Added(A)/Deleted(D) following books

 A  Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/README.txt
A  Numerical_Methods_by_E._Balaguruswamy/chapter10.ipynb
A  Numerical_Methods_by_E._Balaguruswamy/chapter11.ipynb
A  Numerical_Methods_by_E._Balaguruswamy/chapter12.ipynb
A  Numerical_Methods_by_E._Balaguruswamy/chapter13.ipynb
A  Numerical_Methods_by_E._Balaguruswamy/chapter14.ipynb
A  Numerical_Methods_by_E._Balaguruswamy/chapter15.ipynb
A  Numerical_Methods_by_E._Balaguruswamy/chapter3.ipynb
A  Numerical_Methods_by_E._Balaguruswamy/chapter4.ipynb
A  Numerical_Methods_by_E._Balaguruswamy/chapter6.ipynb
A  Numerical_Methods_by_E._Balaguruswamy/chapter7.ipynb
A  Numerical_Methods_by_E._Balaguruswamy/chapter8.ipynb
A  Numerical_Methods_by_E._Balaguruswamy/chapter9.ipynb
A  Numerical_Methods_by_E._Balaguruswamy/screenshots/greatest-precision-4.png
A  Numerical_Methods_by_E._Balaguruswamy/screenshots/rounding-off-4.png
A  Numerical_Methods_by_E._Balaguruswamy/screenshots/truncation-error-4.png
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_4JhcI7F.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_5CfOfQx.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_B30VPml.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_BE8QjoS.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_Gb015bo.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_KQ8ycMr.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_LIZWeY4.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_Opo6g3L.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_Pq40WOu.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_QLXi0uM.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_TdOIeIQ.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_UiM06tF.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_VQabJzR.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_XKPPUxj.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_dfFlLnm.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_fegIkl6.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_g1GxlUN.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_gGvuusH.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_gZeNd4b.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_khAt4Y6.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_oJQM5Mb.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_p22tFeA.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_qNHcrb8.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_qeUxd0G.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_r0nfWNs.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_uWQUwaW.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_vkMAnbH.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_wP2wGMS.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_x09tDSO.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_yCW2orc.ipynb

1 files changed, 317 insertions, 0 deletions

diff --git a/Numerical_Methods_by_E._Balaguruswamy/chapter8.ipynb b/Numerical_Methods_by_E._Balaguruswamy/chapter8.ipynb
new file mode 100644
index 00000000..12e74ff2
--- /dev/null
+++ b/Numerical_Methods_by_E._Balaguruswamy/chapter8.ipynb
@@ -0,0 +1,317 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Chapter 8 - Iterative solutions of linear equations"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Example No. 8_01 Page No. 254"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "x1 = (5 - x2 - x3)/2 \n",
