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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Modeling and Simulation in Python\n",
+    "\n",
+    "Chapter 4\n",
+    "\n",
+    "Copyright 2017 Allen Downey\n",
+    "\n",
+    "License: [Creative Commons Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Configure Jupyter so figures appear in the notebook\n",
+    "%matplotlib inline\n",
+    "\n",
+    "# Configure Jupyter to display the assigned value after an assignment\n",
+    "%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n",
+    "\n",
+    "# import functions from the modsim library\n",
+    "from modsim import *"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Returning values"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Here's a simple function that returns a value:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def add_five(x):\n",
+    "    return x + 5"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "And here's how we call it."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "8"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "y = add_five(3)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "If you run a function on the last line of a cell, Jupyter displays the result:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "10"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "add_five(5)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "But that can be a bad habit, because usually if you call a function and don't assign the result in a variable, the result gets discarded.\n",
+    "\n",
+    "In the following example, Jupyter shows the second result, but the first result just disappears."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "10"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "add_five(3)\n",
+    "add_five(5)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "When you call a function that returns a variable, it is generally a good idea to assign the result to a variable."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "8 10\n"
+     ]
+    }
+   ],
+   "source": [
+    "y1 = add_five(3)\n",
+    "y2 = add_five(5)\n",
+    "\n",
+    "print(y1, y2)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Exercise:** Write a function called `make_state` that creates a `State` object with the state variables `olin=10` and `wellesley=2`, and then returns the new `State` object.\n",
+    "\n",
+    "Write a line of code that calls `make_state` and assigns the result to a variable named `init`."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def make_state():\n",
+    "    state = State(olin=10, wellesley=2)\n",
+    "    return state\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>values</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>olin</th>\n",
+       "      <td>10</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>wellesley</th>\n",
+       "      <td>2</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "olin         10\n",
+       "wellesley     2\n",
+       "dtype: int64"
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "init = make_state()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Running simulations"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Here's the code from the previous notebook."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def step(state, p1, p2):\n",
+    "    \"\"\"Simulate one minute of time.\n",
+    "    \n",
+    "    state: bikeshare State object\n",
+    "    p1: probability of an Olin->Wellesley customer arrival\n",
+    "    p2: probability of a Wellesley->Olin customer arrival\n",
+    "    \"\"\"\n",
+    "    if flip(p1):\n",
+    "        bike_to_wellesley(state)\n",
+    "    \n",
+    "    if flip(p2):\n",
+    "        bike_to_olin(state)\n",
+    "        \n",
+    "def bike_to_wellesley(state):\n",
+    "    \"\"\"Move one bike from Olin to Wellesley.\n",
+    "    \n",
+    "    state: bikeshare State object\n",
+    "    \"\"\"\n",
+    "    if state.olin == 0:\n",
+    "        state.olin_empty += 1\n",
+    "        return\n",
+    "    state.olin -= 1\n",
+    "    state.wellesley += 1\n",
+    "    \n",
+    "def bike_to_olin(state):\n",
+    "    \"\"\"Move one bike from Wellesley to Olin.\n",
+    "    \n",
+    "    state: bikeshare State object\n",
+    "    \"\"\"\n",
+    "    if state.wellesley == 0:\n",
+    "        state.wellesley_empty += 1\n",
+    "        return\n",
+    "    state.wellesley -= 1\n",
+    "    state.olin += 1\n",
+    "    \n",
+    "def decorate_bikeshare():\n",
+    "    \"\"\"Add a title and label the axes.\"\"\"\n",
+    "    decorate(title='Olin-Wellesley Bikeshare',\n",
+    "             xlabel='Time step (min)', \n",
+    "             ylabel='Number of bikes')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Here's a modified version of `run_simulation` that creates a `State` object, runs the simulation, and returns the `State` object."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def run_simulation(p1, p2, num_steps):\n",
+    "    \"\"\"Simulate the given number of time steps.\n",
+    "    \n",
+    "    p1: probability of an Olin->Wellesley customer arrival\n",
+    "    p2: probability of a Wellesley->Olin customer arrival\n",
+    "    num_steps: number of time steps\n",
+    "    \"\"\"\n",
+    "    state = State(olin=10, wellesley=2, \n",
+    "                  olin_empty=0, wellesley_empty=0)\n",
+    "                    \n",
+    "    for i in range(num_steps):\n",
+    "        step(state, p1, p2)\n",
