deletions | additions       diff --git a/IntroductionMath.ipynb b/IntroductionMath.ipynb  new file mode 100644  index 0000000..a79510a  --- /dev/null  +++ b/IntroductionMath.ipynb 
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{  "metadata": {  "name": "IntroductionMath"  },  "nbformat": 3,  "nbformat_minor": 0,  "worksheets": [  {  "cells": [  {  "cell_type": "markdown",  "metadata": {},  "source": [  "[Bondi-Hoyle Accretion](http://en.wikipedia.org/wiki/Bondi_accretion)\n",  "\n",  "$$\\dot{M}_{BH} = \\frac{4 \\pi \\rho G^2 M^2 }{c_s^3} $$"  ]  },  {  "cell_type": "code",  "collapsed": false,  "input": [  "import astropy.units as units\n",  "import astropy.constants as constants"  ],  "language": "python",  "metadata": {},  "outputs": [],  "prompt_number": 1  },  {  "cell_type": "code",  "collapsed": false,  "input": [  "# mdot for some fiducial numbers\n",  "mdot = (4 * pi * constants.G**2 * (10**4 * 2.8 * constants.m_p/units.cm**3) * constants.M_sun**2 / (1. * units.km/units.s)**3).cgs\n",  "mdot # Why does ipython pretty-print this, but \"print mdot\" ugly-prints it?"  ],  "language": "python",  "metadata": {},  "outputs": [  {  "latex": [  "$1.03712\\times 10^{+19} \\; \\mathrm{\\frac{g}{s}}$"  ],  "output_type": "pyout",  "prompt_number": 16,  "text": [  ""  ]  }  ],  "prompt_number": 16  },  {  "cell_type": "code",  "collapsed": false,  "input": [  "# mdot in msun / year\n",  "mdot_msunperyr = (mdot / constants.M_sun * units.year).decompose()\n",  "mdot_msunperyr # \"$M_\\odot \\text{yr}^{-1}$\""  ],  "language": "python",  "metadata": {},  "outputs": [  {  "latex": [  "$1.64542\\times 10^{-07} \\; \\mathrm{}$"  ],  "output_type": "pyout",  "prompt_number": 28,  "text": [  ""  ]  }  ],  "prompt_number": 28  },  {  "cell_type": "markdown",  "metadata": {},  "source": [  "$$\\dot{M}_{BH} = 1.6\\times10^{-7} \\left(\\frac{M}{M_\\odot}\\right)^2 \\left(\\frac{n}{10^4 \\text{cm}^{-3}}\\right) \\left(\\frac{c_s}{1 \\text{km s}^{-1}}\\right)^{-3} $$"  ]  },  {  "cell_type": "code",  "collapsed": false,  "input": [  "def m_bh(mass,density,soundspeed):\n",  " return ((4 * pi * constants.G**2 * (density* 2.8 * constants.m_p/units.cm**3) * (mass*constants.M_sun)**2 / (soundspeed * units.km/units.s)**3) / constants.M_sun * units.year).decompose()"  ],  "language": "python",  "metadata": {},  "outputs": [],  "prompt_number": 18  },  {  "cell_type": "markdown",  "metadata": {},  "source": [  "Some fiducial numbers:"  ]  },  {  "cell_type": "code",  "collapsed": false,  "input": [  "m_bh(1,1e4,1)"  ],  "language": "python",  "metadata": {},  "outputs": [  {  "latex": [  "$1.64542\\times 10^{-07} \\; \\mathrm{}$"  ],  "output_type": "pyout",  "prompt_number": 19,  "text": [  ""  ]  }  ],  "prompt_number": 19  },  {  "cell_type": "code",  "collapsed": false,  "input": [  "10/m_bh(10,1e5,1)"  ],  "language": "python",  "metadata": {},  "outputs": [  {  "latex": [  "$60774.6 \\; \\mathrm{}$"  ],  "output_type": "pyout",  "prompt_number": 24,  "text": [  ""  ]  }  ],  "prompt_number": 24  },  {  "cell_type": "code",  "collapsed": false,  "input": [  "10/m_bh(10,1e6,1)"  ],  "language": "python",  "metadata": {},  "outputs": [  {  "latex": [  "$6077.46 \\; \\mathrm{}$"  ],  "output_type": "pyout",  "prompt_number": 25,  "text": [  ""  ]  }  ],  "prompt_number": 25  },  {  "cell_type": "code",  "collapsed": false,  "input": [],  "language": "python",  "metadata": {},  "outputs": []  }  ],  "metadata": {}  }  ]  }