+      "x2 = (15 - 3x1 - 2x3)/5 \n",
+      "x3 = (8 - 2x1 - x2)/4\n",
+      "\n",
+      " Iteration Number : 1\n",
+      "\n",
+      " \n",
+      " x1 = 2.500000\n",
+      " x2 = 3.000000\n",
+      " x3 = 2.000000\n",
+      "\n",
+      "\n",
+      " Iteration Number : 2\n",
+      "\n",
+      " \n",
+      " x1 = 0.000000\n",
+      " x2 = 0.700000\n",
+      " x3 = 0.000000\n",
+      "\n",
+      "\n",
+      " Iteration Number : 3\n",
+      "\n",
+      " \n",
+      " x1 = 2.150000\n",
+      " x2 = 3.000000\n",
+      " x3 = 1.825000\n",
+      "\n",
+      "\n",
+      " Iteration Number : 4\n",
+      "\n",
+      " \n",
+      " x1 = 0.087500\n",
+      " x2 = 0.980000\n",
+      " x3 = 0.175000\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "from __future__ import division\n",
+    "from numpy import mat\n",
+    "#Gauss Jacobi\n",
+    "\n",
+    "A = mat([[ 2,  1 , 1] ,[3,  5,  2],[2,  1,  4]])\n",
+    "B = mat([[ 5],[ 15],[  8]])\n",
+    "x1old = 0 ;x2old = 0 ; x3old = 0 #intial assumption of x1,x2 & x3\n",
+    "\n",
+    "print 'x1 = (5 - x2 - x3)/2 '\n",
+    "print 'x2 = (15 - 3x1 - 2x3)/5 '\n",
+    "print 'x3 = (8 - 2x1 - x2)/4'\n",
+    "\n",
+    "for i in range(1,5):\n",
+    "    print '\\n Iteration Number : %d\\n'%(i)\n",
+    "    \n",
+    "    x1 = (5 - x2old - x3old)/2 #\n",
+    "    x2 = (15 - 3*x1old - 2*x3old)/5 # \n",
+    "    x3 = (8 - 2*x1old - x2old)/4 #\n",
+    "    \n",
+    "    print ' \\n x1 = %f\\n x2 = %f\\n x3 = %f\\n'%(x1,x2,x3)\n",
+    "   \n",
+    "    x1old = x1#\n",
+    "    x2old = x2#\n",
+    "    x3old = x3#\n",
+    "    \n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Example No. 8_02 Page No.261"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(x1 = 5 - x2 - x3)/2 \n",
+      "(x2 = 15 - 3x1 - 2x3)/5 \n",
+      "(x3 = 8 - 2x1 - x2)/4\n",
+      "\n",
+      " Iteration Number : 1\n",
+      " \n",
+      " x1 = 2.500000\n",
+      " x2 = 1.500000\n",
+      " x3 = 0.375000\n",
+      "\n",
+      "\n",
+      " Iteration Number : 2\n",
+      " \n",
+      " x1 = 1.562500\n",
+      " x2 = 1.912500\n",
+      " x3 = 0.740625\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "from __future__ import division\n",
+    "from numpy import mat\n",
+    "#Gauss Seidel\n",
+    "\n",
+    "A = mat([[ 2,  1 , 1] ,[3,  5,  2],[2,  1,  4]])\n",
+    "B = mat([[ 5],[ 15],[  8]])\n",
+    "\n",
+    "x1old = 0 ;x2old = 0 ; x3old = 0 #intial assumption\n",
+    "\n",
+    "print '(x1 = 5 - x2 - x3)/2 '\n",
+    "print '(x2 = 15 - 3x1 - 2x3)/5 '\n",
+    "print '(x3 = 8 - 2x1 - x2)/4'\n",
+    " \n",
+    "for i in range(1,3):\n",
+    "     \n",
+    "    print '\\n Iteration Number : %d'%(i)\n",
+    "    \n",
+    "    x1 = (5 - x2old - x3old)/2 #\n",
+    "    x1old = x1#   \n",
+    "    x2 = (15 - 3*x1old - 2*x3old)/5 #\n",
+    "    x2old = x2# \n",
+    "    x3 = (8 - 2*x1old - x2old)/4 #\n",
+    "    x3old = x3#\n",
+    "    \n",
+    "    print ' \\n x1 = %f\\n x2 = %f\\n x3 = %f\\n'%(x1,x2,x3)\n",
+    "     \n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Example No. 8_03 page no. 269"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Using a matrix to display the results after each iteration, first row represents initial assumption\n",
+      "x1 = (5-x2)/3\n",
+      "x2 = (x1 - 5)/3\n",
