{
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   "source": [
    "# IPython Notebook for turning in solutions to the problems in the Essentials of Paleomagnetism Textbook by L. Tauxe"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problems in Chapter 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problem 1:  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given that:\n",
    "\n",
    "$$\n",
    "\\nabla V_m = - \\bigl(\n",
    "{ {\\partial}\\over {\\partial r} }\n",
    "{ {m \\cos \\theta} \\over {4 \\pi r^2}} + \n",
    "{ {1\\over r} }\n",
    "{ {\\partial}\\over {\\partial \\theta} }\n",
    " { { m\\cos \\theta}\\over { 4 \\pi r^2} }\n",
    " \\bigr)\n",
    "$$\n",
    "\n",
    "it follows that:\n",
    "\n",
    "Complete this text using LaTeX formatting.  see the above example.  Notice how stand alone equations  look like this: \n",
    "$$\n",
    "\\hbox{Type your equation here}\n",
    "$$\n",
    "and inline math looks like this:  $\\alpha,\\beta,\\gamma$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# code to calculate H_r and H_theta\n",
    "import numpy as np\n",
    "deg2rad=np.pi/180.  # converts degrees to radians\n",
    "#  write code here to calculate H_r and H_theta and convert to B_r, B_theta\n",
    "\n",
    "\n",
    "# This is how you print out nice formatted numbers\n",
    "# floating point variables have the syntax:  \n",
    "# '%X.Yf'%(FP_variable) where X is the number of digits and Y is the \n",
    "# number of didgets after the decimal.  \n",
    "# uncomment this line to print\n",
    "#print 'H_r= ','%7.1f'%(H_r), 'H_theta= ', '%7.1f'%(H_theta)\n",
    "#  to format integers:  use the syntax:\n",
    "# '%i'%(INT_variable)\n",
    "#print 'B_r = ','%i'%(B_r*1e6), 'uT' # B_r in microtesla\n",
    "#print 'B_theta =','%i'%(B_theta*1e6),'uT' # B_theta in microtesla"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 2a:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some text to describe what you are doing.  (Edit this!)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "42.0\n"
     ]
    }
   ],
   "source": [
    "# write a function here with the form\n",
    "def myfunc(B_in):  # edit this line for your own input variables!\n",
    "    # do some math here to define OUTPUT_VARIABLES\n",
    "    B_out=B_in*1.\n",
    "    return B_out\n",
    "B=42 # define your input variables here\n",
    "print myfunc(B)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 2b: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# take your program from 2a and modify it to respond to some input flag\n",
    "# e.g.:\n",
    "def myfunc(B_in,units):\n",
    "    if units=='cgs':\n",
    "        # do cgs conversion.....  \n",
    "        pass\n",
    "    elif units=='SI':\n",
    "        # do SI conversion\n",
    "        pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 3a:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "a) This problem boils down to finding the value for ${\\bf m}$ in Equation 1.8 in Chapter 1 that would give rise to a radial field of 10$\\mu$T at a depth  of 2890 km (radius of the Earth minus radius of the dipole source).  \n",
    "\n",
    "Write text here about how you solve the problem....   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Write code here to calculate the moment, m and print it in ZAm^2\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 3b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "b) To compare 10 $\\mu$T with the field produced by an axial dipole of 80 ZAm$^2$, we need the second part of Equation 1.8 in the text:\n",
    "\n",
    "Type your answer here with nice LaTeX formatting.   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Write some code here that calculates H_r, H_theta, the total field\n",
    "# in H and converted to microtesla.   Use nicely formated print statements \n",
    "# display your results.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 4:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Write your answer in this markdown cell.   Follow the latex examples provided for Problem 1. Also you can look stuff up online for latex math.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
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