]) - 0.5*y[(i-3)])/24))\n",
+    "    m.append(y[(i+1)])\n",
+    "    y.append(y[(i)] + h*(9*(4*exp(0.8*x[(i+1)]) - 0.5*y[(i+1)])/24 +19*(4*exp(0.8*x[(i)]) - 0.5*y[(i)])/24 - 5*(4*exp(0.8*x[(i-1)]) - 0.5*y[(i-1)])/24 + (4*exp(0.8*x[(i-2)]) - 0.5*y[(i-2)])/24))\n",
+    "\n",
+    "print \"x = \",x[4:8]\n",
+    "print \"y0 = \",m[4:8]\n",
+    "print \"y1 = \",y[4:8]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:26.7 Pg: 775"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "x =  [ 0.   0.5  1.   1.5  2.   2.5  3.   3.5  4.   4.5  5.   5.5  6.   6.5  7.\n",
+      "  7.5  8.   8.5  9.   9.5]\n",
+      "\n",
+      "y0(milnes method) =  [1, 0.62312747952608971, 0.60341314566242521, 0.35581682815742122, 0.3173461560388694, -0.073744603832379019, 0.05769466447055438, 0.097016353530268939, 0.21274204327392865, -0.36734037063735558, 0.09724068674400127, 0.43888095058828192, 0.3040024218422181, -0.1934006684100632, -0.1160863384290636, 0.32478026608871907, -0.052055689173705413, -0.36964931180484378, 0.00024232753216428538, 0.55995471612928904]\n",
+      "\n",
+      "corrected y1(milnes method) =  [1, 0.62312747952608971, 0.60341314566242521, 0.35581682815742122, 0.3173461560388694, -0.073744603832379019, 0.05769466447055438, 0.097016353530268939, 0.21274204327392865, -0.36734037063735558, 0.09724068674400127, 0.43888095058828192, 0.3040024218422181, -0.1934006684100632, -0.1160863384290636, 0.32478026608871907, -0.052055689173705413, -0.36964931180484378, 0.00024232753216428538, 0.55995471612928904]\n",
+      "\n",
+      "y0(fourth order adams method) =  [1, 0.27152768648678072, 0.65650943823969443, -0.097035945241965349, 0.90661897200241937, -0.41645854530303128, -0.006339328628468005, 0.0808211944939453, -0.031548281043396395, -0.01627399436000334, 0.0039276970657568626, -0.002208005756050492, -0.0027943948998587478, -0.00042783320198906672, -0.00032845203812321728, -0.00042142028381515442, -0.00017932875240256902, -8.560953717861569e-05, -7.1995388648036731e-05, -4.2020211202092437e-05]\n",
+      "\n",
+      "y1(fourth order adams method) =  [1, 0.56419948638876194, 0.68342664355034821, -0.010131383289966767, -0.11667598191807985, -0.0076991693311919962, -0.015405634984349756, -0.02283279228603189, -0.0093238635936440419, -0.0046392587796136846, -0.0040348813308916029, -0.0023127486894963844, -0.0011969855369064737, -0.00079981133060367615, -0.00049813831748820084, -0.00028031874518611127, -0.00017096177282523818, -0.00010605960387014003, -6.2547086111287706e-05, -3.7396246727791117e-05]\n"
+     ]
+    }
+   ],
+   "source": [
+    "from numpy import arange,exp\n",
+    "#dy/dx = -y\n",
+    "#y = exp(-x)\n",
+    "h = 0.5#\n",
+    "x = arange(-1.5,10.1,h)\n",
+    "y=[exp(-x[0]),exp(-x[1]),exp(-x[2]),1]\n",
+    "m=[0,0,0,y[3]]\n",
+    "for  i in range(3,23):\n",
+    "    y.append(y[(i-3)] + 4*h*(2*(-y[(i)]) + y[(i-1)] + 2*(-y[(i-2)]))/3)\n",
+    "    m.append(y[(i+1)])\n",
+    "    y.append(y[(i-1)] + h*(-y[(i-1)] +4 * (-y[(i)]) + (-y[(i+1)]))/3)\n",
+    "\n",
+    "print \"\\nx = \",x[3:23]\n",
+    "print \"\\ny0(milnes method) = \",m[3:23]\n",
+    "print \"\\ncorrected y1(milnes method) = \",y[3:23]\n",
+    "for i in range(3,23):\n",
+    "    y[(i+1)] = y[(i)] + h *(55* (-y[(i)]) / 24 - 59 * (-y[(i-1)]) / 24 + 37*(-y[(i-2)])/24 - 9*(-y[(i-3)])/24)#\n",
+    "    m[(i+1)] = y[(i+1)]\n",
+    "    y[(i+1)] = y[(i)] + h*(9*(-y[(i+1)])/24 +19*(-y[(i)])/24 - 5*(-y[(i-1)])/24 + (-y[(i-2)])/24)#\n",
+    "\n",
+    "print \"\\ny0(fourth order adams method) = \",m[3:23]\n",
+    "print \"\\ny1(fourth order adams method) = \",y[3:23]"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 2",
+   "language": "python",
+   "name": "python2"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.9"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter3.ipynb b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter3.ipynb
new file mode 100644
index 00000000..b0cdc8c4
--- /dev/null
+++ b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter3.ipynb
@@ -0,0 +1,382 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# CHAPTER 3 : Approximations and Round off Errors"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex : 3.1 Pg : 56"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "a. The true error is\n",
+      "for the bridge :  1 cm\n",
+      "for the rivet :  1 cm\n",
+      "b. The percent relative error is\n",
+      "for the bridge :  0.01 cm\n",
+      "for the rivet :  10.0 cm\n"
+     ]
+    }
+   ],
+   "source": [
+    "from __future__ import division\n",
+    "lbm=9999# #cm, measured length of bridge\n",
+    "lrm=9##cm, measured length of rivet\n",
+    "lbt=10000##cm, true length of bridge\n",
+    "lrt=10##cm,true length of rivet\n",
+    "#calculating true error below#\n",
+    "Etb=lbt-lbm##cm, true error in bridge\n",
+    "Etr=lrt-lrm##cm, true error in rivet\n",
+    "#calculating percent relative error below\n",
+    "etb=Etb*100/lbt##percent relative error for bridge\n",
+    "etr=Etb*100/lrt##percent relative error for rivet\n",
+    "print \"a. The true error is\"\n",
+    "print \"for the bridge : \",Etb,\"cm\"\n",
+    "print \"for the rivet : \",Etr,\"cm\"\n",
+    "print \"b. The percent relative error is\"\n",
+    "print \"for the bridge : \",etb,\"cm\"\n",
+    "print \"for the rivet : \",etr,\"cm\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex 3.2 : Pg : 58"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Terms\t\t\tResult\t\t\t\tet(%)\t\t\t\tea(%)\n",
+      "----------------------------------------------------------------------------------------------------\n",
+      "1 \t\t\t1.00000 \t\t\t39.3469240702 \t\t\t100\n",
+      "----------------------------------------------------------------------------------------------------\n",
+      "2 \t\t\t2.00000 \t\t\t-21.3061518595 \t\t\t50.0\n",
+      "----------------------------------------------------------------------------------------------------\n",
+      "3 \t\t\t2.50000 \t\t\t-51.6326898244 \t\t\t20.0\n",
+      "----------------------------------------------------------------------------------------------------\n",
+      "4 \t\t\t2.62500 \t\t\t-59.2143243156 \t\t\t4.7619047619\n",
+      "----------------------------------------------------------------------------------------------------\n",
+      "5 \t\t\t2.64583 \t\t\t-60.4779300642 \t\t\t0.787401574803\n",
+      "----------------------------------------------------------------------------------------------------\n",
+      "6 \t\t\t2.64844 \t\t\t-60.6358807827 \t\t\t0.0983284169125\n",
+      "----------------------------------------------------------------------------------------------------\n"
+     ]
+    }
+   ],
+   "source": [
+    "from __future__ import division\n",
+    "from math import factorial\n",
+    "n=3##number of significant figures\n",
+    "es=0.5*(10**(2-n))##percent, specified error criterion\n",
+    "x=0.5#\n",
+    "f=[]\n",
+    "f.append(1)##first estimate f=e**x = 1\n",
+    "ft=1.648721##true value of e**0.5=f\n",
+    "et=[]\n",
+    "et.append((ft-f[0])*100/ft)\n",
+    "ea=[]\n",
+    "ea.append(100)\n",
+    "i=1\n",
+    "while ea[i-1]>=es:\n",
+    "    f.append(f[(i-1)]+(x**(i-1))/(factorial(i-1)))\n",
+    "    et.append((ft-f[(i)])*100/ft)\n",
+    "    ea.append((f[(i)]-f[(i-1)])*100/f[(i)])\n",
+    "    i=i+1#\n",
+    "\n",
+    "print \"Terms\\t\\t\\tResult\\t\\t\\t\\tet(%)\\t\\t\\t\\tea(%)\"\n",
+    "print '-'*100\n",
+    "for j in range(0,i-1):\n",
+    "    print j+1,'\\t\\t\\t%0.5f'%f[j],'\\t\\t\\t',et[j],'\\t\\t\\t',ea[j]\n",
+    "    print '-'*100"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex 3.3 Pg: 60"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Thus a 16-bit computer word can store decimal integers ranging from -32767 to 32767\n"
+     ]
+    }
+   ],
+   "source": [
+    "n=16##no of bits\n",
+    "num=0#\n",
+    "for i in range(0,(n-1)):\n",
+    "    num=num+(1*(2**i))#\n",
+    "\n",
+    "print \"Thus a 16-bit computer word can store decimal integers ranging from\",(-1*num),\"to\",num"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex 3.4: Pg :63"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The smallest possible positive number for this system is :  0.0625\n"
+     ]
+    }
+   ],
+   "source": [
+    "n=7##no. of bits\n",
+    "#the maximum value of exponents is given by\n",
+    "max=1*(2**1)+1*(2**0)#\n",
+    "#mantissa is found by\n",
+    "mantissa=1*(2**-1)+0*(2**-3)+0*(2**-3)#\n",
+    "num=mantissa*(2**(max*-1))##smallest possible positive number for this system\n",
+    "print \"The smallest possible positive number for this system is : \",num"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex 3.5: Pg :65"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "value of epsilon= 0.25\n"
+     ]
+    }
+   ],
+   "source": [
+    "b=2##base\n",
+    "t=3##number of mantissa bits\n",
+    "E=2**(1-t)##epsilon\n",
+    "print \"value of epsilon=\",E"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex 3.6: Pg :68"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Input a number: 15\n",
+      "The number summed up 100,000 times is= 1500000\n"
+     ]
+    }
+   ],
+   "source": [
+    "num=input(\"Input a number: \")\n",
+    "Sum=0#\n",
+    "for i in range(0,100000):\n",
+    "    Sum=Sum+num#\n",
+    "\n",
+    "print \"The number summed up 100,000 times is=\",Sum"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex 3.7: Pg :71"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The roots of the quadratic equation (x**2)+(3000.001*x)+3=0 are =  -0.000999999999976 & -3000.0\n"
+     ]
+    }
+   ],
+   "source": [
+    "a=1#\n",
+    "b=3000.001#\n",
+    "c=3#\n",
+    "#the roots of the quadratic equation x**2+3000.001*x+3=0 are found as\n",
+    "D=(b**2)-4*a*c#\n",
+    "x1=(-b+(D**0.5))/(2*a)#\n",
+    "x2=(-b-(D**0.5))/(2*a)#\n",
+    "print \"The roots of the quadratic equation (x**2)+(3000.001*x)+3=0 are = \",x1,'&',x2"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex 3.8: Pg :73"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Input value of x:1.25\n",
+      "sum: 1 term: 1 i: 0\n",
+      "-------------------------------------\n",
+      "sum: 2.25 term: 1.25 i: 1\n",
+      "-------------------------------------\n",
+      "sum: 3.03125 term: 0.78125 i: 2\n",
+      "-------------------------------------\n",
+      "sum: 3.35677083333 term: 0.325520833333 i: 3\n",
+      "-------------------------------------\n",
+      "sum: 3.45849609375 term: 0.101725260417 i: 4\n",
+      "-------------------------------------\n",
+      "sum: 3.48392740885 term: 0.0254313151042 i: 5\n",
+      "-------------------------------------\n",
+      "sum: 3.4892255995 term: 0.0052981906467 i: 6\n",
+      "-------------------------------------\n",
+      "sum: 3.49017170497 term: 0.000946105472625 i: 7\n",
+      "-------------------------------------\n",
+      "sum: 3.49031953395 term: 0.000147828980098 i: 8\n",
+      "-------------------------------------\n",
+      "sum: 3.49034006576 term: 2.05318027913e-05 i: 9\n",
+      "-------------------------------------\n",
+      "sum: 3.49034263223 term: 2.56647534892e-06 i: 10\n",
+      "-------------------------------------\n",
+      "sum: 3.49034292388 term: 2.91644926013e-07 i: 11\n",
+      "-------------------------------------\n",
+      "sum: 3.49034295426 term: 3.03796797931e-08 i: 12\n",
+      "-------------------------------------\n",
+      "sum: 3.49034295718 term: 2.92112305703e-09 i: 13\n",
+      "-------------------------------------\n",
+      "sum: 3.49034295744 term: 2.60814558663e-10 i: 14\n",
+      "-------------------------------------\n",
+      "sum: 3.49034295746 term: 2.17345465553e-11 i: 15\n",
+      "-------------------------------------\n",
+      "sum: 3.49034295746 term: 1.69801144963e-12 i: 16\n",
+      "-------------------------------------\n",
+      "sum: 3.49034295746 term: 1.24853783061e-13 i: 17\n",
+      "-------------------------------------\n",
+      "sum: 3.49034295746 term: 8.67040160146e-15 i: 18\n",
+      "-------------------------------------\n",
+      "sum: 3.49034295746 term: 5.7042115799e-16 i: 19\n",
+      "-------------------------------------\n",
+      "Exact Value: 3.49034295746\n"
+     ]
+    }
+   ],
+   "source": [
+    "from math import exp\n",
+    "def f(x):\n",
+    "    y=exp(x)\n",
+    "    return y\n",
+    "Sum=1#\n",
+    "test=0#\n",
+    "i=0#\n",
