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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#Chapter 1: Preliminaries"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example 1.1, Rounding off Numbers, Page no. 2"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"81.9773 becomes 81.98\n",
"\n",
"\n",
"48.365 becomes 48.37\n",
"\n",
"\n",
"21.385 becomes 21.39\n",
"\n",
"\n",
"12.865 becomes 12.87\n",
"\n",
"\n",
"27.553 becomes 27.55\n",
"\n"
]
}
],
"source": [
"#variable declaration\n",
"a=[81.9773,48.365,21.385,12.865,27.553]\n",
"\n",
"#calculation and result\n",
"for i in xrange (0,5):\n",
" print '\\n%s becomes %.2f\\n' %(a[i],a[i])\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example 1.2, Relative Maximum Error, Page no. 5"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Maximum Error = 0.030\n",
"\n",
"Relative maximum error = 0.006\n"
]
}
],
"source": [
"\n",
" \n",
"#variable declaration\n",
"h=0.001;\n",
"x=1;y=1;z=1;dx=0.001;dy=0.001;dz=0.001;\n",
"def f(x,y,z):\n",
" return (5*x*y**2)/z**3\n",
"\n",
"#calculation\n",
"du=abs(f(x+h,y,z)-f(x,y,z))*dx+abs(f(x,y+h,z)-f(x,y,z))*dy+abs(f(x,y,z+h)-f(x,y,z))*dz;\n",
"du=du/h;\n",
"Er=du/f(x,y,z)\n",
"\n",
"#result\n",
"print '\\nMaximum Error = %.3f\\n\\nRelative maximum error = %.3f' %(du,Er)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example 1.3, Absolute Error, Page no. 6"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Maximum Absolute Error of a+b+c+d = 600.050200\n",
"\n",
"\n",
"Maximum Absolute Error of c^3 = -172.000000\n"
]
}
],
"source": [
"\n",
"\n",
"#Variable declaration\n",
"a=10;b=0.0356;c=15300;d=62000;\n",
"ea=0.05;eb=0.0002;ec=100;ed=500;\n",
"\n",
"#Calculation\n",
"e=ea+eb+ec+ed;\n",
"E=(c+2*ec)^3-(c+ec)^3\n",
"\n",
"#result\n",
"print '\\nMaximum Absolute Error of a+b+c+d = %f\\n' %e\n",
"print '\\nMaximum Absolute Error of c^3 = %f' %E\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
}
|
