{
 "metadata": {
  "name": "chapter1.ipynb"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 1:Vectors"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.1-1,Page no: 8"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Initialisation of Variables\n",
      "\n",
      "f1=120 #lb\n",
      "f2=100 #lb\n",
      "theta=((60*pi)/180) #radians\n",
      "\n",
      "#Calculations\n",
      "\n",
      "R=sqrt(120**2+100**2-(2*120*100*cos(theta))) #Applying Thr rule of Cosines\n",
      "alpha1=(((arcsin(120*sin(theta)/111))*180)/pi) #Applying the Law of Sines\n",
      "alpha=alpha1+270 #As the vector lies in the fourth Quadrant by obsrevaton\n",
      "\n",
      "#Results\n",
      "\n",
      "print'The Resultant of The force system is equal to',round(R),\"lb\" #lb\n",
      "print'The Resultant is at',round(alpha),\"degrees\" #degrees\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Resultant of The force system is equal to 111.0 lb\n",
        "The Resultant is at 339.0 degrees\n"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.1-2,Page no: 9"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Initilization of variables\n",
      "\n",
      "P=100 #lb\n",
      "Q=120 #lb\n",
      "theta=((30*pi)/180) #radians\n",
      "\n",
      "#Calculations\n",
      "\n",
      "R_x=Q*cos(theta) #lb\n",
      "R_y=Q*sin(theta)-P #lb\n",
      "R=sqrt(R_x**2+R_y**2) #lb Triangle law\n",
      "Theta_1=((arctan(R_y/R_x))*180)/pi #degrees\n",
      "Theta_R=360+Theta_1 #degrees\n",
      "\n",
      "#Result\n",
      "\n",
      "print'The resultant of the force system is',round(R),\"lb\"\n",
      "print'The resultant is at',round(Theta_R),\"degrees\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The resultant of the force system is 111.0 lb\n",
        "The resultant is at 339.0 degrees\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.1-3,Page No: 9"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "# Initialization of variables\n",
      "\n",
      "R=400 # N\n",
      "F2=200 # N\n",
      "Theta1=((120*pi)/180) # radians\n",
      "Theta2=((20*pi)/180) # radians\n",
      "Theta=Theta1-Theta2 # radians\n",
      "\n",
      "# Calculation\n",
      "\n",
      "F=sqrt(R**2+F2**2-(2*R*F2*cos(Theta))) # N.Applying the Rule of Cosine\n",
      "Theta_r=arcsin((400*sin(Theta))/F) #radians Applying the rule of sines\n",
      "Theta_R=(Theta_r*180)/pi\n",
      "\n",
      "# Result\n",
      "\n",
      "print'The resultant of the force system is',round(F),\"N\"\n",
      "print'The Angle between F and 200N force is',round(Theta_R,1),\"degrees\"\n",
      "\n",
      "# Theta_R is off by 0.1 degrees"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The resultant of the force system is 477.0 N\n",
        "The Angle between F and 200N force is 55.6 degrees\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.1-4, Page No: 9"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "# Initilization of variables\n",
      "\n",
      "F1=280 # N\n",
      "F2=130 # N\n",
      "Theta1=((320*pi)/180) # Radians\n",
      "Theta2=((60*pi)/180) # Radians\n",
      "\n",
      "# Calculations\n",
      "\n",
      "R_x=-F1*cos(Theta1)+F2*cos(Theta2) # N\n",
      "R_y=F1*sin(Theta1)-F2*sin(Theta2) # N\n",
      "R=sqrt(R_x**2+R_y**2) # N Applying Triangle Law\n",
      "ThetaR=arctan(R_y/R_x) # radians\n",
      "Theta_R=360-(ThetaR*180/pi) # degrees\n",
      "\n",
      "# Result\n",
      "\n",
      "print'The resultant of the force system is',round(R),\"N\"\n",
      "print'The resultant is at',round(Theta_R),\"degrees\"\n",
      "\n",
      "# The answer for R waries from textbook. "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The resultant of the force system is 329.0 N\n",
        "The resultant is at 297.0 degrees\n"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.1-5, Page No: 10"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "# Initialization of variables\n",
      "\n",
      "F1=26 #lb\n",
      "F2=39 #lb\n",
      "F3=63 #lb\n",
      "F4=57 #lb\n",
      "T1=((10*pi)/180) #Radians\n",
      "T2=((114*pi)/180) #Radians\n",
      "T3=((183*pi)/180) #radians\n",
      "T4=((261*pi)/180) #radians\n",