+    "term=1#\n",
+    "x=input(\"Input value of x:\")\n",
+    "while Sum!=test:\n",
+    "    print \"sum:\",Sum,\"term:\",term,\"i:\",i\n",
+    "    print \"-------------------------------------\"\n",
+    "    i=i+1#\n",
+    "    term=term*x/i#\n",
+    "    test=Sum#\n",
+    "    Sum=Sum+term#\n",
+    "\n",
+    "print \"Exact Value:\",f(x)"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 2",
+   "language": "python",
+   "name": "python2"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.9"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter4.ipynb b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter4.ipynb
new file mode 100644
index 00000000..ac35f0f7
--- /dev/null
+++ b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter4.ipynb
@@ -0,0 +1,513 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Chapter 4 : Truncation Errors and the Taylor Series"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Example: 4.1 Page No:79"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The value of f at x=0 : 1.2\n",
+      "The value of f at x=1 due to zero order approximation : 1.2\n",
+      "Truncation error : -1.0\n",
+      "----------------------------------------------\n",
+      "The value of first derivative of f at x=0 : -0.4\n",
+      "The value of f at x=1 due to first order approximation : 0.8\n",
+      "Truncation error : -0.6\n",
+      "----------------------------------------------\n",
+      "The value of second derivative of f at x=0 : -1.8\n",
+      "The value of f at x=1 due to second order approximation : -0.1\n",
+      "Truncation error : 0.3\n",
+      "----------------------------------------------\n",
+      "The value of third derivative of f at x=0 : -0.9\n",
+      "The value of f at x=1 due to third order approximation : -0.25\n",
+      "Truncation error : 0.45\n",
+      "----------------------------------------------\n",
+      "The value of fourth derivative of f at x=0 : -2.4\n",
+      "The value of f at x=1 due to fourth order approximation : -0.35\n",
+      "Truncation error : 0.55\n",
+      "----------------------------------------------\n"
+     ]
+    }
+   ],
+   "source": [
+    "from math import factorial\n",
+    "from scipy.misc import derivative\n",
+    "def f(x):\n",
+    "    y=-0.1*x**4-0.15*x**3-0.5*x**2-0.25*x+1.2#\n",
+    "    return y\n",
+    "xi=0#\n",
+    "xf=1#\n",
+    "h=xf-xi#\n",
+    "fi=f(xi)##function value at xi\n",
+    "ffa=f(xf)##actual function value at xf\n",
+    "\n",
+    "#for n=0, i.e, zero order approximation\n",
+    "ff=fi#\n",
+    "Et_1=ffa-ff##truncation error at x=1\n",
+    "print \"The value of f at x=0 :\",fi\n",
+    "print \"The value of f at x=1 due to zero order approximation :\",ff\n",
+    "print \"Truncation error :\",Et_1\n",
+    "print \"----------------------------------------------\"\n",
+    "\n",
+    "#for n=1, i.e, first order approximation\n",
+    "def f1(x):\n",
+    "    y=derivative(f,x)\n",
+    "    return y\n",
+    "f1i=f1(xi)##value of first derivative of function at xi\n",
+    "f1f=fi+f1i*h##value of first derivative of function at xf\n",
+    "Et_2=ffa-f1f##truncation error at x=1\n",
+    "print \"The value of first derivative of f at x=0 :\",f1i\n",
+    "print \"The value of f at x=1 due to first order approximation :\",f1f\n",
+    "print \"Truncation error :\",Et_2\n",
+    "print \"----------------------------------------------\"\n",
+    "\n",
+    "\n",
+    "#for n=2, i.e, second order approximation\n",
+    "def f2(x):\n",
+    "    y=derivative(f1,x)\n",
+    "    return y\n",
+    "f2i=f2(xi)##value of second derivative of function at xi\n",
+    "f2f=f1f+f2i*(h**2)/factorial(2)##value of second derivative of function at xf\n",
+    "Et_3=ffa-f2f##truncation error at x=1\n",
+    "print \"The value of second derivative of f at x=0 :\",f2i\n",
+    "print \"The value of f at x=1 due to second order approximation :\",f2f\n",
+    "print \"Truncation error :\",Et_3\n",
+    "print \"----------------------------------------------\"\n",
+    "\n",
+    "#for n=3, i.e, third order approximation\n",
+    "def f3(x):\n",
+    "    y=derivative(f2,x)\n",
+    "    return y\n",
+    "f3i=f3(xi)##value of third derivative of function at xi\n",
+    "f3f=f2f+f3i*(h**3)/factorial(3)##value of third derivative of function at xf\n",
+    "Et_4=ffa-f3f##truncation error at x=1\n",
+    "print \"The value of third derivative of f at x=0 :\",f3i\n",
+    "print \"The value of f at x=1 due to third order approximation :\",f3f\n",
+    "print \"Truncation error :\", Et_4\n",
+    "print \"----------------------------------------------\"\n",
+    "\n",
+    "#for n=4, i.e, fourth order approximation\n",
+    "def f4(x):\n",
+    "    y=derivative(f3,x)\n",
+    "    return y\n",
+    "f4i=f4(xi)##value of fourth derivative of function at xi\n",
+    "f4f=f3f+f4i*(h**4)/factorial(4)##value of fourth derivative of function at xf\n",
+    "Et_5=ffa-f4f##truncation error at x=1\n",
+    "print \"The value of fourth derivative of f at x=0 :\",f4i\n",
+    "print \"The value of f at x=1 due to fourth order approximation :\",f4f\n",
+    "print \"Truncation error :\",Et_5\n",
+    "print \"----------------------------------------------\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Example 4.2:  Page No:82"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The value of f at x=1 due to zero order approximation : 0.707106781187\n",
+      "% relative error : -41.4213562373\n",
+      "----------------------------------------------\n",
+      "The value of f at x=1 due to first order approximation : 0.551333569463\n",
+      "% relative error : -10.2667138927\n",
+      "----------------------------------------------\n",
+      "The value of f at x=1 due to second order approximation : 0.534175415889\n",
+      "% relative error : -6.83508317772\n",
+      "----------------------------------------------\n",
+      "The value of f at x=1 due to third order approximation : 0.535435376789\n",
+      "% relative error : -7.08707535775\n",
+      "----------------------------------------------\n",
+      "The value of f at x=1 due to fourth order approximation : 0.535504768061\n",
+      "% relative error : -7.10095361216\n",
+      "----------------------------------------------\n",
+      "The value of f at x=1 due to fifth order approximation : 0.535501917392\n",
+      "% relative error : -7.10038347839\n",
+      "----------------------------------------------\n",
+      "The value of f at x=1 due to sixth order approximation : 0.535501819651\n",
+      "% relative error : -7.10036393016\n",
+      "----------------------------------------------\n"
+     ]
+    }
+   ],
+   "source": [
+    "from math import pi,cos,factorial\n",
+    "from scipy.misc import derivative\n",
+    "def f(x):\n",
+    "    y=cos(x)\n",
+    "    return y\n",
+    "xi=pi/4#\n",
+    "xf=pi/3#\n",
+    "h=xf-xi#\n",
+    "fi=f(xi)##function value at xi\n",
+    "ffa=f(xf)##actual function value at xf\n",
+    "\n",
+    "#for n=0, i.e, zero order approximation\n",
+    "ff=fi#\n",
+    "et1=(ffa-ff)*100/ffa##percent relative error at x=1\n",
+    "print \"The value of f at x=1 due to zero order approximation :\",ff\n",
+    "print \"% relative error :\",et1\n",
+    "print \"----------------------------------------------\"\n",
+    "\n",
+    "#for n=1, i.e, first order approximation\n",
+    "def f1(x):\n",
+    "    y=derivative(f,x)\n",
+    "    return y\n",
+    "f1i=f1(xi)##value of first derivative of function at xi\n",
+    "f1f=fi+f1i*h##value of first derivative of function at xf\n",
+    "et2=(ffa-f1f)*100/ffa##% relative error at x=1\n",
+    "print \"The value of f at x=1 due to first order approximation :\",f1f\n",
+    "print \"% relative error :\",et2\n",
+    "print \"----------------------------------------------\"\n",
+    "\n",
+    "\n",
+    "#for n=2, i.e, second order approximation\n",
+    "def f2(x):\n",
+    "    y=derivative(f1,x)\n",
+    "    return y\n",
+    "f2i=f2(xi)##value of second derivative of function at xi\n",
+    "f2f=f1f+f2i*(h**2)/factorial(2)##value of second derivative of function at xf\n",
+    "et3=(ffa-f2f)*100/ffa##% relative error at x=1\n",
+    "print \"The value of f at x=1 due to second order approximation :\",f2f\n",
+    "print \"% relative error :\",et3\n",
+    "print \"----------------------------------------------\"\n",
+    "\n",
+    "\n",
+    "#for n=3, i.e, third order approximation\n",
+    "def f3(x):\n",
+    "    y=derivative(f2,x)\n",
+    "    return y\n",
+    "f3i=f3(xi)##value of third derivative of function at xi\n",
+    "f3f=f2f+f3i*(h**3)/factorial(3)##value of third derivative of function at xf\n",
+    "et4=(ffa-f3f)*100/ffa##% relative error at x=1\n",
+    "print \"The value of f at x=1 due to third order approximation :\",f3f\n",
+    "print \"% relative error :\",et4\n",
+    "print \"----------------------------------------------\"\n",
+    "\n",
+    "\n",
+    "#for n=4, i.e, fourth order approximation\n",
+    "def f4(x):\n",
+    "    y=derivative(f3,x)\n",
+    "    return y\n",
+    "f4i=f4(xi)##value of fourth derivative of function at xi\n",
+    "f4f=f3f+f4i*(h**4)/factorial(4)##value of fourth derivative of function at xf\n",
+    "et5=(ffa-f4f)*100/ffa##% relative error at x=1\n",
+    "print \"The value of f at x=1 due to fourth order approximation :\",f4f\n",
+    "print \"% relative error :\",et5\n",
+    "print \"----------------------------------------------\"\n",
+    "\n",
+    "\n",
+    "#for n=5, i.e, fifth order approximation\n",
+    "f5i=(f4(1.1*xi)-f4(0.9*xi))/(2*0.1)##value of fifth derivative of function at xi (central difference method)\n",
+    "f5f=f4f+f5i*(h**5)/factorial(5)##value of fifth derivative of function at xf\n",
+    "et6=(ffa-f5f)*100/ffa##% relative error at x=1\n",
+    "print \"The value of f at x=1 due to fifth order approximation :\",f5f\n",
+    "print \"% relative error :\",et6\n",
+    "print \"----------------------------------------------\"\n",
+    "\n",
+    "\n",
+    "#for n=6, i.e, sixth order approximation\n",
+    "def f6(x):\n",
+    "    y=derivative(f5,x)\n",
+    "    return y\n",
+    "f6i=(f4(1.1*xi)-2*f4(xi)+f4(0.9*xi))/(0.1**2)##value of sixth derivative of function at xi (central difference method)\n",
+    "f6f=f5f+f6i*(h**6)/factorial(6)##value of sixth derivative of function at xf\n",
+    "et6=(ffa-f6f)*100/ffa##% relative error at x=1\n",
+    "print \"The value of f at x=1 due to sixth order approximation :\",f6f\n",
+    "print \"% relative error :\", et6\n",
+    "print \"----------------------------------------------\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Example 4.3 :  Page No:85"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Input value of m:4\n",
+      "Input value of h:5\n",
+      "\n",
+      "Remainder: 21 \n",
+      "The value by first order approximation: 1275\n",
+      "True Value at x2: 1296\n"
+     ]
+    }
+   ],
+   "source": [
+    "from math import pi,cos,factorial\n",
+    "m=input(\"Input value of m:\")\n",
+    "h=input(\"Input value of h:\")\n",
+    "def f(x):\n",
+    "    y=x**m\n",
+    "    return y\n",
+    "x1=1#\n",
+    "x2=x1+h#\n",
+    "fx1=f(x1)#\n",
+    "fx2=fx1+m*(fx1**(m-1))*h#\n",
+    "if m==1:\n",
+    "    R=0#\n",
+    "elif m==2 :\n",
+    "    R=2*(h**2)/factorial(2)#\n",
+    "    \n",
+    "elif m==3:\n",
+    "    R=(6*(x1)*(h**2)/factorial(2))+(6*(h**3)/factorial(3))#\n",
+    "    \n",
+    "elif m==4:\n",
+    "    R=(12*(x1**2)*(h**2)/factorial(2))+(24*(x1)*(h**3)/factorial(3))+(24*(h**4)/factorial(4))\n",
+    "  \n",
+    "print \"\\nRemainder:\",fx2,\"\\nThe value by first order approximation:\",R\n",
+    "print \"True Value at x2:\",f(x2)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Example 4.4:  Page No:92"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Input h:1.232323\n",
+      "For h= 1.232323\n",
+      "and percent error= -2.70944264922 Derivative at x by forward difference method= 114.60931875\n",
+      "and percent error= -0.178591334206 Derivative at x by backward difference method= 85.854151746\n",
+      "and percent error= -1.44401699172 Derivative at x by central difference method= 14.3775835022\n"
+     ]
+    }
+   ],
+   "source": [
+    "from scipy.misc import derivative\n",
+    "def f(x):\n",
+    "    y=-0.1*(x**4)-0.15*(x**3)-0.5*(x**2)-0.25*(x)+1.2\n",
+    "    return y\n",