+    "        \n",
+    "    return state"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Now `run_simulation` doesn't plot anything:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>values</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>olin</th>\n",
+       "      <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>wellesley</th>\n",
+       "      <td>12</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>olin_empty</th>\n",
+       "      <td>7</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>wellesley_empty</th>\n",
+       "      <td>0</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "olin                0\n",
+       "wellesley          12\n",
+       "olin_empty          7\n",
+       "wellesley_empty     0\n",
+       "dtype: int64"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "state = run_simulation(0.4, 0.2, 60)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "But after the simulation, we can read the metrics from the `State` object."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "7"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "state.olin_empty"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Now we can run simulations with different values for the parameters.  When `p1` is small, we probably don't run out of bikes at Olin."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "0"
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "state = run_simulation(0.2, 0.2, 60)\n",
+    "state.olin_empty"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "When `p1` is large, we probably do."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "22"
+      ]
+     },
+     "execution_count": 14,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "state = run_simulation(0.6, 0.2, 60)\n",
+    "state.olin_empty"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## More for loops"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "`linspace` creates a NumPy array of equally spaced numbers."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([0.  , 0.25, 0.5 , 0.75, 1.  ])"
+      ]
+     },
+     "execution_count": 15,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "p1_array = linspace(0, 1, 5)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We can use an array in a `for` loop, like this:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.0\n",
+      "0.25\n",
+      "0.5\n",
+      "0.75\n",
+      "1.0\n"
+     ]
+    }
+   ],
+   "source": [
+    "for p1 in p1_array:\n",
+    "    print(p1)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "This will come in handy in the next section.\n",
+    "\n",
+    "`linspace` is defined in `modsim.py`.  You can get the documentation using `help`."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Help on function linspace in module modsim:\n",
+      "\n",
+      "linspace(start, stop, num=50, **options)\n",
+      "    Returns an array of evenly-spaced values in the interval [start, stop].\n",
+      "    \n",
+      "    start: first value\n",
+      "    stop: last value\n",
+      "    num: number of values\n",
+      "    \n",
+      "    Also accepts the same keyword arguments as np.linspace.  See\n",
+      "    https://docs.scipy.org/doc/numpy/reference/generated/numpy.linspace.html\n",
+      "    \n",
+      "    returns: array or Quantity\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "help(linspace)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "`linspace` is based on a NumPy function with the same name.  [Click here](https://docs.scipy.org/doc/numpy/reference/generated/numpy.linspace.html) to read more about how to use it."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Exercise:** \n",
+    "Use `linspace` to make an array of 10 equally spaced numbers from 1 to 10 (including both)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([ 1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10.])"
+      ]
+     },
+     "execution_count": 19,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "linspace(1, 10, 10)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Exercise:** The `modsim` library provides a related function called `linrange`.  You can view the documentation by running the following cell:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Help on function linrange in module modsim:\n",
+      "\n",
+      "linrange(start=0, stop=None, step=1, **options)\n",
+      "    Returns an array of evenly-spaced values in the interval [start, stop].\n",
+      "    \n",
+      "    This function works best if the space between start and stop\n",
+      "    is divisible by step; otherwise the results might be surprising.\n",
+      "    \n",
+      "    By default, the last value in the array is `stop-step`\n",
+      "    (at least approximately).\n",
+      "    If you provide the keyword argument `endpoint=True`,\n",
+      "    the last value in the array is `stop`.\n",
+      "    \n",
+      "    start: first value\n",
+      "    stop: last value\n",
+      "    step: space between values\n",
+      "    \n",
+      "    Also accepts the same keyword arguments as np.linspace.  See\n",
+      "    https://docs.scipy.org/doc/numpy/reference/generated/numpy.linspace.html\n",
+      "    \n",
+      "    returns: array or Quantity\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "help(linrange)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Use `linrange` to make an array of numbers from 1 to 11 with a step size of 2."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([1., 3., 5., 7., 9.])"