      "\n",
      "# Calculations\n",
      "\n",
      "R_x=F1*cos(T1)+F2*cos(T2)+F3*cos(T3)+F4*cos(T4) # lb Resolving vectors\n",
      "R_y=F1*sin(T1)+F2*sin(T2)+F3*sin(T3)+F4*sin(T4) # lb resolving vectors\n",
      "R=sqrt(R_x**2+R_y**2) # lb Applying Triangle Law\n",
      "theta=arctan(R_y/R_x)# radians\n",
      "Theta=(theta*180)/pi # degrees\n",
      "Theta_R=180+Theta\n",
      "\n",
      "# Results\n",
      "\n",
      "print'The Resultant of the force system is',round(R),\"lb\"\n",
      "print'The resultant is at',round(Theta_R),\"degrees\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Resultant of the force system is 65.0 lb\n",
        "The resultant is at 197.0 degrees\n"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.1-6, Page No: 11"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Initilization of variables\n",
      "\n",
      "F=10 #lb\n",
      "theta1=((60*pi)/180) #radians\n",
      "theta2=((45*pi)/180) #radians\n",
      "theta=theta1-theta2 #radians\n",
      "\n",
      "#Calculation\n",
      "\n",
      "F_OH=F/cos(theta) #lb resolving vectors\n",
      "\n",
      "# Result\n",
      "\n",
      "print'The component of F in the direction of OH is',round(F_OH,2),\"lb\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The component of F in the direction of OH is 10.35 lb\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.1-7, Page No: 11"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Initilization of variables\n",
      "\n",
      "weight=80 #kg\n",
      "theta=((20*pi)/180) #radians\n",
      "theta_p=((70*pi)/180) # radians\n",
      "\n",
      "#Calcuations\n",
      "\n",
      "#Part (a)\n",
      "F=weight*9.81 # N\n",
      "R=F*cos(theta) #N\n",
      "#part (b)\n",
      "R_p=F*cos(theta_p) #N\n",
      "\n",
      "#Result\n",
      "\n",
      "print'The normal component is',round(R),\"N\"\n",
      "print'The parallel component is',round(R_p),\"N\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The normal component is 737.0 N\n",
        "The parallel component is 268.0 N\n"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.1-8, Page No: 11"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Initilization of variables\n",
      "\n",
      "P=235 #N\n",
      "theta=((60*pi)/180) #radians\n",
      "bet=((22*pi)/180) #radians\n",
      "gam=((38*pi)/180) #radians\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Part (a)\n",
      "P_h=P*cos(theta) #N\n",
      "P_v=P*sin(theta) #N\n",
      "#Part (b)\n",
      "P_l=P*cos(theta-bet) #N\n",
      "P_p=P*sin(gam) #N\n",
      "\n",
      "#Result\n",
      "\n",
      "print'The horizontal component is',round(P_h,1),\"N\"\n",
      "print'The vertical component is',round(P_v,1),\"N\"\n",
      "print'The component parallel to plane is',round(P_l),\"N\"\n",
      "print'The component perpendicular to the plane is',round(P_p,1),\"N\"\n",
      "\n",
      "#The decimal point accuracy might cause a small discrepancy in the answers\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The horizontal component is 117.5 N\n",
        "The vertical component is 203.5 N\n",
        "The component parallel to plane is 185.0 N\n",
        "The component perpendicular to the plane is 144.7 N\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.1-9, Page No: 12"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Initilization of variables\n",
      "\n",
      "F1=90 #lb\n",
      "theta1=((40*pi)/180) #radians\n",
      "theta2=((30*pi)/180) #radians\n",
      "\n",
      "# Calculations\n",
      "\n",
      "R_x=0 #lb\n",
      "R_y=20 # lb\n",
      "#Taking the sum of forces in the X-Direction\n",
      "P=((F1*cos(theta1))/cos(theta2)) # lb\n",
      "# Taking the sum of the forces in the Y-Direction\n",
      "F=(P*sin(theta2))+(F1*sin(theta1))-20 #lb\n",
      "\n",
      "# Results\n",
      "\n",
      "print'The value of P is',round(P,1),\"lb\"\n",
      "print'The value of F is',round(F,1),\"lb\"\n",
      "\n",
      "# Decimal point error may cause a small discrepancy in the answers."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The value of P is 79.6 lb\n",