+    "x=0.5#\n",
+    "h=input(\"Input h:\")\n",
+    "x1=x-h#\n",
+    "x2=x+h#\n",
+    "#forward difference method\n",
+    "fdx1=(f(x2)-f(x))/h##derivative at x\n",
+    "et1=abs((fdx1-derivative(f,x))/derivative(f,x))*100#\n",
+    "#backward difference method\n",
+    "fdx2=(f(x)-f(x1))/h##derivative at x\n",
+    "et2=abs((fdx2-derivative(f,x))/derivative(f,x))*100#\n",
+    "#central difference method\n",
+    "fdx3=(f(x2)-f(x1))/(2*h)##derivative at x\n",
+    "et3=abs((fdx3-derivative(f,x))/derivative(f,x))*100#\n",
+    "print \"For h=\",h\n",
+    "print \"and percent error=\",fdx1,\"Derivative at x by forward difference method=\",et1\n",
+    "print \"and percent error=\",fdx2,\"Derivative at x by backward difference method=\",et2\n",
+    "print \"and percent error=\",fdx3,\"Derivative at x by central difference method=\",et3"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Example 4.5:  Page No: 95"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "true value is between :  15.4275 and 15.8225\n"
+     ]
+    }
+   ],
+   "source": [
+    "from scipy.misc import derivative\n",
+    "def f(x):\n",
+    "    y=x**3\n",
+    "    return y\n",
+    "x=2.5#\n",
+    "delta=0.01#\n",
+    "deltafx=abs(derivative(f,x))*delta#\n",
+    "fx=f(x)#\n",
+    "print \"true value is between : \",fx-deltafx,\"and\",fx+deltafx"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Example 4.6:  Page No: 96"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The value of y is between: 0.528721343471 and 0.596278656529\n",
+      "ymin is calculated at lower extremes of F, L, E, I values as = 0.524066539965\n",
+      "ymax is calculated at higher extremes of F, L, E, I values as = 0.602846335915\n"
+     ]
+    }
+   ],
+   "source": [
+    "def f(F,L,E,I):\n",
+    "    y=(F*(L**4))/(8*E*I)\n",
+    "    return y\n",
+    "Fbar=50##lb/ft\n",
+    "Lbar=30##ft\n",
+    "Ebar=1.5*(10**8)##lb/ft**2\n",
+    "Ibar=0.06##ft**4\n",
+    "deltaF=2##lb/ft\n",
+    "deltaL=0.1##ft\n",
+    "deltaE=0.01*(10**8)##lb/ft**2\n",
+    "deltaI=0.0006##ft**4\n",
+    "ybar=(Fbar*(Lbar**4))/(8*Ebar*Ibar)#\n",
+    "def f1(F):\n",
+    "    y=(F*(Lbar**4))/(8*Ebar*Ibar)\n",
+    "    return y\n",
+    "def f2(L):\n",
+    "    y=(Fbar*(L**4))/(8*Ebar*Ibar)\n",
+    "    return y\n",
+    "def f3(E):\n",
+    "    y=(Fbar*(Lbar**4))/(8*E*Ibar)\n",
+    "    return y\n",
+    "def f4(I):\n",
+    "    y=(Fbar*(Lbar**4))/(8*Ebar*I)\n",
+    "    return y\n",
+    "\n",
+    "deltay=abs(derivative(f1,Fbar))*deltaF+abs(derivative(f2,Lbar))*deltaL+abs(derivative(f3,Ebar))*deltaE+abs(derivative(f4,Ibar))*deltaI#\n",
+    "\n",
+    "print \"The value of y is between:\",ybar-deltay,\"and\",ybar+deltay\n",
+    "ymin=((Fbar-deltaF)*((Lbar-deltaL)**4))/(8*(Ebar+deltaE)*(Ibar+deltaI))#\n",
+    "ymax=((Fbar+deltaF)*((Lbar+deltaL)**4))/(8*(Ebar-deltaE)*(Ibar-deltaI))#\n",
+    "print \"ymin is calculated at lower extremes of F, L, E, I values as =\",ymin\n",
+    "print \"ymax is calculated at higher extremes of F, L, E, I values as =\",ymax"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Example 4.7 :  Page No:98"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The condition number of function for x = 0.18201112073 is : 1.72787595947\n",
+      "The condition number of function for x = 0.0160083243793 is : 1.58650429006\n"
+     ]
+    }
+   ],
+   "source": [
+    "from math import pi,tan\n",
+    "from scipy.misc import derivative\n",
+    "def f(x):\n",
+    "    y=tan(x)\n",
+    "    return y\n",
+    "x1bar=(pi/2)+0.1*(pi/2)#\n",
+    "x2bar=(pi/2)+0.01*(pi/2)#\n",
+    "#computing condition number for x1bar\n",
+    "condnum1=x1bar*derivative(f,x1bar)/f(x1bar)#\n",
+    "print \"The condition number of function for x =\",condnum1,\"is :\",x1bar\n",
+    "if abs(condnum1)>1:\n",
+    "    print \"Function is ill-conditioned for x =\",x1bar\n",
+    "\n",
+    "#computing condition number for x2bar\n",
+    "condnum2=x2bar*derivative(f,x2bar)/f(x2bar)#\n",
+    "print \"The condition number of function for x =\",condnum2,\"is :\",x2bar\n",
+    "if abs(condnum2)>1:\n",
+    "    print \"Function is ill-conditioned for x =\",x2bar"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 2",
+   "language": "python",
+   "name": "python2"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.9"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter5.ipynb b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter5.ipynb
new file mode 100644
index 00000000..2b0b77e2
--- /dev/null
+++ b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter5.ipynb
@@ -0,0 +1,528 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Chapter 5 : Bracketing Methods"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex5.1: Pg:120"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "For various values of c and f(c) is found as:\n",
+      "[4, 34.114844174677984]\n",
+      "[8, 17.653427509399428]\n",
+      "[12, 6.066935998372109]\n",
+      "[16, -2.2687619693477643]\n",
+      "[20, -8.400628721768179]\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7fa7dfe0c990>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "from numpy import arange\n",
+    "from math import exp\n",
+    "%matplotlib inline\n",
+    "from matplotlib.pyplot import plot, title, xlabel, ylabel, show\n",
+    "m=68.1##kg\n",
+    "v=40##m/s\n",
+    "t=10##s\n",
+    "g=9.8##m/s**2\n",
+    "def f(c):\n",
+    "    y=g*m*(1-exp(-c*t/m))/c - v#\n",
+    "    return y\n",
+    "print \"For various values of c and f(c) is found as:\"\n",
+    "i=0#\n",
+    "Fc=[]\n",
+    "for c in arange(4,21,4):\n",
+    "    i=i+1#\n",
+    "    bracket=[c, f(c)]\n",
+    "    print bracket\n",
+    "    Fc.append(f(c))\n",
+    "\n",
+    "c=arange(4,21,4)\n",
+    "plot(c,Fc)\n",
+    "title('f(c) vs c')\n",
+    "xlabel('c')\n",
+    "ylabel('f(c) (m/s)')\n",
+    "show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex5.2: Pg:123"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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qb1/47LMwwUw/FGR5jjsurGLw0EOxk0gMaonIT/zjH3DjjfDii9C6dew0UiqefRZ69Qqd\n7c2bx04jmVJLRHLq8cfhr38N8wBUQKQhdtsNunSBv/0tdhIpNLVEBIDXXgu72Q0bBjvuGDuNlKL3\n34fOnWHCBFh//dhpJBNqiUhOvP8+9OgRhmmqgEi2NtgATj0V+qXdXk7KlVoiFW7OHNh119A5euaZ\nsdNIqZs/Pwz5vfde6No1dhpZHg3xTaiIZOe776B7d9hqK7j+eo3EktwYMgSuugpeeQWaNImdRpZF\nl7Mka0uXdW/RAq69VgVEcqdnzzBC6847YyeRQlBLpEINGBD2BBkzJhQSkVwaPz7sfllTAy1bxk4j\n9VFLRLJy993ht8Rhw1RAJD86dw4bWA0YEDuJ5JtaIhVm9Gg4/PDw95Zbxk4j5Wz27NDf9sIL0LFj\n7DSSjloi0iBTpoTr1fffrwIi+de2LZx3XtgFUcqXikiFmD07XKO++mrYY4/YaaRSnHYaTJ8eVkGQ\n8qTLWRVg8eKwoVSXLmFZE5FCGj48zEF6801o1ix2GqlNl7MkIwMGhCG96uSUGPbbDzbeGAYOjJ1E\n8iFaS8TMWgMPABsAM4DD3H1OnWPaA3cDawEO3OruN6R5L7VE6vH003DssWFtrHbtYqeRSlVTE2aw\nayvd4lLSM9bN7CrgM3e/ysz6AWu4e/86x7QD2rn7RDNbFXgNONjdp9Y5TkUkjVmzYPvtQ0d6KhU7\njVS6s88O+44MGhQ7iSxV6kWkBtjd3WcnxaLa3TdfzmuGAje6+3/rPK4iUseiRWF72/32C3uki8S2\ndCvd4cPDPBKJr9SLyJfuvkZy24Avlt6v5/gOwBhgK3efV+c5FZE6+vYNHZlPPAErqOdLisSgQWGy\n67PPaqmdYpCLItI0V2HSMbORQLor8efXvuPubmb1VoHkUtbDwBl1C8hSVVVVP9xOpVKkKvj6zWOP\nhUXwxo9XAZHi8oc/wM03wwMPhEmvUljV1dVUV1fn9D1jX85KufvHZrY2MDrd5SwzWxEYBjzp7tfV\n815qiSRmzAh7ggwdCjvtFDuNyM899xwcdVTobNdWunGV+hDfx4Deye3ewNC6BySXuW4HptRXQORH\nCxfCoYdC//4qIFK8unaFnXcOy8VL6Ys9xPdBYH1qDfE1s3WAQe6+v5ntCjwLvEEY4gtwnruPqPNe\naokQZgfPmgX//reuN0tx+9//Quf6+PHaSjemku5YzyUVEXjwwbBO0WuvQatWsdOILN8ll4T13B54\nIHaSyqUikqj0IvL227DLLjBiBGy3Xew0IpmZPx+22AL+9S/YbbfYaSpTqfeJSA4sWBD6QQYMUAGR\n0tK8eegXOeOMsL6blCYVkRJ3+ulhz4aTToqdRKThDjsMVlsNbr89dhLJli5nlbC774bLLoNXXgn/\nEUVK0YQJ0L17GPKr/rzCUp9IohKLyKRJYVmTZ56BrbeOnUakcU48EVZdFa65JnaSyqIikqi0IjJv\nXlhYsV8/OOaY2GlEGu/TT8Num889F9bXksJQEUlUUhFxh9//HlZaCe64I3Yakdy59tqwdcHw4Zrn\nVCganVWBBg0KCytqgx8pN6ecAu+9p610S41aIiVk/HjYd194/nno2DF2GpHce/LJMOR30iRtpVsI\naolUkLlzw3yQgQNVQKR8de8Om20GN/xs/1IpVmqJlAB3OOSQsL3tP/4RO41Ifr39dligcfJkaNs2\ndprypo71RLkXkeuvD0tDvPBC6FAXKXfnnBN2QrzttthJypuKSKKci8hLL0GPHjBuHGy4Yew0IoUx\nd24Y6jtsmJbzySf1iZS5zz8Pu78NGqQCIpWlZUu49NLQyV6mvx+WDRWRIrVkCRx9dOgLOeig2GlE\nCu+YY8ICo0OGxE4iy6LLWUXqiivCXuljxsCKK8ZOIxLHCy+E1nhNDbRoETtN+VGfSKLcisiYMdCz\nZ1hYsX372GlE4jrySNhkk7DdgeRWQYqImbUCdgI6ELaonQGMdfe5jfngXCqnIjJ7duhIvO026NYt\ndhqR+GbOhE6dwq6dHTrETlNe8lpEzKwrcC6heEwAPgQMWBvYllBMrnL35xsTIBfKpYgsXhxmpO+0\nE/zlL7HTiBSPAQPCLPYHH4ydpLzku4hcA9zs7tPqeX4z4CR3P6vBH2rWGngA2IBQjA5z9zn1HNsE\neBWY5e4H1nNMWRSRiy8Oq5iOHAlNmsROI1I8FiwIW+nedRekUrHTlI+S7RMxs6uAz9z9KjPrB6zh\n7v3rOfYsYDtgNXfvUc8xJV9Enn4ajj02NNnbtYudRqT4PPRQGPY7frx+ycqVgswTMbN7kn6Rpfc7\nmNkzjflQoAcwOLk9GDi4ns9eD9gPuI1wKa0sffAB9O4N996rAiJSn0MOgTXW0Cz2YpPJPJHngHFm\ntr+ZnQg8DVzbyM9t6+6zk9uzgfpWyLmW0C+zpJGfV7QWLQpDGE87Tc10kWUxg+uuC5d9v/wydhpZ\nqunyDnD3W8xsCvAM8BnQ2d0/Wt7rzGwkkO736vPrvL+b2c+uRZnZAcAn7j7BzFLL+7yqqqofbqdS\nKVIl8hP5ggvCtqD9017ME5HaOnWCgw+GSy4JBUUaprq6murq6py+ZyZDfHsBFyV/fgl0A45194lZ\nf6hZDZBy94/NbG1gtLtvXueYy4BewPfAysDqwCPufnSa9yvJPpHHHw8b8YwfD23axE4jUhqWbqU7\nZkz4W7JXqHkiQ4ET3f2T5P4OwK3u3inrDw0d65+7+5Vm1h9oVV/HenL87sA55TQ6a8YM2HFHePTR\nsOy1iGTuuuvCBlYjRmgr3cYoSMe6ux+8tIAk918GdmzMhwJXAHub2dvAHsl9zGwdM3uiviiN/Myi\nsXAhHHYY9OunAiKSjVNOgf/9L6zyK3Eta55IFWGeyOx6nl+bME/k4vzFy0yptUROPz3Mwv33v/Vb\nlEi2nnoKTj01TELUPjvZyUVLZFkd668AQ8ysGTAe+IgwzLYd0BlYCFzdmA+vRA89BE88EeaDqICI\nZG/ffcOeIzfcAOeeGztN5VpWS+Rf7t7LzC4ApvHj2lnvAy+4+6yCpVyOUmmJTJsWLl+NGKGNdkRy\nYdq0sEzQpEmaY5WNfC97MgXYCxgBpPjpZD939y8a88G5VApFZMEC6NIFTjoJTj45dhqR8tG3L3z2\nGdxxR+wkpSffReR04GRgI8Lii7W5u2/UmA/OpVIoIiecAPPmwX336TKWSC599VW4rPWf/8D228dO\nU1oKNcT3n+5+UmM+JN+KvYjcfTdcdlnYH2S11WKnESk/d94ZtpF+4QX9ktYQJbsAY64VcxGZPDks\nZ/LMM7D11rHTiJSnJUtghx3gzDPhqKNipykdKiKJYi0i8+aFb+y+fcN+0SKSPy++GOZf1dSEpYRk\n+VREEsVYRNyhVy9o1kwdfiKFctRRsNFG2tQtUyoiiWIsIrfeCjfeCOPGQfPmsdOIVIaZM2GbbeCt\nt+AXv4idpvipiCSKrYiMHx8mQj3/PHTsGDuNSGU5+eSw78hll8VOUvxURBLFVERqamCPPWDgQPjt\nb2OnEak8778PnTuHiYitW8dOU9wKsgCjZO6dd2DvveHyy1VARGLZYIPw/0/7jRSGWiI5MnMm7LZb\nGImlGekicb37bhgZOW1auLQl6aklUiQ+/hj23DNscasCIhLfRhvBgQeGxRklv9QSaaTPPguTCXv2\nhAsvjBJBRNKYPj0szjh9OrRsGTtNcVJLJLI5c8IorAMPDHuli0jx2GQT6N49DHKR/FFLJEvz5sE+\n+4QF3667Tuv1iBSjt96Crl3DoBetW/dzaolEsmBBaH1stRVce60KiEix6tgR9toLbropdpLypZZI\nAy1cCAcfHMaf3303NGlSkI8VkSxNmQK//nVojWhNrZ8q2ZaImbU2s5Fm9raZPW1mreo5rpWZPWxm\nU81sipl1KXTW2hYtgiOOCMuYDB6sAiJSCrbcMgx++ec/YycpT1FaImZ2FfCZu19lZv2ANdy9f5rj\nBgNj3P0OM2sKtHD3uWmOy3tLZPHisKDi3Lnw6KNhYUURKQ1vvhn6MN95R2vZ1Vayy56YWQ2wu7vP\nNrN2QLW7b17nmJbAhEx2UMx3EVmyBE48Ed57D4YNg1VWydtHiUie/O53oZP9T3+KnaR4lHIR+dLd\n10huG/DF0vu1jukE3AJMAbYBXgPOcPf5ad4vb0XEHU4/PSyq+NRTuqYqUqomToT99gutEf0iGOSi\niDTNVZi6zGwk0C7NU+fXvuPubmbpKkBToDNwqru/YmbXAf2Bi9J9XlVV1Q+3U6kUqVQqu+A/yQb9\n+8PYsfDf/6qAiJSyTp3CkPzbbgurS1Si6upqqqurc/qeMS9npdz9YzNbGxid5nJWO2Csu2+Y3N8V\n6O/uB6R5v7y0RAYMgIcegupqWHPNnL+9iBTYa6/BQQeFWewrrxw7TXwlOzoLeAzondzuDQyte4C7\nfwzMNLPNkof2AiYXJh5cfTXcey+MGqUCIlIuttsutEjuvDN2kvIRqyXSGngQWB+YARzm7nPMbB1g\nkLvvnxy3DXAb0Ax4Bzi2EKOzbropFJFnn4X11svZ24pIERg3Dg49NLRGKn2UZcl2rOdaLovInXfC\nxRfDmDGw4YY5eUsRKTLduoXRWiecEDtJXCoiiVwVkSFD4KyzYPRobWsrUs5efBGOOgrefhtWXDF2\nmnhKuU+k6PznP2H8+FNPqYCIlLudd4aNN4Z//St2ktKnlgihcPTqBcOHw69+lcNgIlK0nnsOjjkm\nrPTbNG+THYqbWiI5MGYM/P73YSkTFRCRytG1K6y/Ptx3X+wkpa2iWyIvvQQ9eoS+kD32yEMwESlq\no0dDnz4wdWplLqiqlkgjTJgQJh3ddZcKiEilSqWgbVt44IHYSUpXRbZEJk8OG9UMHBiG+YlI5Ro5\nMqyPN2lS5bVG1BLJwrRpYUnoq69WARGR8AvlGmvAww/HTlKaKqol8v77sNtucMEFmmQkIj8aMQLO\nOQfeeANWqKBfrdUSaYAPP4Q994Szz1YBEZGf2nffsFnVo4/GTlJ6KqKIfPJJKCDHHx+ufYqI1GYG\nF10UVu5esiR2mtJS9kXkiy9CH8ghh4S9QURE0tl//zDp8PHHYycpLWXdJ/LVV7D33rDrrqEj3Rp1\n5U9Eyt1//gOXXBL2HamEnxfqE1mGb76BAw6Azp1VQEQkMz16hMtZTzwRO0npKMuWyLffhm+GtdcO\nS7tX0mgLEWmcRx6BK68M+46U+y+faomksWgRHHYYtGoFt9+uAiIiDfOb38D8+WFhVlm+svoR+/33\nYY8AgHvuqdyVOUUkeyusABdeGPpGyuBCTd6VTRFZsgSOOw7mzIEHH9S2lyKSvUMOCT9LRo2KnaT4\nlU0ROeUUeO+9MFlo5ZVjpxGRUtakiVojmYpSRMystZmNNLO3zexpM2tVz3HnmdlkM3vTzO4zs5Xq\ne8/x42HYMGjRIn+5RaRy9OwJn34K1dWxkxS3WC2R/sBId98M+G9y/yfMrANwAtDZ3bcGmgCH1/eG\nTz4Jq6+el6wiUoGaNIHzzw+z2KV+sYpID2BwcnswcHCaY74CFgHNzawp0Bz4oL43bN061xFFpNId\neSTMnAnPPhs7SfGKVUTauvvs5PZsoG3dA9z9C+DvwP+AD4E57q5uLhEpmKZN4c9/hr/8JXaS4pW3\nQbBmNhJol+ap82vfcXc3s591XZnZxsCfgA7AXOAhMzvK3e9N93lVVVU/3E6lUqRSqWyji4j8oFev\nUERefBF23jl2msaprq6mOsedPFFmrJtZDZBy94/NbG1gtLtvXueYnsDe7n58cr8X0MXdT0nzflnt\nsS4ikolBg8JM9hEjYifJrVKesf4Y0Du53RsYmuaYGqCLma1iZgbsBUwpUD4RkR/07g1Tp4alUOSn\nYhWRK4C9zextYI/kPma2jpk9AeDurwN3A68CbySvuzVCVhGpcM2aha0k1Dfyc2W5AKOISK4tXAib\nbAJDh8J228VOkxulfDlLRKSkrLQS9OuneSN1qSUiIpKhb7+FjTcOq2Nsu23sNI2nloiISAGtvDKc\ney5cemnsJMVDLRERkQaYPz+0Rp5+GrbeOnaaxlFLRESkwJo3h7PPVmtkKbVEREQa6JtvYKONYPRo\n2HLL2Gktw5xbAAAI20lEQVSyp5aIiEgELVrAWWepNQJqiYiIZOXrr0PfyLPPwuabL//4YqSWiIhI\nJKutBmecAZddFjtJXGqJiIhkae7cMIt97Njwd6lRS0REJKKWLeHUUyu7NaKWiIhII8yZE1ohL78c\nRmyVErVEREQia9UK/vhHuPzy2EniUEtERKSRvvgCNt0Uxo+HDTaInSZzaomIiBSB1q2hTx+44orY\nSQpPLRERkRz47DPo2BEmToT27WOnyYxaIiIiRaJNGzj+eLjqqthJCkstERGRHPnkE9hiC3jzTVhn\nndhplq9kWyJmdqiZTTazxWbWeRnHdTOzGjObZmb9CplRRKSh1loLjjmmslojUVoiZrY5sAS4BTjb\n3cenOaYJ8BawF/AB8ApwhLtPTXOsWiIiUhQ++gi22gqmTIF27WKnWbaSbYm4e427v72cw3YAprv7\nDHdfBAwBDsp/OhGR7K29NvTqBVdfHTtJYRRzx/q6wMxa92clj4mIFLW+feHOO0MfSbnLWxExs5Fm\n9maaPwdm+Ba6PiUiJWnddeGII+Dvf4+dJP+a5uuN3X3vRr7FB0Dt0dbtCa2RtKqqqn64nUqlSKVS\njfx4EZHs9esHnTrBueeG4b/FoLq6murq6py+Z9QhvmY2GjjH3V9L81xTQsf6nsCHwMuoY11ESshJ\nJ8Gaa8Jf/xo7SXq56FiPNTrrN8ANQBtgLjDB3bub2TrAIHffPzmuO3Ad0AS43d3TLnGmIiIixWjG\nDNhuO5g2LSyNUmxKtojkmoqIiBSr448PfSSXXBI7yc+piCRURESkWL37Luy5Z2iNNM1bL3R2VEQS\nKiIiUswWLIBVVomd4udURBIqIiIiDVeyM9ZFRKQ8qIiIiEjWVERERCRrKiIiIpI1FREREcmaioiI\niGRNRURERLKmIiIiIllTERERkaypiIiISNZUREREJGsqIiIikjUVERERyZqKiIiIZE1FREREsqYi\nIiIiWYtWRMzsUDObbGaLzaxzPce0N7PRyXGTzOz0QucUEZH6xWyJvAn8Bnh2GccsAs50962ALsAp\nZrZFIcI1VnV1dewIP6NMmSvGXMqUGWUqrGhFxN1r3P3t5RzzsbtPTG7PA6YC6xQiX2MV4zeNMmWu\nGHMpU2aUqbBKpk/EzDoA2wLj4iYREZGlmubzzc1sJNAuzVN/dvfHG/A+qwIPA2ckLRIRESkC5u5x\nA5iNBs529/H1PL8iMAx40t2vq+eYuF+EiEiJcndrzOvz2hJpgLRfhJkZcDswpb4CAo0/CSIikp2Y\nQ3x/Y2YzCaOunjCzJ5PH1zGzJ5LDdgF+D/zazCYkf7pFiiwiInVEv5wlIiKlq6hHZ5lZNzOrMbNp\nZtYvzfMpM5tbq5VyYa3nZpjZG8njLxcyV61sE5JJktUNeW2ETHk5Vxn8+51T69/uTTP73sxaZfr1\nRMgU6zy1MbMRZjYx+bc7JtPXRswV61ytYWaPmtnrZjbOzLbK9LWRMuX8PJnZHWY228zeXMYxNyR5\nXzezbTP9WtJy96L8AzQBpgMdgBWBicAWdY5JAY/V8/r3gNaRcrUCJgPrJffbZPraQmfK17lq6NcK\nHACMin2e6ssU8zwBVcDlS//dgM8J/Zl5OU+NzRX5XP0NuDC53bEYvqfqy5TH89SVMB3izXqe3w8Y\nntzeEXipMeeomFsiOwDT3X2Guy8ChgAHpTluWZ3q+ehwzyTXkcAj7j4LwN0/a8BrC51pqVyfq4Z+\nrUcC92f52kJkWirGefoIWD25vTrwubt/n+FrY+RaKsa52gIYDeDubwEdzGytDF9byEy/qPV8Ts+T\nuz8HfLmMQ3oAg5NjxwGtzKwdWZ6jYi4i6wIza92flTxWmwM7J02y4Wa2ZZ3nRpnZq2Z2QoFzbQq0\ntrDu16tm1qsBry10JsjPucr4azWz5sC+wCMNfW0BM0G88zQI2MrMPgReB85owGtj5IJ45+p14LcA\nZrYDsAGwXoavLXQmyN/PqWWpL/M69Ty+TMUyxDedTHr8xwPt3X2+mXUHhgKbJc/t4u4fJRV/pJnV\nJBW6ELlWBDoDewLNgbFm9lKGry1oJnefBuzq7h/m+Fw15Gs9EHje3edk8dqGaEwmyM/3VCaZ/gxM\ndPeUmW2cfPY2jfzcvOVy96+Jd66uAK43swmE9fkmAIszfG2hM0F+/u9lImetn2JuiXwAtK91vz2h\nMv7A3b929/nJ7SeBFc2sdXL/o+TvT4FHCU21guQiVPOn3X2Bu39OWGRymwxfW+hMuPuHyd+5PFcN\n+VoP56eXjWKep/oy5et7KpNMOwMPJZ/9DuE6esfkuHycp8bminaukp8Jf3D3bd39aOAXwDsZfj2F\nzPRu8lw+/u81NPN6SebszlEuO3Ry+YfQSnqH0MnTjPQdVm35cZjyDsCM5HZzYLXkdgvgBWCfAuba\nHBhF6KhqTvjtY8tMXhshU17OVaZfK9CS0CG7SkNfW+BM0c4TcA1wca3v+VlA63ydpxzkinmuWgLN\nktsnAHfF/p5aRqZ8/pzqQGYd6134sWM9q3PU6LD5/AN0B94ijBg4L3msD9AnuX0KMCn5Yl8EuiSP\nb5Q8NjF5/rxC5krun0MYDfUmcPqyXhszUz7PVYaZegP3ZfLamJmADWOdJ8LIp8cJ19bfBI7M93lq\nTK6Y31PATsnzNYT19lrG/p6qL1O+vqcILegPge8IVyD+kOZ7fGCS93Wgc2POkSYbiohI1oq5T0RE\nRIqcioiIiGRNRURERLKmIiIiIllTERERkaypiIiISNZUREREJGsqIiIikjUVEZE8MLPtk9WlVzKz\nFsmmTVsu/5UipUUz1kXyxMz+AqwMrALMdPcrI0cSyTkVEZE8MbMVgVeBBcBOrv9sUoZ0OUskf9oQ\nVmddldAaESk7aomI5ImZPQbcR1jVdm13Py1yJJGcK+adDUVKlpkdDSx09yFmtgLwopml3L06cjSR\nnFJLREREsqY+ERERyZqKiIiIZE1FREREsqYiIiIiWVMRERGRrKmIiIhI1lREREQkayoiIiKStf8H\njXMbWAkg26AAAAAASUVORK5CYII=\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f01da57e590>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.55 \t0.60 \t0.65 \t0.70 \t0.75 \t0.80 \t0.85 \t0.90 \t0.95 \t"
+     ]
+    }
+   ],
+   "source": [
+    "from numpy import arange\n",
+    "from math import sin,cos\n",
+    "%matplotlib inline\n",
+    "from matplotlib.pyplot import plot, title, xlabel, ylabel, show\n",
+    "\n",
+    "def f(x):\n",
+    "    y=sin(10*x)+cos(3*x)#\n",
+    "    return y\n",
+    "count=1#\n",
+    "func=[]\n",
+    "val=[]\n",
+    "for i in arange(0.55,1,0.05):\n",
+    "    val.append(i)\n",
+    "    func.append(f(i))\n",
+    "    count=count+1#\n",
+    "\n",
+    "plot(val,func)\n",
+    "title(\"x vs f(x)\")\n",
+    "xlabel('x')\n",
+    "ylabel('f(x)')\n",
+    "show()\n",
+    "for v in val:\n",
+    "    print '%0.2f'%v,'\\t',"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex5.3: Pg:125"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "enter the tolerable true percent error=1.24\n"
+     ]
+    }
+   ],
+   "source": [
+    "from math import exp\n",
+    "m=68.1##kg\n",
+    "v=40##m/s\n",
+    "t=10##s\n",
+    "g=9.8##m/s**2\n",
+    "def f(c):\n",
+    "    y=g*m*(1-exp(-c*t/m))/c - v#\n",
+    "    return y\n",
+    "x1=12#\n",
+    "x2=16#\n",
+    "xt=14.7802##true value\n",
+    "e=input(\"enter the tolerable true percent error=\")\n",
+    "xr=(x1+x2)/2#\n",
+    "etemp=abs(xr-xt)/xt*100##error\n",
+    "while etemp>e:\n",
+    "    if f(x1)*f(xr)>0:\n",
+    "        x1=xr#\n",
+    "        xr=(x1+x2)/2#\n",
+    "        etemp=abs(xr-xt)/xt*100#\n",
+    "    \n",
+    "    if f(x1)*f(xr)<0:\n",
+    "        x2=xr#\n",
+    "        xr=(x1+x2)/2#\n",
+    "        etemp=abs(xr-xt)/xt*100#\n",
+    "    \n",
+    "    if f(x1)*f(xr)==0:\n",
+    "        break\n",
+    "    \n",
+    "print \"The result is =\",xr"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex5.4: Pg:126"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "enter the tolerable approximate error=21.03\n",
+      "Iteration: 1\n",
+      "xl: 12\n",
+      "xu: 16\n",
+      "xr: 14\n",
+      "et: 5.27868364433 %\n",
+      "----------------------------------------\n",
+      "Iteration: 2\n",
+      "xl: 14\n",
+      "xu: 15\n",
+      "xr: 14\n",
+      "et(%): 5.27868364433 %\n",
+      "ea 0 %\n",
+      "----------------------------------------\n",
+      "The result is= 14\n"
+     ]
+    }
+   ],
+   "source": [
+    "from math import exp\n",
+    "m=68.1##kg\n",
+    "v=40##m/s\n",
+    "t=10##s\n",
+    "g=9.8##m/s**2\n",
+    "def f(c):\n",
+    "    y=g*m*(1-exp(-c*t/m))/c - v#\n",
+    "    return y\n",
+    "x1=12#\n",
+    "x2=16#\n",
+    "xt=14.7802##true value\n",
+    "e=input(\"enter the tolerable approximate error=\")\n",
+    "xr=(x1+x2)/2#\n",
+    "i=1#\n",
+    "et=abs(xr-xt)/xt*100##error\n",
+    "print \"Iteration:\",i\n",
+    "print \"xl:\",x1\n",
+    "print \"xu:\",x2\n",
+    "print \"xr:\",xr\n",
+    "print \"et:\",et,\"%\"\n",
+    "print \"----------------------------------------\"\n",
+    "etemp=100#\n",
+    "while etemp>e:\n",
+    "    if f(x1)*f(xr)>0:\n",
+    "        x1=xr\n",
+    "        xr=(x1+x2)/2\n",
+    "        etemp=abs(xr-x1)/xr*100\n",
+    "        et=abs(xr-xt)/xt*100\n",
+    "    \n",
+    "    if f(x1)*f(xr)<0:\n",
+    "            x2=xr\n",
+    "            xr=(x1+x2)/2\n",
+    "            etemp=abs(xr-x2)/xr*100\n",
+    "            et=abs(xr-xt)/xt*100\n",
+    "    \n",
+    "    if f(x1)*f(xr)==0:\n",
+    "        break#\n",
+    "    \n",
+    "    i=i+1#\n",
+    "    print \"Iteration:\",i\n",
+    "    print \"xl:\",x1\n",
+    "    print \"xu:\",x2\n",
+    "    print \"xr:\",xr\n",
+    "    print \"et(%):\",et,\"%\"\n",
+    "    print \"ea\",etemp,\"%\"\n",
+    "    print \"----------------------------------------\"\n",
+    "\n",
+    "\n",
+    "print \"The result is=\",xr"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex5.5: Pg:133"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "enter the tolerable true percent error=24.36\n",
+      "The result is= 14.9113031791\n"
+     ]
+    }
+   ],
+   "source": [
+    "from math import exp\n",
+    "m=68.1##kg\n",
+    "v=40##m/s\n",
+    "t=10##s\n",
+    "g=9.8##m/s**2\n",
+    "def f(c):\n",
+    "    y=g*m*(1-exp(-c*t/m))/c - v#\n",
+    "    return y\n",
+    "x1=12#\n",
+    "x2=16#\n",
+    "xt=14.7802##true value\n",
+    "e=input(\"enter the tolerable true percent error=\")\n",
+    "xr=x1-(f(x1)*(x2-x1))/(f(x2)-f(x1))#\n",
+    "etemp=abs(xr-xt)/xt*100##error\n",
+    "while etemp>e:\n",
+    "    if f(x1)*f(xr)>0:\n",
+    "        x1=xr\n",
+    "        xr=x1-(f(x1)*(x2-x1))/(f(x2)-f(x1))\n",
+    "        etemp=abs(xr-xt)/xt*100\n",
+    "    \n",
+    "    if f(x1)*f(xr)<0:\n",
+    "            x2=xr\n",
+    "            xr=x1-(f(x1)*(x2-x1))/(f(x2)-f(x1))\n",
+    "            etemp=abs(xr-xt)/xt*100\n",
+    "    \n",
+    "    if f(x1)*f(xr)==0:\n",
+    "        break\n",
+    "    \n",
+    "\n",
+    "print \"The result is=\",xr"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex5.6: Pg:135"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "BISECTION METHOD:\n",
+      "Iteration: 1\n",
+      "xl: 0\n",
+      "xu: 1.3\n",
+      "xr: 0.65\n",
+      "et(%): 35.0 %\n",
+      "----------------------------------------\n",
+      "Iteration: 2\n",
+      "xl: 0.65\n",
+      "xu: 1.3\n",
+      "xr: 0.975\n",
+      "et(%): 2.5 %\n",
+      "ea(%) 33.3333333333 %\n",
+      "----------------------------------------\n",
+      "Iteration: 3\n",
+      "xl: 0.975\n",
+      "xu: 1.3\n",
+      "xr: 1.1375\n",
+      "et(%): 13.75 %\n",
+      "ea(%) 14.2857142857 %\n",
+      "----------------------------------------\n",
+      "Iteration: 4\n",
+      "xl: 0.975\n",
+      "xu: 1.1375\n",
+      "xr: 1.05625\n",
+      "et(%): 5.625 %\n",
+      "ea(%) 7.69230769231 %\n",
+      "----------------------------------------\n",
+      "Iteration: 5\n",
+      "xl: 0.975\n",
+      "xu: 1.05625\n",
+      "xr: 1.015625\n",
+      "et(%): 1.5625 %\n",
+      "ea(%) 4.0 %\n",
+      "----------------------------------------\n",
+      "FALSE POSITION METHOD:\n",
+      "Iteration: 1\n",
+      "xl: 0\n",
+      "xu: 1.3\n",
+      "xr: 0.0942995953723\n",
+      "et(%): 90.5700404628 %\n",
+      "----------------------------------------\n",
+      "Iteration: 2\n",
+      "xl: 0.0942995953723\n",
+      "xu: 1.3\n",
+      "xr: 0.181758872519\n",
+      "et(%): 81.8241127481 %\n",
+      "ea(%) 48.1182986748 %\n",
+      "----------------------------------------\n",
+      "Iteration: 3\n",
+      "xl: 0.181758872519\n",
+      "xu: 1.3\n",
+      "xr: 0.26287401252\n",
+      "et(%): 73.712598748 %\n",
+      "ea(%) 30.8570403075 %\n",
+      "----------------------------------------\n",
+      "Iteration: 4\n",
+      "xl: 0.26287401252\n",
+      "xu: 1.3\n",
+      "xr: 0.338105103322\n",
+      "et(%): 66.1894896678 %\n",
+      "ea(%) 22.2508001396 %\n",
+      "----------------------------------------\n",
+      "Iteration: 5\n",
+      "xl: 0.338105103322\n",
+      "xu: 1.3\n",
+      "xr: 0.407877916593\n",
+      "et(%): 59.2122083407 %\n",
+      "ea(%) 17.1062983388 %\n",
+      "----------------------------------------\n"
+     ]
+    }
+   ],
+   "source": [
+    "def f(x):\n",
+    "    y=x**10 - 1#\n",
+    "    return y\n",
+    "x1=0#\n",
+    "x2=1.3#\n",
+    "xt=1#\n",
+    "\n",
+    "#using bisection method\n",
+    "print \"BISECTION METHOD:\"\n",
+    "xr=(x1+x2)/2#\n",
+    "et=abs(xr-xt)/xt*100##error\n",
+    "print \"Iteration:\",1\n",
+    "print \"xl:\",x1\n",
+    "print \"xu:\",x2\n",
+    "print \"xr:\",xr\n",
+    "print \"et(%):\",et,\"%\"\n",
+    "print \"----------------------------------------\"\n",
+    "for i in range(2,6):\n",
+    "    if f(x1)*f(xr)>0:\n",
+    "        x1=xr\n",
+    "        xr=(x1+x2)/2\n",
+    "        ea=abs(xr-x1)/xr*100#\n",
+    "        et=abs(xr-xt)/xt*100#\n",
+    "    else:\n",
+    "        if f(x1)*f(xr)<0:\n",
+    "            x2=xr#\n",
+    "            xr=(x1+x2)/2#\n",
+    "            ea=abs(xr-x2)/xr*100#\n",
+    "            et=abs(xr-xt)/xt*100#\n",
+    "        \n",
+    "    \n",
+    "    if f(x1)*f(xr)==0:\n",
+    "        break\n",
+    "    \n",
+    "    print \"Iteration:\",i\n",
+    "    print \"xl:\",x1\n",
+    "    print \"xu:\",x2\n",
+    "    print \"xr:\",xr\n",
+    "    print \"et(%):\",et,\"%\"\n",
+    "    print \"ea(%)\",ea,\"%\"\n",
+    "    print \"----------------------------------------\"\n",
+    "\n",
+    "\n",
+    "#using false position method\n",
+    "print \"FALSE POSITION METHOD:\"\n",
+    "x1=0#\n",
+    "x2=1.3#\n",
+    "xt=1#\n",
+    "xr=x1-(f(x1)*(x2-x1))/(f(x2)-f(x1))##\n",
+    "et=abs(xr-xt)/xt*100##error\n",
+    "print \"Iteration:\",1\n",
+    "print \"xl:\",x1\n",
+    "print \"xu:\",x2\n",
+    "print \"xr:\",xr\n",
+    "print \"et(%):\",et,\"%\"\n",
+    "print \"----------------------------------------\"\n",
+    "for i in range(2,6):\n",
+    "    if f(x1)*f(xr)>0:\n",
+    "        x1=xr#\n",
+    "        xr=x1-(f(x1)*(x2-x1))/(f(x2)-f(x1))#\n",
+    "        ea=abs(xr-x1)/xr*100#\n",
+    "        et=abs(xr-xt)/xt*100#\n",
+    "    \n",
+    "    elif f(x1)*f(xr)<0:\n",
+    "            x2=xr#\n",
+    "            xr=x1-(f(x1)*(x2-x1))/(f(x2)-f(x1))#\n",