+      ]
+     },
+     "execution_count": 21,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "linrange(1, 11, 2)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Sweeping parameters"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "`p1_array` contains a range of values for `p1`."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. ])"
+      ]
+     },
+     "execution_count": 22,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "p2 = 0.2\n",
+    "num_steps = 60\n",
+    "p1_array = linspace(0, 1, 11)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The following loop runs a simulation for each value of `p1` in `p1_array`; after each simulation, it prints the number of unhappy customers at the Olin station:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.0 0\n",
+      "0.1 0\n",
+      "0.2 0\n",
+      "0.30000000000000004 0\n",
+      "0.4 7\n",
+      "0.5 0\n",
+      "0.6000000000000001 15\n",
+      "0.7000000000000001 23\n",
+      "0.8 28\n",
+      "0.9 31\n",
+      "1.0 42\n"
+     ]
+    }
+   ],
+   "source": [
+    "for p1 in p1_array:\n",
+    "    state = run_simulation(p1, p2, num_steps)\n",
+    "    print(p1, state.olin_empty)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Now we can do the same thing, but storing the results in a `SweepSeries` instead of printing them.\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "sweep = SweepSeries()\n",
+    "\n",
+    "for p1 in p1_array:\n",
+    "    state = run_simulation(p1, p2, num_steps)\n",
+    "    sweep[p1] = state.olin_empty"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "And then we can plot the results."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Saving figure to file figs/chap02-fig02.pdf\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot(sweep, label='Olin')\n",
+    "\n",
+    "decorate(title='Olin-Wellesley Bikeshare',\n",
+    "         xlabel='Arrival rate at Olin (p1 in customers/min)', \n",
+    "         ylabel='Number of unhappy customers')\n",
+    "\n",
+    "savefig('figs/chap02-fig02.pdf')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Exercises\n",
+    "\n",
+    "**Exercise:** Wrap this code in a function named `sweep_p1` that takes an array called `p1_array` as a parameter.  It should create a new `SweepSeries`, run a simulation for each value of `p1` in `p1_array`, store the results in the `SweepSeries`, and return the `SweepSeries`.\n",
+    "\n",
+    "Use your function to plot the number of unhappy customers at Olin as a function of `p1`.  Label the axes."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def sweep_p1(p1_array):\n",
+    "    sweep = SweepSeries()\n",
+    "    for p1 in p1_array:\n",
+    "        state = run_simulation(p1, p2, num_steps)\n",
+    "        sweep[p1] = state.olin_empty\n",
+    "    \n",
+    "    return sweep"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Saving figure to file figs/chap02-fig02.pdf\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "sweep = sweep_p1(linspace(0,1,10))\n",
+    "\n",
+    "plot(sweep, label='Olin')\n",
+    "\n",
+    "decorate(title='Olin-Wellesley Bikeshare',\n",
+    "         xlabel='Arrival rate at Olin (p1 in customers/min)', \n",
+    "         ylabel='Number of unhappy customers')\n",
+    "\n",
+    "savefig('figs/chap02-fig02.pdf')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Exercise:** Write a function called `sweep_p2` that runs simulations with `p1=0.5` and a range of values for `p2`.  It should store the results in a `SweepSeries` and return the `SweepSeries`.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 36,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "p1=0.5\n",
+    "\n",
+    "def sweep_p2(p2_array):\n",
+    "    sweep = SweepSeries()\n",
+    "    for p2 in p2_array:\n",
+    "        state = run_simulation(p1, p2, num_steps)\n",
+    "        sweep[p2] = state.olin_empty\n",
+    "    \n",
+    "    return sweep\n",
+    "    \n",
+    "    "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 38,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Saving figure to file figs/chap02-fig02.pdf\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "sweep = sweep_p2(linspace(0,1,10))\n",
+    "\n",
+    "plot(sweep, label='Olin')\n",
+    "\n",
+    "decorate(title='Olin-Wellesley Bikeshare',\n",
+    "         xlabel='Arrival rate at Olin (p1 in customers/min)', \n",
+    "         ylabel='Number of unhappy customers')\n",
+    "\n",
+    "savefig('figs/chap02-fig02.pdf')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.000000    25\n",
+      "0.111111    14\n",
+      "0.222222     8\n",
+      "0.333333     2\n",
+      "0.444444     1\n",
+      "0.555556     0\n",
+      "0.666667     0\n",
+      "0.777778     0\n",
+      "0.888889     0\n",
+      "1.000000     0\n",
+      "dtype: int64\n"
+     ]
+    }
+   ],
+   "source": [
+    "print (sweep)\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Optional exercises\n",
+    "\n",