        "The value of F is 77.7 lb\n"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.1-10, Page No: 12"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Initilization of variables\n",
      "\n",
      "x=4 # m\n",
      "y=3 # m\n",
      "z=2 # m\n",
      "F=50 #N\n",
      "\n",
      "# Calculations\n",
      "\n",
      "OP=sqrt(x**2+y**2+z**2) #m\n",
      "thetax=(x/OP) #radians\n",
      "thetay=(y/OP) #Radians\n",
      "thetaz=(z/OP) #radians\n",
      "P_x=F*(thetax) #N\n",
      "P_y=F*(thetay) #N\n",
      "P_z=F*(thetaz) #N\n",
      "\n",
      "# Result\n",
      "\n",
      "print'The vector P is',round(P_x,1),\"i +\",round(P_y,1),\"j +\",round(P_z,1),\"k\"\n",
      "\n",
      "# component of i is off by 0.1 units"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The vector P is 37.1 i + 27.9 j + 18.6 k\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.1-11, Page No: 12"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Initilization of variables\n",
      "\n",
      "x=2 \n",
      "y=-4\n",
      "z=1\n",
      "F=100 #N\n",
      "\n",
      "#Calculation\n",
      "\n",
      "thetax=x/sqrt(x**2+y**2+z**2) #radians\n",
      "thetay=y/sqrt(x**2+y**2+z**2) #radians\n",
      "thetaz=z/sqrt(x**2+y**2+z**2) #radians\n",
      "P_x=F*thetax #N\n",
      "P_y=F*thetay #N\n",
      "P_z=F*thetaz #N\n",
      "\n",
      "#Result\n",
      "\n",
      "print'The vector P is',round(P_x,1),\"i\",round(P_y,1),\"j +\",round(P_z,1),\"k\"\n",
      "\n",
      "# component off i is off by 0.1 units"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The vector P is 43.6 i -87.3 j + 21.8 k\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.1-12, Page No: 13"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Solution\n",
      "\n",
      "print'P X Q=(Pxi+Pyj+Pzk)x(Qxi+Qyj+Qzk)'\n",
      "print'       =(PxQx)i x i+(PxQy)i x j +(PxQz)i x k'\n",
      "print'But i x i = j x j = k x k =0; and i x j =k and j x i= -k, etc. Hence'\n",
      "print'P X Q= (PxQy)k-(PxQz)j-(PyQx)k+(PxQz)i+(PzQx)j-(PzQy)i'\n",
      "print'These terms can be grouped as'\n",
      "print'P X Q=(PyQz-PzQy)i+(PzQx-PxQz)j+(PxQy-PyQx)k'\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "P X Q=(Pxi+Pyj+Pzk)x(Qxi+Qyj+Qzk)\n",
        "       =(PxQx)i x i+(PxQy)i x j +(PxQz)i x k\n",
        "But i x i = j x j = k x k =0; and i x j =k and j x i= -k, etc. Hence\n",
        "P X Q= (PxQy)k-(PxQz)j-(PyQx)k+(PxQz)i+(PzQx)j-(PzQy)i\n",
        "These terms can be grouped as\n",
        "P X Q=(PyQz-PzQy)i+(PzQx-PxQz)j+(PxQy-PyQx)k\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.1-13,Page No: 13"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Initilization of variables\n",
      "\n",
      "Fx=2.63 #N\n",
      "Fy=4.28 #N\n",
      "Fz=-5.92 #N\n",
      "\n",
      "#Calculation\n",
      "\n",
      "F=sqrt(Fx**2+Fy**2+Fz**2) #N\n",
      "thetax=((arccos(Fx/F))*180)/pi #degrees\n",
      "thetay=((arccos(Fy/F))*180)/pi #degrees\n",
      "thetaz=((arccos(Fz/F))*180)/pi #degrees\n",
      "\n",
      "#Result\n",
      "\n",
      "print'The magnitude of force is',round(F,2),\"N\"\n",
      "print'Thetax',round(thetax,1),\"degrees\"\n",
      "print'Thetay',round(thetay,1),\"degrees\"\n",
      "print'Thetaz',round(thetaz,1),\"degrees\"\n",
      "\n",
      "# Decimal point error may cause a small discrepancy in the answers."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The magnitude of force is 7.76 N\n",
        "Thetax 70.2 degrees\n",
        "Thetay 56.5 degrees\n",
        "Thetaz 139.7 degrees\n"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.1-14, Page No: 13"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Initilization of variables\n",
      "\n",
      "P=[4.82, -2.33, 5.47] #N\n",
      "Q=[-2.81,-6.09,1.12 ] #m\n",
      "\n",
      "#Calculations\n",
      "\n",
      "M=P[0]*Q[0]+P[1]*Q[1]+P[2]*Q[2] #Nm\n",
      "\n",
      "#Results\n",
      "\n",
      "print'Result is',round(M,2),\"N.m\"\n",
      "\n",
      "# Decimal point error in calculation causes a small discrepancy in the answer."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Result is 6.77 N.m\n"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.1-15, Page No: 13"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "import numpy as np\n",