+    "            ea=abs(xr-x2)/xr*100#\n",
+    "            et=abs(xr-xt)/xt*100#\n",
+    "        \n",
+    "    \n",
+    "    elif f(x1)*f(xr)==0:\n",
+    "        break#\n",
+    "    \n",
+    "    print \"Iteration:\",i\n",
+    "    print \"xl:\",x1\n",
+    "    print \"xu:\",x2\n",
+    "    print \"xr:\",xr\n",
+    "    print \"et(%):\",et,'%'\n",
+    "    print \"ea(%)\",ea,\"%\"\n",
+    "    print \"----------------------------------------\""
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 2",
+   "language": "python",
+   "name": "python2"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.9"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter6.ipynb b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter6.ipynb
new file mode 100644
index 00000000..01ab6a06
--- /dev/null
+++ b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter6.ipynb
@@ -0,0 +1,686 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Chapter 6 : Open Methods"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex6.1: Pg: 143"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "x = :\n",
+      "0\n",
+      "1.0\n",
+      "0.367879441171\n",
+      "0.692200627555\n",
+      "0.500473500564\n",
+      "0.606243535086\n",
+      "0.545395785975\n",
+      "0.579612335503\n",
+      "0.560115461361\n",
+      "0.57114311508\n",
+      "0.564879347391\n",
+      "\n",
+      "e = :\n",
+      "100.0\n",
+      "-171.828182846\n",
+      "46.8536394613\n",
+      "-38.3091465933\n",
+      "17.4467896812\n",
+      "-11.1566225254\n",
+      "5.90335081441\n",
+      "-3.48086697962\n",
+      "1.93080393126\n",
+      "-1.10886824205\n"
+     ]
+    }
+   ],
+   "source": [
+    "from math import exp\n",
+    "#f(x) = exp(-x) - x#\n",
+    "#using simple fixed point iteration, Xi+1 = exp(-Xi)\n",
+    "x = 0##initial guess\n",
+    "y=[]\n",
+    "e=[]\n",
+    "y.append(0)\n",
+    "e.append(0)\n",
+    "for i in range(1,12):\n",
+    "    if i == 1 :\n",
+    "        y.append(x)\n",
+    "    else:\n",
+    "         y.append(exp(-y[(i-1)]))\n",
+    "         e.append((y[(i)] - y[(i-1)]) * 100 / y[(i)])\n",
+    "    \n",
+    "print \"x = :\"\n",
+    "for x in y[1:]:\n",
+    "    print x\n",
+    "print \"\\ne = :\"\n",
+    "for e in e[1:]:\n",
+    "    print e\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex6.2: Pg: 144"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "x =  [0, 0.2, 0.4, 0.6000000000000001, 0.8, 1.0]\n",
+      "y1 =  [0, 0.2, 0.4, 0.6000000000000001, 0.8, 1.0]\n",
+      "y2 =  [1.0, 0.8187307530779818, 0.6703200460356393, 0.5488116360940264, 0.44932896411722156, 0.36787944117144233]\n",
+      "answer using two curve graphical method =   5.7\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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Vau4JRG1dRKJFzT1BqK2LSDRF1NzNbLCZrTazdWZ2WxmPX25mK8xspZm9aWad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\nAElFTkSuQmCC\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f6dbdac5f50>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "from math import exp\n",
+    "%matplotlib inline\n",
+    "from matplotlib.pyplot import plot,title,xlabel,ylabel,show\n",
+    "#y1 = x\n",
+    "#y2 = exp(-x)\n",
+    "x=[]\n",
+    "y1=[]\n",
+    "y2=[]\n",
+    "for i in range(0,6):\n",
+    "    if i == 0:\n",
+    "        x.append(0)\n",
+    "    else:\n",
+    "        x.append(x[(i-1)] + 0.2)\n",
+    "    \n",
+    "    y1.append(x[(i)])\n",
+    "    y2.append(exp(-x[(i)]))\n",
+    "\n",
+    "print \"x = \",x\n",
+    "print \"y1 = \",y1\n",
+    "print \"y2 = \",y2\n",
+    "plot(x,y1)\n",
+    "plot(x,y2)#\n",
+    "title(\"f(x) vs x\")\n",
+    "xlabel(\"x\")\n",
+    "y=(\"f(x)\")\n",
+    "# from the graph, we get\n",
+    "x7 = 5.7#\n",
+    "print  \"answer using two curve graphical method =  \",x7"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex6.3: Pg: 149"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "x = [0.5, 0.5663110031972182, 0.5671431650348622, 0.5671432904097811, 0.5671432904097811]\n",
+      "et = [100.0, 11.709290976662398, 0.14672870783743905, 2.2106391984397626e-05]\n"
+     ]
+    }
+   ],
+   "source": [
+    "from math import exp\n",
+    "#f(x) = exp(-x)-x\n",
+    "#f'(x) = -exp(-x)-1\n",
+    "x=[]\n",
+    "et=[]\n",
+    "for i in range(0,5):\n",
+    "    if i == 0:\n",
+    "        x.append(0)\n",
+    "    else:\n",
+    "         x.append(x[(i-1)] - (exp(-x[(i-1)])-x[(i-1)])/(-exp(-x[(i-1)])-1))\n",
+    "         et.append((x[(i)] - x[(i-1)]) * 100 / x[(i)])\n",
+    "         x[(i-1)] = x[(i)]\n",
+    "    \n",
+    "\n",
+    "print \"x =\",x\n",
+    "print \"et =\",et"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex6.4: Pg: 150"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Et1 =  0.0582022389721 which is close to the true error of 0.06714329\n",
+      "Et2 =  0.000815754223141 which is close to the true error of 0.0008323\n",
+      "Et3 =  1.253469828e-07 which is close to the true error of 0.0008323\n",
+      "Et4 =  2.84303276339e-15 which is close to the true error of 0.0008323\n",
+      "Thus it illustratres that the error of newton raphson method for this case is proportional(by a factor of 0.18095) to the square of the error of the previous iteration\n"
+     ]
+    }
+   ],
+   "source": [
+    "from math import exp\n",
+    "#f(x) = exp(-x) - x\n",
+    "#f'(x) = -exp(-x) - 1\n",
+    "#f\"(x) = exp(-x)\n",
+    "xr = 0.56714329#\n",
+    "#E(ti+1) = -f\"(x)* E(ti) / 2 * f'(x)\n",
+    "Et0 = 0.56714329#\n",
+    "Et1 = -exp(-xr)* ((Et0)**2) / (2 * (-exp(-xr) - 1))#\n",
+    "print \"Et1 = \",Et1,\"which is close to the true error of 0.06714329\"\n",
+    "Et1true = 0.06714329#\n",
+    "Et2 =  -exp(-xr)* ((Et1true)**2) / (2 * (-exp(-xr) - 1))#\n",
+    "print \"Et2 = \",Et2,\"which is close to the true error of 0.0008323\"\n",
+    "Et2true = 0.0008323#\n",
+    "Et3 =  -exp(-xr)* ((Et2true)**2) / (2 * (-exp(-xr) - 1))#\n",
+    "print \"Et3 = \",Et3,\"which is close to the true error of 0.0008323\"\n",
+    "Et4 =  -exp(-xr)* ((Et3)**2) / (2 * (-exp(-xr) - 1))#\n",
+    "print \"Et4 = \",Et4,\"which is close to the true error of 0.0008323\"\n",
+    "print \"Thus it illustratres that the error of newton raphson method for this case is proportional(by a factor of 0.18095) to the square of the error of the previous iteration\"\n",
+    " "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex6.5: Pg: 151"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "y =\n",
+      "0.5\n",
+      "51.65\n",
+      "46.485\n",
+      "41.8365\n",
+      "37.65285\n",
+      "33.887565\n",
+      "30.4988085\n",
+      "27.44892765\n",
+      "24.704034885\n",
+      "22.2336313965\n",
+      "20.0102682569\n",
+      "18.0092414312\n",
+      "16.208317288\n",
+      "14.5874855592\n",
+      "13.1287370033\n",
+      "11.815863303\n",
+      "10.6342769727\n",
+      "9.57084927551\n",
+      "8.61376434811\n",
+      "7.75238791368\n",
+      "6.9771491233\n",
+      "6.27943421352\n",
+      "5.65149079876\n",
+      "5.08634173588\n",
+      "4.57770760618\n",
+      "4.11993695885\n",
+      "3.70794355537\n",
+      "3.33714995458\n",
+      "3.00343690726\n",
+      "2.70309824497\n",
+      "2.43280139954\n",
+      "2.18955475922\n",
+      "1.97068573981\n",
+      "1.7738402371\n",
+      "1.59703134797\n",
+      "1.43880793143\n",
+      "1.29871134273\n",
+      "1.17835471562\n",
+      "1.08334975351\n",
+      "1.02366466118\n",
+      "Thus, after the first poor prediction, the technique is converging on to the true root of 1 but at a very slow rate\n"
+     ]
+    }
+   ],
+   "source": [
+    "z = 0.5#\n",
+    "#f(x) = x**10 - 1\n",
+    "#f'(x) = 10*x**9\n",
+    "y=[]\n",
+    "for i in range(0,40):\n",
+    "    if i==0:\n",
+    "        y.append(z)\n",
+    "    else:\n",
+    "        y.append(y[(i-1)] - (y[(i-1)]**10 - 1)/(10*y[(i-1)]**9))\n",
+    "    \n",
+    "print \"y =\"\n",
+    "for yy in y:\n",
+    "    print yy\n",
+    "print \"Thus, after the first poor prediction, the technique is converging on to the true root of 1 but at a very slow rate\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex6.6: Pg: 155"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "x =\n",
+      "0\n",
+      "1\n",
+      "0.61269983678\n",
+      "0.563838389161\n",
+      "0.56717035842\n",
+      "\n",
+      "et =\n",
+      "-8.03263435953\n",
+      "0.582727662867\n",
+      "-0.00477276558181\n"
+     ]
+    }
+   ],
+   "source": [
+    "from math import exp\n",
+    "#f(x) = exp(-x)-x\n",
+    "x=[]\n",
+    "er=[]\n",
+    "for i in range(0,5):\n",
+    "    if i==0:\n",
+    "        x.append(0)\n",
+    "    else:\n",
+    "        if i==1:\n",
+    "            x.append(1)\n",
+    "        else:\n",
+    "            x.append(x[(i-1)] - (exp(-x[(i-1)])-x[(i-1)])*(x[(i-2)] - x[(i-1)])/((exp(-x[(i-2)])-x[(i-2)])-(exp(-x[(i-1)])-x[(i-1)])))\n",
+    "            er.append((0.56714329 - x[(i)]) * 100 / 0.56714329)\n",
+    "        \n",
+    "print \"x =\"\n",
+    "for xx in x:\n",
+    "    print xx\n",
+    "\n",
+    "print \"\\net =\"\n",
+    "for xx in er:\n",
+    "    print xx\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex6.7: Pg: 156"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "secant method\n",
+      "x =\n",
+      "[0.5, 5, 1.8546349804879152, -0.1043807923822424]\n",
+      "[0.5, 5, 1.8546349804879152, -0.1043807923822424]\n",
+      "[0.5, 5, 1.8546349804879152, -0.1043807923822424]\n",
+      "[0.5, 5, 1.8546349804879152, -0.1043807923822424]\n",
+      "thus, secant method is divergent\n",
+      "Now, False position method\n",
+      "xr =  1.85463498049\n",
+      "xr =  1.21630781847\n",
+      "xr =  1.05852096245\n",
+      "thus, false position method is convergent\n"
+     ]
+    }
+   ],
+   "source": [
+    "from math import log\n",
+    "#f(x) = log(x)\n",
+    "print \"secant method\"\n",
+    "x=[]\n",
+    "for i in range(0,4):\n",
+    "    if i==0:\n",
+    "        x.append(0.5)\n",
+    "    else:\n",
+    "        if i==1:\n",
+    "            x.append(5)\n",
+    "        else:\n",
+    "            x.append(x[(i-1)] - log(x[(i-1)]) * (x[(i-2)] - x[(i-1)])/(log(x[(i-2)]) - log(x[(i-1)])))\n",
+    "        \n",
+    "    \n",
+    "print \"x =\"\n",
+    "for xx in x:\n",
+    "    print x\n",
+    "print \"thus, secant method is divergent\"\n",
+    "print \"Now, False position method\"\n",
+    "xl = 0.5#\n",
+    "xu = 5#\n",
+    "for i in range(0,3):\n",
+    "    m = log(xl)#\n",
+    "    n = log(xu)#\n",
+    "    xr = xu - n*(xl - xu)/(m - n)#\n",
+    "    print \"xr = \",xr\n",
+    "    w = log(xr)#\n",
+    "    if m*w < 0:\n",
+    "        xu = xr#\n",
+    "    else:\n",
+    "        xl = xr#\n",
+    "    \n",
+    "\n",
+    " \n",
+    "print \"thus, false position method is convergent\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex6.8: Pg: 158"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "x1 =  1\n",
+      "x =  0.537262665537\n",
+      "error =  5.26861993966 %\n",
+      "x =  0.567009685365\n",
+      "error =  0.0235574743537 %\n",
+      "x =  0.567143424147\n",
+      "error =  -2.3653190891e-05 %\n"
+     ]
+    }
+   ],
+   "source": [
+    "from math import exp\n",
+    "Del = 0.01#\n",
+    "z = 0.56714329\n",
+    "x1 = 1#\n",
+    "#f(x) = exp(-x) - x\n",
+    "x=[]\n",
+    "print \"x1 = \",x1\n",
+    "for i in range(0,4):\n",
+    "    if i == 0:\n",
+    "        x.append(1)\n",
+    "    else :\n",
+    "        w = x[(i-1)]\n",
+    "        m = exp(-x[(i-1)]) - x[(i-1)]\n",
+    "        x[(i-1)] = x[(i-1)]*(1+Del)#\n",
+    "        n = exp(-x[(i-1)]) - x[(i-1)]#\n",
+    "        x.append(w - (x[(i-1)]- w) * m/(n-m))\n",
+    "        em = (z - x[(i)])*100/z#\n",
+    "        print \"x = \",x[(i)]\n",
+    "        print \"error = \",em,\"%\"\n",
+    "    "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex6.9: Pg: 161"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "standard Newton Raphson method\n",
+      "x =  0.428571428571\n",
+      "error =  57.1428571429 %\n",
+      "x =  0.685714285714\n",
+      "error =  31.4285714286 %\n",
+      "x =  0.832865400495\n",
+      "error =  16.7134599505 %\n",
+      "x =  0.913329893257\n",
+      "error =  8.66701067434 %\n",
+      "x =  0.955783292966\n",
+      "error =  4.42167070343 %\n",
+      "x =  0.977655101273\n",