+      "The system converges to the solution ( 1.999949 , -1.000017 ) in 4 iterations\n",
+      "\n",
+      "Final Result is as : \n",
+      "0.0000000000 \t0.0000000000 \t1.9999491947 \t1.00001693509\n",
+      "-1.1111111111 \t1.6666666667 \t0.3332825281 \t0.111094176023\n",
+      "-0.9876543210 \t2.0370370370 \t0.0370878423 \t0.0123626141002\n",
+      "-1.0013717421 \t1.9958847737 \t0.0040644211 \t0.00135480702467\n",
+      "-0.9998475842 \t2.0004572474 \t0.0005080526 \t0.000169350878084\n"
+     ]
+    }
+   ],
+   "source": [
+    "from __future__ import division\n",
+    "from numpy import array,zeros,ones,nditer,vstack,hstack\n",
+    "\n",
+    "#Gauss Seidel\n",
+    "\n",
+    "\n",
+    "A = array([[ 3, 1],[ 1 ,-3]])\n",
+    "B = array([[ 5],[5 ]])\n",
+    "\n",
+    "X=zeros([6,2])\n",
+    "print ('Using a matrix to display the results after each iteration, first row represents initial assumption')\n",
+    "X[0,0] = 0; X[0,1] = 0 ;#initial assumption\n",
+    "\n",
+    "maxit = 1000;#Maximum number of iterations\n",
+    "err = 0.0003 ;\n",
+    "\n",
+    "print('x1 = (5-x2)/3');\n",
+    "print('x2 = (x1 - 5)/3');\n",
+    "\n",
+    "for i in range(1,maxit):\n",
+    "    \n",
+    "    X[i,0] = (5 - X[i-1,1])/3 ;\n",
+    "    X[i,1] = (X[i,0] - 5)/3 ;\n",
+    "    \n",
+    "    #Error Calculations\n",
+    "    err1 =abs((X[i,0] - X[i-1,0])/X[i,0]) \n",
+    "    err2 =abs((X[i,1]- X[i-1,1])/X[i,1])\n",
+    "    \n",
+    "    #Terminating Condition \n",
+    "    if err >= err1 and err >= err2:\n",
+    "        print 'The system converges to the solution ( %f , %f ) in %d iterations\\n'%(X[i,0],X[i,1],i-1) \n",
+    "        break\n",
+    "    \n",
+    "       \n",
+    "\n",
+    "#calcution of true error i.e. difference between final result and results from each iteration\n",
+    "trueerr1 = abs(X[:,0] - X[i,0]*ones([i+1,1])) ;\n",
+    "trueerr2 = abs(X[:,1] - X[i,1]*ones([i+1,1])) ;\n",
+    "\n",
+    "#displaying final results\n",
+    "print 'Final Result is as : '\n",
+    "for i in range(0,5):\n",
+    "    print '%.10f'%X[i,:][1],'\\t%.10f'%X[i,:][0],'\\t%.10f'%trueerr1[0,i],'\\t',trueerr2[0,i]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Example No. 8_04 Page No.261"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "x1 = 5 + 3*x2 \n",
+      "x2 = 5 - 3*x1 \n",
+      "\n",
+      " Iteration : 1  x1 = 5 and x2 = -10\n",
+      "\n",
+      "\n",
+      " Iteration : 2  x1 = -25 and x2 = 80\n",
+      "\n",
+      "\n",
+      " Iteration : 3  x1 = 245 and x2 = -730\n",
+      "\n",
+      "It is clear that the process do not converge towards the solution, rather it diverges.\n"
+     ]
+    }
+   ],
+   "source": [
+    "from numpy import mat\n",
+    "#Gauss Seidel\n",
+    "\n",
+    "A = mat([[ 1, -3],[3, 1 ]])\n",
+    "B = mat([[ 5],[5] ])\n",
+    "x1old = 0 #intial assumption\n",
+    "x2old = 0  #intial assumption\n",
+    "\n",
+    "print 'x1 = 5 + 3*x2 '\n",
+    "print 'x2 = 5 - 3*x1 '\n",
+    " \n",
+    "for i in range(1,4):\n",
+    "    x1 = 5 + 3*x2old \n",
+    "    x1old = x1\n",
+    "    x2 = 5 - 3*x1old \n",
+    "    x2old = x2\n",
+    "    \n",
+    "    print '\\n Iteration : %d  x1 = %d and x2 = %d\\n'%(i,x1,x2)\n",
+    "     \n",
+    "print 'It is clear that the process do not converge towards the solution, rather it diverges.'"
+   ]
+  }
+ ],
+ "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
+}