      "#Initilization of variables\n",
      "\n",
      "x1=2 #units\n",
      "x2=-2 #units\n",
      "y1=3 #units\n",
      "y2=4 #units\n",
      "z1=0 #units\n",
      "z2=6 #units\n",
      "P=np.array([2,3,-1]) #units\n",
      "\n",
      "#Calculations\n",
      "\n",
      "X=sqrt((x2-x1)**2+(y2-y1)**2+(z2-z1)**2) #units\n",
      "eLx=(x2-x1)/X #units\n",
      "eLy=(y2-y1)/X #units\n",
      "eLz=(z2-z1)/X #units\n",
      "Q=np.array([eLx,eLy,eLz]) #units\n",
      "Z=P[0]*Q[0]+P[1]*Q[1]+P[2]*Q[2] # units\n",
      "\n",
      "#Result\n",
      "\n",
      "print'The unit vector is',round(eLx,3),\"i +\",round(eLy,3),\"j +\",round(eLz,3),\"k\"\n",
      "print'The projection of P is',round(Z,2),\"units\"\n",
      "\n",
      "#Note:The final answer for the projection of P is off by 0.1 units\n",
      "#The answer mentioned in the textbook is -1.41\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The unit vector is -0.549 i + 0.137 j + 0.824 k\n",
        "The projection of P is -1.51 units\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.1-16, Page No: 14"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "import numpy as np\n",
      "#Initilization of variables\n",
      "\n",
      "x1=2 #units\n",
      "x2=5 #units\n",
      "y1=-5 #units\n",
      "y2=2 #units\n",
      "z1=3 #units\n",
      "z2=-4 #units\n",
      "P=np.array([10,-8,14]) #units\n",
      "\n",
      "#Calculations\n",
      "\n",
      "X=sqrt((x2-x1)**2+(y2-y1)**2+(z2-z1)**2) #units\n",
      "eLx=(x2-x1)/X #units\n",
      "eLy=(y2-y1)/X #units\n",
      "eLz=(z2-z1)/X #units\n",
      "Q=np.array([eLx,eLy,eLz]) #units\n",
      "Z=P[0]*Q[0]+P[1]*Q[1]+P[2]*Q[2] #units\n",
      "\n",
      "#Result\n",
      "\n",
      "print'The unit vector is',round(eLx,3),\"i +\",round(eLy,3),\"j\",round(eLz,3),\"k\" \n",
      "print'The projection of P is',round(Z),\"lb\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The unit vector is 0.29 i + 0.677 j -0.677 k\n",
        "The projection of P is -12.0 lb\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.1-17, Page No: 14\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "Px=2.85 #ft\n",
      "Py=4.67 #ft\n",
      "Pz=-8.09 #ft\n",
      "Qx=28.3 #lb\n",
      "Qy=44.6 #lb\n",
      "Qz=53.3 #lb\n",
      "\n",
      "#Calculations\n",
      "\n",
      "X=(Py*Qz-Pz*Qy) #N.m \n",
      "Y=(Pz*Qx-Px*Qz) #N.m\n",
      "Z=(Px*Qy-Py*Qx) #N.m\n",
      "\n",
      "#Result\n",
      "\n",
      "print'The cross product is',round(X),\"i\",round(Y),\"j\",round(Z),\"k lb-ft\"\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The cross product is 610.0 i -381.0 j -5.0 k lb-ft\n"
       ]
      }
     ],
     "prompt_number": 45
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.1-18, Page No: 14"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Result\n",
      "#As this is symbolic solution directly print command is being used to give the required output\n",
      "\n",
      "print'The Time derivative is '\n",
      "print'dr/dt=(dx/dt)i+12*y(dy/dt)j-3*(dz/dt)k'\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Time derivative is \n",
        "dr/dt=(dx/dt)i+12*y(dy/dt)j-3*(dz/dt)k\n"
       ]
      }
     ],
     "prompt_number": 47
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.1-19, Page No: 14"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from scipy.integrate import quad\n",
      "def integrand(x, a, b):\n",
      "    return x**2\n",
      "a=1\n",
      "b=1\n",
      "I=quad(integrand, 1, 3, args=(a,b))\n",
      "\n",
      "def integrand(y, a, b):\n",
      "    return 2*y\n",
      "a=1\n",
      "b=1\n",
      "J=quad(integrand, 1, 3, args=(a,b))\n",
      "\n",
      "def integrand(z, a, b):\n",
      "    return 1\n",
      "a=1\n",
      "b=1\n",
      "K=quad(integrand, 1, 3, args=(a,b))\n",
      "\n",
      "# Results\n",
      "print'The answer is',round(I[0],2),\"i +\",round(J[0]),\"j -\",round(K[0]),\"k.\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The answer is 8.67 i + 8.0 j - 2.0 k.\n"
       ]
      }
     ],
     "prompt_number": 5
    }
   ],
   "metadata": {}
  }
 ]
}