+      "error =  2.23448987271 %\n",
+      "Modified Newton Raphson method\n",
+      "x =  1.10526315789\n",
+      "error =  -10.5263157895 %\n",
+      "x =  1.0030816641\n",
+      "error =  -0.30816640986 %\n",
+      "x =  1.00000238149\n",
+      "error =  -0.000238149381548 %\n"
+     ]
+    }
+   ],
+   "source": [
+    "from __future__ import division\n",
+    "#f(x) = x**3 - 5*x**2 + 7*x -3\n",
+    "#f'(x) = 3*x**2 - 10*x + 7\n",
+    "print \"standard Newton Raphson method\"\n",
+    "x=[]\n",
+    "et=[]\n",
+    "for i in range(0,7):\n",
+    "    if i == 0:\n",
+    "        x.append(0)\n",
+    "    else:\n",
+    "         x.append(x[(i-1)] - ((x[(i-1)])**3 - 5*(x[(i-1)])**2 + 7*x[(i-1)] -3)/(3*(x[(i-1)])**2 - 10*(x[(i-1)]) + 7))      \n",
+    "         et.append((1 - x[(i)]) * 100 / 1)\n",
+    "         print \"x = \",x[i]\n",
+    "         print \"error = \",et[(i-1)],\"%\"\n",
+    "         x[(i-1)] = x[(i)]\n",
+    "    \n",
+    "\n",
+    "print \"Modified Newton Raphson method\"\n",
+    "#f\"(x) = 6*x - 10\n",
+    "x=[]\n",
+    "et=[]\n",
+    "for i in range(0,4):\n",
+    "    if i == 0:\n",
+    "        x.append(0)\n",
+    "    else:\n",
+    "         x.append(x[(i-1) ]- ((x[(i-1)])**3 - 5*(x[(i-1)])**2 + 7*x[(i-1)] -3)*((3*(x[(i-1)])**2 - 10*(x[(i-1)]) + 7))/((3*(x[(i-1)])**2 - 10*(x[(i-1)]) + 7)**2 - ((x[(i-1)])**3 - 5*(x[(i-1)])**2 + 7*x[(i-1)] -3) * (6*x[(i-1)] - 10)))\n",
+    "         et.append((1 - x[(i)]) * 100 / 1)\n",
+    "         print \"x = \",x[i]\n",
+    "         print \"error = \",et[i-1],'%'\n",
+    "         x[(i-1) ]= x[(i)]\n",
+    "    \n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex6.10: Pg: 165"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "x = 2.17944947177\n",
+      "y = 2.86050598812\n",
+      "x = 1.94053387891\n",
+      "y = 3.04955067322\n",
+      "x = 2.02045628588\n",
+      "y = 2.98340474674\n",
+      "Thus the approaching to the true value 0f x = 2 and y = 3\n"
+     ]
+    }
+   ],
+   "source": [
+    "from math import sqrt\n",
+    "#u(x,y) = x**2 + x*y - 10\n",
+    "#v(x,y) = y + 3*x*y**2 -57\n",
+    "x=[]\n",
+    "y=[]\n",
+    "for i in range(0,4):\n",
+    "    if i == 0:\n",
+    "        x.append(1.5)\n",
+    "        y.append(3.5)\n",
+    "    else:\n",
+    "        x.append(sqrt(10 - (x[(i-1)])*(y[(i-1)])))\n",
+    "        y.append(sqrt((57 - y[(i-1)])/(3*x[(i)])))\n",
+    "        print \"x =\",x[(i)]\n",
+    "        print \"y =\",y[i]\n",
+    "    \n",
+    "\n",
+    "print \"Thus the approaching to the true value 0f x = 2 and y = 3\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex6.11:Pg 168"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "bracket: [1.9999999838762603, 2.9999994133889132]\n"
+     ]
+    }
+   ],
+   "source": [
+    "from numpy import mat\n",
+    "from numpy.linalg import det\n",
+    "def u(x,y):\n",
+    "    z=x**2+x*y-10\n",
+    "    return z\n",
+    "def v(x,y):\n",
+    "    z=y+3*x*y**2-57\n",
+    "    return z\n",
+    "x=1.5#\n",
+    "y=3.5#\n",
+    "e=[100,100]#\n",
+    "while  e[0]>0.0001 and e[1]>0.0001:\n",
+    "    J=mat([[2*x+y, x],[3*y**2, 1+6*x*y]])\n",
+    "    deter=det(J)#\n",
+    "    u1=u(x,y)#\n",
+    "    v1=v(x,y)#\n",
+    "    x=x-((u1*J[1,1]-v1*J[0,1])/deter)#\n",
+    "    y=y-((v1*J[0,0]-u1*J[1,0])/deter)#\n",
+    "    e[(0)]=abs(2-x)#\n",
+    "    e[(1)]=abs(3-y)#\n",
+    "\n",
+    "bracket=[x ,y]#\n",
+    "print \"bracket:\",bracket"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 2",
+   "language": "python",
+   "name": "python2"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.9"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter7.ipynb b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter7.ipynb
new file mode 100644
index 00000000..022a81d0
--- /dev/null
+++ b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter7.ipynb
@@ -0,0 +1,717 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Chapter 7 : Roots of polynomials"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex7.1: Pg: 179"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The quptient is a(1)+a(2)*x where :\n",
+      "a(1)= 6\n",
+      "a(2)= 1\n",
+      "remainder= 0\n"
+     ]
+    }
+   ],
+   "source": [
+    "from numpy import arange\n",
+    "def f(x):\n",
+    "    y=(x-4)*(x+6)\n",
+    "    return y\n",
+    "n=2\n",
+    "a=[0,-24,2,1]\n",
+    "t=4\n",
+    "r=a[(3)]\n",
+    "a[(3)]=0\n",
+    "for i in arange(n,0,-1):\n",
+    "    s=a[(i)]\n",
+    "    a[(i)]=r\n",
+    "    r=s+r*t\n",
+    "\n",
+    "print \"The quptient is a(1)+a(2)*x where :\"\n",
+    "print \"a(1)=\",a[1]\n",
+    "print \"a(2)=\",a[2]\n",
+    "print \"remainder=\",r"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex7.2: Pg: 183"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "iteration: 0\n",
+      "xr: 5\n",
+      "---------------------------------------------\n",
+      "iteration: 0\n",
+      "xr: 3.97648704224\n",
+      "ea(%): 25.7391246818 %\n",
+      "---------------------------------------------\n",
+      "iteration: 1\n",
+      "xr: 4.00105049882\n",
+      "ea(%): 0.613925182444 %\n",
+      "---------------------------------------------\n",
+      "iteration: 2\n",
+      "xr: 4.00000070527\n",
+      "ea(%): 0.026244833989 %\n",
+      "---------------------------------------------\n",
+      "iteration: 3\n",
+      "xr: 4.0\n",
+      "ea(%): 1.76317506373e-05 %\n",
+      "---------------------------------------------\n"
+     ]
+    }
+   ],
+   "source": [
+    "def f(x):\n",
+    "    y=x**3 - 13*x - 12\n",
+    "    return y\n",
+    "\n",
+    "x1t=-3\n",
+    "x2t=-1\n",
+    "x3t=4\n",
+    "x0=4.5\n",
+    "x1=5.5\n",
+    "x2=5\n",
+    "print \"iteration:\",0\n",
+    "print \"xr:\",x2\n",
+    "print \"---------------------------------------------\"\n",
+    "for i in range(0,4):\n",
+    "\n",
+    "    h0=x1-x0\n",
+    "    h1=x2-x1\n",
+    "    d0=(f(x1)-f(x0))/(x1-x0)\n",
+    "    d1=(f(x2)-f(x1))/(x2-x1)\n",
+    "    a=(d1-d0)/(h1+h0)\n",
+    "    b=a*h1+d1\n",
+    "    c=f(x2)\n",
+    "    d=(b**2 - 4*a*c)**0.5\n",
+    "    if abs(b+d)>abs(b-d):\n",
+    "        x3=x2+((-2*c)/(b+d))\n",
+    "    else:\n",
+    "        x3=x2+((-2*c)/(b-d))\n",
+    "    ea=abs(x3-x2)*100/x3\n",
+    "    x0=x1\n",
+    "    x1=x2\n",
+    "    x2=x3\n",
+    "    print \"iteration:\",i\n",
+    "    print \"xr:\",x2\n",
+    "    print \"ea(%):\",ea,\"%\"\n",
+    "    print \"---------------------------------------------\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex7.3: Pg: 187"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Iteration: 1\n",
+      "delata r: 0.212481426449\n",
+      "delata s: 1.61961367013\n",
+      "r: -0.787518573551\n",
+      "s: 0.619613670134\n",
+      "Error in r: 26.9811320755\n",
+      "Error in s: 261.39088729\n",
+      "-----------------------------------------------------\n",
+      "Iteration: 2\n",
+      "delata r: 4.04595826496\n",
+      "delata s: 5.2325468461\n",
+      "r: 3.25843969141\n",
+      "s: 5.85216051623\n",
+      "Error in r: 124.168579079\n",
+      "Error in s: 89.4122235982\n",
+      "-----------------------------------------------------\n",
+      "Iteration: 3\n",
+      "delata r: 2.4536017174\n",
+      "delata s: -24.7953826358\n",
+      "r: 5.71204140882\n",
+      "s: -18.9432221196\n",
+      "Error in r: 42.9549007403\n",
+      "Error in s: 130.893163155\n",
+      "-----------------------------------------------------\n",
+      "Iteration: 4\n",
+      "delata r: -7.89009085\n",
+      "delata s: 22.0401977474\n",
+      "r: -2.17804944119\n",
+      "s: 3.09697562788\n",
+      "Error in r: 362.254901143\n",
+      "Error in s: 711.668427386\n",
+      "-----------------------------------------------------\n",
+      "Iteration: 5\n",
+      "delata r: -58.1023530819\n",
+      "delata s: 185.887882155\n",
+      "r: -60.2804025231\n",
+      "s: 188.984857783\n",
+      "Error in r: 96.386803422\n",
+      "Error in s: 98.3612572646\n",
+      "-----------------------------------------------------\n",
+      "Iteration: 6\n",
+      "delata r: 1160.70485616\n",
+      "delata s: 90001.7445985\n",
+      "r: 1100.42445363\n",
+      "s: 90190.7294562\n",
+      "Error in r: 105.477922844\n",
+      "Error in s: 99.7904608834\n",
+      "-----------------------------------------------------\n",
+      "Iteration: 7\n",
+      "delata r: -21882.7802726\n",
+      "delata s: 31520060.138\n",
+      "r: -20782.355819\n",
+      "s: 31610250.8675\n",
+      "Error in r: 105.294993807\n",
+      "Error in s: 99.7146788558\n",
+      "-----------------------------------------------------\n",
+      "Iteration: 8\n",
+      "delata r: 411986.000256\n",
+      "delata s: 11197461422.1\n",
+      "r: 391203.644438\n",
+      "s: 11229071673.0\n",
+      "Error in r: 105.312413653\n",
+      "Error in s: 99.7184963122\n",
+      "-----------------------------------------------------\n",
+      "Iteration: 9\n",
+      "delata r: -7758767.67604\n",
+      "delata s: 3.9700158833e+12\n",
+      "r: -7367564.0316\n",
+      "s: 3.98124495498e+12\n",
+      "Error in r: 105.309809901\n",
+      "Error in s: 99.7179507466\n",
+      "-----------------------------------------------------\n",
+      "Iteration: 10\n",
+      "delata r: 146111056.094\n",
+      "delata s: 1.4079763212e+15\n",
+      "r: 138743492.063\n",
+      "s: 1.41195756615e+15\n",
+      "Error in r: 105.310205129\n",
+      "Error in s: 99.7180336683\n",
+      "-----------------------------------------------------\n",
+      "Iteration: 11\n",
+      "delata r: -2751543853.16\n",
+      "delata s: 4.99319657786e+17\n",
+      "r: -2612800361.1\n",
+      "s: 5.00731615352e+17\n",
+      "Error in r: 105.310145166\n",
+      "Error in s: 99.718021087\n",
+      "-----------------------------------------------------\n",
+      "Iteration: 12\n",
+      "delata r: 51816650788.5\n",
+      "delata s: 1.77078151694e+20\n",
+      "r: 49203850427.4\n",
+      "s: 1.7757888331e+20\n",
+      "Error in r: 105.310154263\n",
+      "Error in s: 99.7180229957\n",
+      "-----------------------------------------------------\n",
+      "Iteration: 13\n",
+      "delata r: -9.75803357309e+11\n",
+      "delata s: 6.27987270746e+22\n",
+      "r: -9.26599506881e+11\n",
+      "s: 6.29763059579e+22\n",
+      "Error in r: 105.310152883\n",
+      "Error in s: 99.7180227061\n",
+      "-----------------------------------------------------\n",
+      "Iteration: 14\n",
+      "delata r: 1.83761812944e+13\n",
+      "delata s: 2.22708488435e+25\n",
+      "r: 1.74495817875e+13\n",
+      "s: 2.23338251495e+25\n",
+      "Error in r: 105.310153092\n",
+      "Error in s: 99.7180227501\n",
+      "-----------------------------------------------------\n",
+      "Iteration: 15\n",
+      "delata r: -3.46057469143e+14\n",
+      "delata s: 7.89810111349e+27\n",
+      "r: -3.28607887356e+14\n",
+      "s: 7.92043493864e+27\n",
+      "Error in r: 105.310153061\n",
+      "Error in s: 99.7180227434\n",
+      "-----------------------------------------------------\n",
+      "Iteration: 16\n",
+      "delata r: 6.51690195935e+15\n",
+      "delata s: 2.80097098525e+30\n",
+      "r: 6.18829407199e+15\n",
+      "s: 2.80889142018e+30\n",
+      "Error in r: 105.310153065\n",
+      "Error in s: 99.7180227444\n",
+      "-----------------------------------------------------\n",
+      "Iteration: 17\n",
+      "delata r: -1.22725312811e+17\n",
+      "delata s: 9.93332238103e+32\n",
+      "r: -1.16537018739e+17\n",
+      "s: 9.96141129523e+32\n",
+      "Error in r: 105.310153065\n",
+      "Error in s: 99.7180227443\n",
+      "-----------------------------------------------------\n",
+      "Iteration: 18\n",
+      "delata r: 2.31114454359e+18\n",
+      "delata s: 3.5227388664e+35\n",
+      "r: 2.19460752485e+18\n",
+      "s: 3.53270027769e+35\n",
+      "Error in r: 105.310153065\n",
+      "Error in s: 99.7180227443\n",
+      "-----------------------------------------------------\n",
+      "Iteration: 19\n",
+      "delata r: -4.35231247656e+19\n",
+      "delata s: 1.24929893994e+38\n",
+      "r: -4.13285172407e+19\n",
+      "s: 1.25283164021e+38\n",
+      "Error in r: 105.310153065\n",
+      "Error in s: 99.7180227443\n",
+      "-----------------------------------------------------\n",
+      "Iteration: 20\n",
+      "delata r: 8.19620908009e+20\n",
+      "delata s: 4.43049541996e+40\n",
+      "r: 7.78292390768e+20\n",
+      "s: 4.44302373636e+40\n",
+      "Error in r: 105.310153065\n",
+      "Error in s: 99.7180227443\n",
+      "-----------------------------------------------------\n",
+      "Iteration: 21\n",
+      "delata r: -1.54349770717e+22\n",
+      "delata s: 1.57122439144e+43\n",
+      "r: -1.46566846809e+22\n",
+      "s: 1.57566741518e+43\n",
+      "Error in r: 105.310153065\n",
+      "Error in s: 99.7180227443\n",
+      "-----------------------------------------------------\n",
+      "Iteration: 22\n",
+      "delata r: 2.90669155552e+23\n",
+      "delata s: 5.57216711507e+45\n",
+      "r: 2.76012470871e+23\n",
+      "s: 5.58792378922e+45\n",
+      "Error in r: 105.310153065\n",
+      "Error in s: 99.7180227443\n",
+      "-----------------------------------------------------\n",
+      "Iteration: 23\n",
+      "delata r: -5.47383760902e+24\n",
+      "delata s: 1.97610516534e+48\n",
+      "r: -5.19782513815e+24\n",
+      "s: 1.98169308913e+48\n",
+      "Error in r: 105.310153065\n",
+      "Error in s: 99.7180227443\n",
+      "-----------------------------------------------------\n",
+      "Iteration: 24\n",
+      "delata r: 1.03082482601e+26\n",
+      "delata s: 7.00803034767e+50\n",
+      "r: 9.78846574632e+25\n",
+      "s: 7.02784727856e+50\n",
+      "Error in r: 105.310153065\n",
+      "Error in s: 99.7180227443\n",
+      "-----------------------------------------------------\n",
+      "Iteration: 25\n",
+      "delata r: -1.94123373367e+27\n",
+      "delata s: 2.48531759419e+53\n",
+      "r: -1.8433490762e+27\n",
+      "s: 2.49234544147e+53\n",
+      "Error in r: 105.310153065\n",
+      "Error in s: 99.7180227443\n",
+      "-----------------------------------------------------\n",
+      "Iteration: 26\n",
+      "delata r: 3.6557020297e+28\n",
+      "delata s: 8.81389382974e+55\n",
+      "r: 3.47136712208e+28\n",
+      "s: 8.83881728416e+55\n",
+      "Error in r: 105.310153065\n",
+      "Error in s: 99.7180227443\n",
+      "-----------------------------------------------------\n",
+      "Iteration: 27\n",
+      "delata r: -6.88436281433e+29\n",
+      "delata s: 3.12574636833e+58\n",
+      "r: -6.53722610212e+29\n",
+      "s: 3.13458518562e+58\n",
+      "Error in r: 105.310153065\n",
+      "Error in s: 99.7180227443\n",
+      "-----------------------------------------------------\n",
+      "Iteration: 28\n",
+      "delata r: 1.29645280097e+31\n",
+      "delata s: 1.10851010324e+61\n",
+      "r: 1.23108053995e+31\n",
+      "s: 1.11164468843e+61\n",
+      "Error in r: 105.310153065\n",
+      "Error in s: 99.7180227443\n",
+      "-----------------------------------------------------\n",
+      "Iteration: 29\n",
+      "delata r: -2.44146032172e+32\n",
+      "delata s: 3.93120395638e+63\n",
+      "r: -2.31835226773e+32\n",
+      "s: 3.94232040327e+63\n",
+      "Error in r: 105.310153065\n",
+      "Error in s: 99.7180227443\n",
+      "-----------------------------------------------------\n",
+      "Iteration: 30\n",
+      "delata r: 4.59772118049e+33\n",
+      "delata s: 1.39415639979e+66\n",
+      "r: 4.36588595372e+33\n",
+      "s: 1.3980987202e+66\n",
+      "Error in r: 105.310153065\n",
+      "Error in s: 99.7180227443\n",
+      "-----------------------------------------------------\n",
+      "Iteration: 31\n",
+      "delata r: -8.65835904252e+34\n",
+      "delata s: 4.94421578898e+68\n",
+      "r: -8.22177044714e+34\n",
+      "s: 4.95819677619e+68\n",
+      "Error in r: 105.310153065\n",
+      "Error in s: 99.7180227443\n",
+      "-----------------------------------------------------\n",
+      "Iteration: 32\n",
+      "delata r: 1.63052908966e+36\n",
+      "delata s: 1.75340942893e+71\n",
+      "r: 1.54831138518e+36\n",
+      "s: 1.75836762571e+71\n",
+      "Error in r: 105.310153065\n",
+      "Error in s: 99.7180227443\n",
+      "-----------------------------------------------------\n",
+      "Iteration: 33\n",
+      "delata r: -3.07058773973e+37\n",
+      "delata s: 6.21826545742e+73\n",
+      "r: -2.91575660121e+37\n",
+      "s: 6.23584913368e+73\n",
+      "Error in r: 105.310153065\n",
+      "Error in s: 99.7180227443\n",
+      "-----------------------------------------------------\n",
+      "Iteration: 34\n",
+      "delata r: 5.78248442618e+38\n",
+      "delata s: 2.20523653295e+76\n",
+      "r: 5.49090876606e+38\n",
+      "s: 2.21147238208e+76\n",
+      "Error in r: 105.310153065\n",
+      "Error in s: 99.7180227443\n",
+      "-----------------------------------------------------\n",
+      "Iteration: 35\n",
+      "delata r: -inf\n",
+      "delata s: inf\n",
+      "r: -inf\n",
+      "s: inf\n",
+      "Error in r: nan\n",
+      "Error in s: nan\n",
+      "-----------------------------------------------------\n",
+      "[nan, -inf] The roots are:\n",
+      "x**3 - 4*x**2 + 5.25*x - 2.5 The quotient is:\n",
+      "-----------------------------------------------------\n"
+     ]
+    }
+   ],
+   "source": [
+    "def f(x):\n",
+    "    y=x**5-3.5*x**4+2.75*x**3+2.125*x**2-3.875*x+1.25\n",
+    "    return y\n",
+    "r=-1\n",
+    "s=-1\n",
+    "es=1##%\n",
+    "n=6\n",
+    "count=1\n",
+    "ear=100\n",
+    "eas=100\n",
+    "a=[0,1.25, -3.875, 2.125, 2.75, -3.5, 1]\n",
+    "b=a\n",
+    "c=a\n",
+    "while (ear>es) and (eas>es):\n",
+    "  \n",
+    "    b[(n)]=a[(n)]\n",
+    "    b[(n-1)]=a[(n-1)]+r*b[(n)]\n",
+    "    for i in arange(n-2,0,-1):\n",
+    "        b[(i)]=a[(i)]+r*b[(i+1)]+s*b[(i+2)]\n",
+    "\n",
+    "    c[(n)]=b[(n)]\n",
+    "    c[(n-1)]=b[(n-1)]+r*c[(n)]\n",
+    "    for i in arange((n-2),1,-1):\n",
+    "        c[(i)]=b[(i)]+r*c[(i+1)]+s*c[(i+2)]\n",
+    "    \n",
+    "    #c(3)*dr+c(4)*ds=-b(2)\n",
+    "    #c(2)*dr+c(3)*ds=-b(1)\n",
+    "    ds=((-b[(1)])+(b[(2)]*c[(2)]/c[(3)]))/(c[(3)]-(c[(4)]*c[(2)]/c[(3)]))\n",
+    "    dr=(-b[(2)]-c[(4)]*ds)/c[(3)]\n",
+    "    r=r+dr\n",
+    "    s=s+ds\n",
+    "    ear=abs(dr/r)*100\n",
+    "    eas=abs(ds/s)*100\n",
+    "    print \"Iteration:\",count\n",
+    "    print \"delata r:\",dr\n",
+    "    print \"delata s:\",ds\n",
+    "    print \"r:\",r\n",
+    "    print \"s:\",s\n",
+    "    print \"Error in r:\",ear\n",
+    "    print \"Error in s:\",eas\n",
+    "    print \"-----------------------------------------------------\"\n",
+    "    count=count+1\n",
+    "\n",
+    "x1=(r+(r**2 + 4*s)**0.5)/2\n",
+    "x2=(r-(r**2 + 4*s)**0.5)/2\n",
+    "bracket=[x1, x2]\n",
+    "print bracket,\"The roots are:\"\n",
+    "print \"x**3 - 4*x**2 + 5.25*x - 2.5\",\"The quotient is:\"\n",
+    "print \"-----------------------------------------------------\"\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex7.4: Pg: 191"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The root is= 0.738868466337\n"
+     ]
+    }
+   ],
+   "source": [
+    "from math import cos\n",
+    "def f(x):\n",
+    "    y=x-cos(x)\n",
+    "    return y\n",
+    "x1=0\n",
+    "if f(x1)<0:\n",
+    "    x2=x1+0.001\n",
+    "    while f(x2)<0:\n",
+    "        x2=x2+0.001\n",
+    "    \n",
+    "elif x20==x1+0.001:\n",
+    "    while f(x2)>0:\n",
+    "        x2=x2+0.001\n",
+    "    \n",
+    "else:\n",
+    "    print \"The root is=\",x1\n",
+    "\n",
+    "x=x2-(x2-x1)*f(x2)/(f(x2)-f(x1))\n",
+    "print \"The root is=\",x"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex7.5: Pg: 191"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "x= 2\n",
+      "y= 3.0\n"
+     ]
+    }
+   ],
+   "source": [
+    "def u(x,y):\n",
+    "    z=x**2+x*y-10\n",
+    "    return z\n",
+    "def v(x,y):\n",
+    "    z=y+3*x*y**2-57\n",
+    "    return z\n",
+    "x=1\n",
+    "y=3.5\n",
+    "while u(x,y)!=v(x,y):\n",
+    "    x=x+1\n",
+    "    y=y-0.5\n",
+    "\n",
+    "print \"x=\",x\n",
+    "print \"y=\",y"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex7.6: Pg: 194"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The roots of the polynomial are:\n",
+      "-1\n",
+      "1\n",
+      "-1/4 + sqrt(5)/4 - I*sqrt(sqrt(5)/8 + 5/8)\n",
+      "-1/4 + sqrt(5)/4 + I*sqrt(sqrt(5)/8 + 5/8)\n",
+      "1/4 + sqrt(5)/4 - I*sqrt(-sqrt(5)/8 + 5/8)\n",
+      "1/4 + sqrt(5)/4 + I*sqrt(-sqrt(5)/8 + 5/8)\n",
+      "-sqrt(5)/4 - 1/4 - I*sqrt(-sqrt(5)/8 + 5/8)\n",
+      "-sqrt(5)/4 - 1/4 + I*sqrt(-sqrt(5)/8 + 5/8)\n",
+      "-sqrt(5)/4 + 1/4 - I*sqrt(sqrt(5)/8 + 5/8)\n",
+      "-sqrt(5)/4 + 1/4 + I*sqrt(sqrt(5)/8 + 5/8)\n"
+     ]
+    }
+   ],
+   "source": [
+    "from sympy import symbols,solve\n",
+    "x=symbols('s')\n",
+    "p=x**10 -1\n",
+    "print \"The roots of the polynomial are:\"\n",
+    "for r in solve(p):\n",
+    "    print r"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex7.7: Pg: 195"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The roots of the polynomial are:\n",
+      "-1.00000000000000\n",
+      "0.500000000000000\n",
+      "2.00000000000000\n",
+      "1.0 - 0.5*I\n",
+      "1.0 + 0.5*I\n"
+     ]
+    }
+   ],
+   "source": [
+    "from sympy import symbols,solve\n",
+    "x=symbols('s')\n",
+    "p=x**5 - 3.5*x**4 +2.75*x**3 +2.125*x**2 - 3.875*x + 1.25\n",
+    "print \"The roots of the polynomial are:\"\n",
+    "for r in solve(p):\n",
+    "    print r"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex7.8: Pg: 196"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The root is= 0.739083980074\n"
+     ]
+    }
+   ],
+   "source": [
+    "from math import cos\n",
+    "def f(x):\n",
+    "    y=x-cos(x)\n",
+    "    return y\n",
+    "x1=0\n",
+    "if f(x1)<0:\n",
+    "    x2=x1+0.00001\n",
+    "    while f(x2)<0:\n",
+    "        x2=x2+0.00001\n",
+    "    \n",
+    "elif x2==x1+0.00001:\n",
+    "    while f(x2)>0:\n",
+    "        x2=x2+0.00001\n",
+    "    \n",
+    "else:\n",
+    "    print x1,\"The root is=\"\n",
+    "\n",
+    "x=x2-(x2-x1)*f(x2)/(f(x2)-f(x1))\n",
+    "print \"The root is=\",x"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 2",
+   "language": "python",
+   "name": "python2"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.9"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter9.ipynb b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter9.ipynb
new file mode 100644
index 00000000..83d8625a
--- /dev/null
+++ b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/Chapter9.ipynb
@@ -0,0 +1,606 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Chapter - 9 : Gauss Eliminations"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:9.1 Pg: 242"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The lines meet at=x2= 3 and x1= 4\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7fc740383550>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "from __future__ import division\n",
+    "%matplotlib inline\n",
+    "from matplotlib.pyplot import plot,title,xlabel,ylabel,show\n",
+    "#the equations are:\n",
+    "#3*x1 + 2*x2=18 and -x1 + 2*x2=2\n",
+    "\n",
+    "#equation 1 becomes,\n",
+    "#x2=-(3/2)*x1 + 9\n",
+    "#equation 2 becomes,\n",
+    "#x2=-(1/2)*x1 + 1\n",
+    "\n",
+    "#plotting equation 1\n",
+    "x2=[0]\n",
+    "for x1 in range(1,7):\n",
+    "    x2.append(-(3/2)*x1 + 9)\n",
+    "\n",
+    "x1=[1, 2, 3, 4, 5, 6]\n",
+    "#plotting equation 2\n",
+    "x4=[0]\n",
+    "for x3 in range(1,7):\n",
+    "    x4.append((1/2)*x3 + 1)\n",
+    "\n",
+    "x3=[1, 2, 3, 4, 5, 6]\n",
+    "plot(x1,x2[1:])\n",
+    "plot(x3,x4[1:])\n",
+    "title(\"x2 vs x1\")\n",
+    "xlabel(\"x1\")\n",
+    "ylabel(\"x2\")\n",
+    "#the lines meet at x1=4 amd x2=3\n",
+    "print \"The lines meet at=x2=\",3,\"and x1=\",4"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:9.2 Pg: 244"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The value of determinant for system repesented in fig 9.1 = 8.0\n",
+      "The value of determinant for system repesented in fig 9.2 (a) = 0.0\n",
+      "The value of determinant for system repesented in fig 9.2 (b) = 0.0\n",
+      "The value of determinant for system repesented in fig 9.2 (c) = -0.04\n"
+     ]
+    }
+   ],
+   "source": [
+    "from numpy.linalg import det\n",
+    "from numpy import mat\n",
+    "#For fig9.1\n",
+    "a=mat([[3, 2],[-1, 2]])\n",
+    "print \"The value of determinant for system repesented in fig 9.1 =\",det(a)\n",
+    "#For fig9.2 (a)\n",
+    "a=mat([[-0.5, 1],[-0.5, 1]])\n",
+    "print \"The value of determinant for system repesented in fig 9.2 (a) =\",det(a)\n",
+    "#For fig9.2 (b)\n",
+    "a=mat([[-0.5, 1],[-1, 2]])\n",
+    "print \"The value of determinant for system repesented in fig 9.2 (b) =\",det(a)\n",
+    "#For fig9.2 (c)\n",
+    "a=mat([[-0.5, 1],[-2.3/5, 1]])\n",
+    "print \"The value of determinant for system repesented in fig 9.2 (c) =\",det(a)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:9.3 Pg: 245"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The values are:\n",
+      "x1= -14.9\n",
+      "x2= -29.5\n",
+      "x3= 19.8\n"
+     ]
+    }
+   ],
+   "source": [
+    "from numpy import mat\n",
+    "from numpy.linalg import det\n",
+    "#the matrix or the system\n",
+    "b1=-0.01#\n",
+    "b2=0.67#\n",
+    "b3=-0.44#\n",
+    "a=mat([[0.3, 0.52, 1],[0.5, 1, 1.9],[0.1, 0.3, 0.5]])\n",
+    "a1=mat([[a[1,1], a[1,2]],[a[2,1], a[2,2]]])\n",
+    "A1=det(a1)\n",
+    "a2=mat([[a[1,0], a[1,2]],[a[2,0], a[2,2]]])\n",
+    "A2=det(a2)\n",
+    "a3=mat([[a[1,0], a[1,1]],[a[2,0], a[2,1]]])\n",
+    "A3=det(a3)\n",
+    "D=a[0,0]*A1-a[0,1]*A2+a[0,2]*A3\n",
+    "p=mat([[b1, 0.52, 1],[b2, 1, 1.9],[b3, 0.3, 0.5]])\n",
+    "q=mat([[0.3, b1, 1],[0.5, b2, 1.9],[0.1, b3, 0.5]])\n",
+    "r=mat([[0.3, 0.52, b1],[0.5, 1, b2],[0.1 ,0.3, b3]])\n",
+    "x1=det(p)/D#\n",
+    "x2=det(q)/D#\n",
+    "x3=det(r)/D#\n",
+    "print \"The values are:\"\n",
+    "print \"x1=\",x1\n",
+    "print \"x2=\",x2\n",
+    "print \"x3=\",x3"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:9.4 Pg: 246"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "x1= 4.0\n",
+      "x2= 3.0\n"
+     ]
+    }
+   ],
+   "source": [
+    "#the equations are:\n",
+    "#3*x1+2*x2=18\n",
+    "#-x1+2*x2=2\n",
+    "a11=3#\n",
+    "a12=2#\n",
+    "b1=18#\n",
+    "a21=-1#\n",
+    "a22=2#\n",
+    "b2=2#\n",
+    "x1=(b1*a22-a12*b2)/(a11*a22-a12*a21)#\n",
+    "x2=(b2*a11-a21*b1)/(a11*a22-a12*a21)#\n",
+    "print \"x1=\",x1\n",
+    "print \"x2=\",x2"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:9.5 Pg: 251"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "x1= 2.61666666667\n",
+      "x2= -2.79319371728\n",
+      "x3= 7.0\n"
+     ]
+    }
+   ],
+   "source": [
+    "from numpy import arange\n",
+    "\n",
+    "n=3#\n",
+    "b=[7.85,-19.3,71.4] # ################################\n",
+    "a=mat([[3, -0.1, -0.2],[0.1, 7, -0.3],[0.3, -0.2, 10]])\n",
+    "for k in range(1,n):\n",
+    "    for i in range(k+1,n+1):\n",
+    "        fact=a[i-1,k-1]/a[k-1,k-1]\n",
+    "        for j in range(k+1,n+1):\n",
+    "            a[i-1,j-1]=a[i-1,j-1]-fact*(a[k-1,j-1])\n",
+    "        \n",
+    "        b[(i-1)]=b[(i-1)]-fact*b[(k-1)]\n",
+    "    \n",
+    "x=[0,0,b[(n-1)]/a[n-1,n-1]]\n",
+    "for i in arange(n-1,0,-1):\n",
+    "    s=b[i-1]#\n",
+    "    for j in range(i+1,n+1):\n",
+    "        s=s-a[i-1,j-1]*x[j-1]\n",
+    "    \n",
+    "    x[i-1]=b[i-1]/a[i-1,i-1]\n",
+    "\n",
+    "print \"x1=\",x[0]\n",
+    "print \"x2=\",x[1]\n",
+    "print \"x3=\",x[2]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:9.6 Pg:255"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "For the original system:\n",
+      "x1= 4.0\n",
+      "x2= 3.0\n",
+      "For the new system:\n",
+      "x1= 8.0\n",
+      "x2= 1.0\n"
+     ]
+    }
+   ],
+   "source": [
+    "a11=1#\n",
+    "a12=2#\n",
+    "b1=10#\n",
+    "a21=1.1#\n",
+    "a22=2#\n",
+    "b2=10.4#\n",
+    "x1=(b1*a22-a12*b2)/(a11*a22-a12*a21)#\n",
+    "x2=(b2*a11-a21*b1)/(a11*a22-a12*a21)#\n",
+    "print \"For the original system:\"\n",
+    "print \"x1=\",x1\n",
+    "print \"x2=\",x2\n",
+    "a21=1.05#\n",
+    "x1=(b1*a22-a12*b2)/(a11*a22-a12*a21)#\n",
+    "x2=(b2*a11-a21*b1)/(a11*a22-a12*a21)#\n",
+    "print \"For the new system:\"\n",
+    "print \"x1=\",x1\n",
+    "print \"x2=\",x2"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:9.7 Pg: 257"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The determinant for part(a)= 8.0\n",
+      "The determinant for part(b)= -0.2\n",
+      "The determinant for part(c)= -20.0\n"
+     ]
+    }
+   ],
+   "source": [
+    "from numpy.linalg import det\n",
+    "from numpy import mat\n",
+    "#part a\n",
+    "a=mat([[3, 2],[-1, 2]])\n",
+    "b1=18#\n",
+    "b2=2#\n",
+    "print \"The determinant for part(a)=\",det(a)\n",
+    "#part b\n",
+    "a=mat([[1, 2],[1.1, 2]])\n",
+    "b1=10\n",
+    "b2=10.4#\n",
+    "print \"The determinant for part(b)=\",det(a)\n",
+    "#part c\n",
+    "a1=a*10#\n",
+    "b1=100#\n",
+    "b2=104#\n",
+    "print \"The determinant for part(c)=\",det(a1)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:9.8 Pg: 258"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The determinant for part(a)= 1.3335\n",
+      "The determinant for part(b)= -0.05\n",
+      "The determinant for part(c)= -0.05\n"
+     ]
+    }
+   ],
+   "source": [
+    "from numpy.linalg import det\n",
+    "from numpy import mat\n",
+    "#part a\n",
+    "a=mat([[1, 0.667],[-0.5, 1]])\n",
+    "b1=6#\n",
+    "b2=1#\n",
+    "print \"The determinant for part(a)=\",det(a)\n",
+    "#part b\n",
+    "a=mat([[0.5, 1],[0.55, 1]])\n",
+    "b1=5\n",
+    "b2=5.2\n",
+    "print \"The determinant for part(b)=\",det(a)\n",
+    "#part c\n",
+    "b1=5#\n",
+    "b2=5.2#\n",
+    "print \"The determinant for part(c)=\",det(a)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:9.9 Pg: 260"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "x2 =  0.666666666667\n",
+      "x1 =  0.333333333334\n",
+      "The error varies depending on the no. of significant figures used\n"
+     ]
+    }
+   ],
+   "source": [
+    "#0.0003*x1 + 3*x2 = 2.0001\n",
+    "#1*x1 + 1*x2 = 1\n",
+    "a11 = 0.000#\n",
+    "#multiplying first equation by 1/0.0003, we get, x1 + 10000*x2 = 6667\n",
+    "x2 = (6667-1)/(10000-1)#\n",
+    "x1 = 6667 - 10000*x2#\n",
+    "print \"x2 = \",x2\n",
+    "print \"x1 = \",x1\n",
+    "print \"The error varies depending on the no. of significant figures used\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:9.10 Pg: 262"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "without scaling, applying forward elimination\n",
+      "x2 =  1.0\n",
+      "x1 =  0\n",
+      "error for x1 =  100.0\n",
+      "with scaling\n",
+      "x1 =  1\n",
+      "x2 =  1\n",
+      "pivot and retaining original coefficients\n",
+      "x1 =  1\n",
+      "x2 =  1.0\n"
+     ]
+    }
+   ],
+   "source": [
+    "from __future__ import division\n",
+    "#2*x1 + 10000*x2 = 10000\n",
+    "#x1 + x2 = 2\n",
+    "x1 = 1#\n",
+    "x2 = 1#\n",
+    "print \"without scaling, applying forward elimination\"\n",
+    "#x1 is too small and can be neglected\n",
+    "x21 = 10000/10000#\n",
+    "x11 = 0#\n",
+    "e1 = (x1 - x11)*100/x1#\n",
+    "print \"x2 = \",x21\n",
+    "print \"x1 = \",x11\n",
+    "print \"error for x1 = \",e1\n",
+    "print \"with scaling\"\n",
+    "#0.00002*x1 + x2 = 1\n",
+    "#now x1 is neglected because of the co efficient\n",
+    "x22 = 1#\n",
+    "x12 = 2 - x1#\n",
+    "print \"x1 = \",x12\n",
+    "print \"x2 = \",x22\n",
+    "#using original co efficient\n",
+    "#x1 can be neglected\n",
+    "print \"pivot and retaining original coefficients\"\n",
+    "x22 = 10000/10000#\n",
+    "x12 = 2 - x1#\n",
+    "print \"x1 = \",x12\n",
+    "print \"x2 = \",x22"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:9.11 Pg: 265"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "a= 8.59411764706 m/s**2\n",
+      "T= 34.4117647059 N\n",
+      "R= 36.7647058824 N\n"
+     ]
+    }
+   ],
+   "source": [
+    "from numpy import mat\n",
+    "from numpy.linalg import solve\n",
+    "a=mat([[70, 1, 0],[60, -1, 1],[40, 0, -1]])\n",
+    "b=mat([[636],[518],[307]])\n",
+    "x=abs(solve(a,b))\n",
+    "print \"a=\",x[0,0],\"m/s**2\"\n",
+    "print \"T=\",x[1,0],\"N\"\n",
+    "print \"R=\",x[2,0],\"N\"\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ex:9.12 Pg: 269"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Equation in matrix form can be written as : \n",
+      "[[  3.    -0.1   -0.2    7.85]\n",
+      " [  0.1    7.    -0.3  -19.3 ]\n",
+      " [  0.3   -0.2   10.    71.4 ]]\n",
+      "final matrix = \n",
+      "[[ 1.   0.   0.   3. ]\n",
+      " [ 0.   1.   0.  -2.5]\n",
+      " [ 0.   0.   1.   7. ]]\n",
+      "\n",
+      "x1 =  3.0\n",
+      "x2 =  -2.5\n",
+      "x3 =  7.0\n"
+     ]
+    }
+   ],
+   "source": [
+    "from numpy import mat,vstack\n",
+    "from numpy.linalg import det\n",
+    "#3*x1 - 0.1*x2 - 0.2*x3 = 7.85\n",
+    "#0.1*x1 + 7*x2 - 0.3*x3 = -19.3\n",
+    "#0.3*x1 - 0.2*x2 + 10*x3 = 71.4\n",
+    "# this can be written in matrix form as\n",
+    "A = mat([[3,-0.1,-0.2,7.85],[0.1,7,-0.3,-19.3],[0.3,-0.2,10,71.4]])\n",
+    "print \"Equation in matrix form can be written as : \\n\",A\n",
+    "X = A[0:1] / (A[0,0])#\n",
+    "Y = A[1:2] - 0.1*X#\n",
+    "Z = A[2:3] - 0.3*X#\n",
+    "\n",
+    "Y = Y/(Y[0,1])\n",
+    "X = X - Y * (X[0,1])\n",
+    "Z = Z - Y * (Z[0,1])#\n",
+    "Z = Z/(Z[0,2])#\n",
+    "X = X - Z*(X[0,2])#\n",
+    "Y = Y - Z*(Y[0,2])#\n",
+    "A = vstack((X,Y,Z))\n",
+    "print \"final matrix = \\n\",A\n",
+    "print \"\\nx1 = \",A[0,3]\n",
+    "print \"x2 = \",A[1,3]\n",
+    "print \"x3 = \",A[2,3]"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 2",
+   "language": "python",
+   "name": "python2"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.9"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/screenshots/Ch14PathOfAscent.png b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/screenshots/Ch14PathOfAscent.png
new file mode 100644
index 00000000..f4f76738
--- /dev/null
+++ b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/screenshots/Ch14PathOfAscent.png
diff --git a/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/screenshots/Ch14RandomNumberGenerator.png b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/screenshots/Ch14RandomNumberGenerator.png
new file mode 100644
index 00000000..de7353a3
--- /dev/null
+++ b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/screenshots/Ch14RandomNumberGenerator.png
diff --git a/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/screenshots/Ch26EulerMethod.png b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/screenshots/Ch26EulerMethod.png
new file mode 100644
index 00000000..0bf7e18d
--- /dev/null
+++ b/Numerical_Methods_For_Engineers_by_S._C._Chapra_And_R._P._Canale/screenshots/Ch26EulerMethod.png
diff --git a/sample_notebooks/testingtesting/fameetha.ipynb b/sample_notebooks/testingtesting/fameetha.ipynb
new file mode 100644
index 00000000..70f5ad4b
--- /dev/null
+++ b/sample_notebooks/testingtesting/fameetha.ipynb
@@ -0,0 +1,87 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Chapter 7:Starting And Speed Control Of Induction Motor "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Example 7.1,Page 7-6"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "x= 0.7453\n",
+      "Thus 74.53 % tapping is required\n",
+      "Ist= 3.33 IF.L\n",
+      "Thus supply starting current is 3.33 times the full load current\n"
+     ]
+    }
+   ],
+   "source": [
+    "import math\n",
+    "\n",
+    "#variable declaration\n",
+    "Isc=6     # starting current at rated voltage(amp)\n",
+    "Sf=5      # full load slip\n",
+    "Tfl=Tst=1 # full load torque=starting torque(N-m)\n",
+    "Ifl=1     # full load current(amp)\n",
+    "\n",
+    "#calculation\n",
+    "x=math.sqrt((Tst/Tfl) * ((float(Ifl)/float(Isc))**2)*(1/(float(Sf)/100)))\n",
+    "print 'x=',str (x)[:6]\n",
+    "print 'Thus',str(x*100)[:5],'% tapping is required'\n",
+    "\n",
+    "#Ist(supply)=x**2 * 6\n",
+    "Ist=(x**2) * Isc    # supply starting current(IF.L)\n",
+    "Ist=round(Ist,2)\n",
+    "print 'Ist=',Ist,'IF.L'\n",
+    "print 'Thus supply starting current is',Ist,'times the full load current'"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 2",
+   "language": "python",
+   "name": "python2"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.6"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
author	Trupti Kini	2016-05-02 23:30:25 +0600
committer	Trupti Kini	2016-05-02 23:30:25 +0600
commit	09174527d359bd85404d15d76fabd891c7e5ad6b (patch)
tree	7f243aba0ba204ce510633f2b32607e2b13fb22f
parent	a50c96a8653eda4256bb1e27242273373ad94732 (diff)
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