+    "The following two exercises are a little more challenging.  If you are comfortable with what you have learned so far, you should give them a try.  If you feel like you have your hands full, you might want to skip them for now.\n",
+    "\n",
+    "**Exercise:** Because our simulations are random, the results vary from one run to another, and the results of a parameter sweep tend to be noisy.  We can get a clearer picture of the relationship between a parameter and a metric by running multiple simulations with the same parameter and taking the average of the results.\n",
+    "\n",
+    "Write a function called `run_multiple_simulations` that takes as parameters `p1`, `p2`, `num_steps`, and `num_runs`.\n",
+    "\n",
+    "`num_runs` specifies how many times it should call `run_simulation`.\n",
+    "\n",
+    "After each run, it should store the total number of unhappy customers (at Olin or Wellesley) in a `TimeSeries`.  At the end, it should return the `TimeSeries`.\n",
+    "\n",
+    "Test your function with parameters\n",
+    "\n",
+    "```\n",
+    "p1 = 0.3\n",
+    "p2 = 0.3\n",
+    "num_steps = 60\n",
+    "num_runs = 10\n",
+    "```\n",
+    "\n",
+    "Display the resulting `TimeSeries` and use the `mean` function provided by the `TimeSeries` object to compute the average number of unhappy customers."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "# Solution goes here"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Solution goes here"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Exercise:**  Continuting the previous exercise, use `run_multiple_simulations` to run simulations with a range of values for `p1` and\n",
+    "\n",
+    "```\n",
+    "p2 = 0.3\n",
+    "num_steps = 60\n",
+    "num_runs = 20\n",
+    "```\n",
+    "\n",
+    "Store the results in a `SweepSeries`, then plot the average number of unhappy customers as a function of `p1`.  Label the axes.\n",
+    "\n",
+    "What value of `p1` minimizes the average number of unhappy customers?"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [],
+   "source": [
+    "# Solution goes here"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Solution goes here"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.6.6"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/code/chap08_mine.ipynb b/code/chap08_mine.ipynb
new file mode 100644
index 00000000..5c493e06
--- /dev/null
+++ b/code/chap08_mine.ipynb
@@ -0,0 +1,932 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Modeling and Simulation in Python\n",
+    "\n",
+    "Chapter 8\n",
+    "\n",
+    "Copyright 2017 Allen Downey\n",
+    "\n",
+    "License: [Creative Commons Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Configure Jupyter so figures appear in the notebook\n",
+    "%matplotlib inline\n",
+    "\n",
+    "# Configure Jupyter to display the assigned value after an assignment\n",
+    "%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n",
+    "\n",
+    "# import functions from the modsim.py module\n",
+    "from modsim import *\n",
+    "\n",
+    "from pandas import read_html"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Functions from the previous chapter"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def plot_results(census, un, timeseries, title):\n",
+    "    \"\"\"Plot the estimates and the model.\n",
+    "    \n",
+    "    census: TimeSeries of population estimates\n",
+    "    un: TimeSeries of population estimates\n",
+    "    timeseries: TimeSeries of simulation results\n",
+    "    title: string\n",
+    "    \"\"\"\n",
+    "    plot(census, ':', label='US Census')\n",
+    "    plot(un, '--', label='UN DESA')\n",
+    "    plot(timeseries, color='gray', label='model')\n",
+    "    \n",
+    "    decorate(xlabel='Year', \n",
+    "             ylabel='World population (billion)',\n",
+    "             title=title)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def run_simulation(system, update_func):\n",
+    "    \"\"\"Simulate the system using any update function.\n",
+    "    \n",
+    "    system: System object\n",
+    "    update_func: function that computes the population next year\n",
+    "    \n",
+    "    returns: TimeSeries\n",
+    "    \"\"\"\n",
+    "    results = TimeSeries()\n",
+    "    results[system.t_0] = system.p_0\n",
+    "    \n",
+    "    for t in linrange(system.t_0, system.t_end):\n",
+    "        results[t+1] = update_func(results[t], t, system)\n",
+    "        \n",
+    "    return results"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Reading the data"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "filename = 'data/World_population_estimates.html'\n",
+    "tables = read_html(filename, header=0, index_col=0, decimal='M')\n",
+    "table2 = tables[2]\n",
+    "table2.columns = ['census', 'prb', 'un', 'maddison', \n",
+    "                  'hyde', 'tanton', 'biraben', 'mj', \n",
+    "                  'thomlinson', 'durand', 'clark']"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "un = table2.un / 1e9\n",
+    "census = table2.census / 1e9\n",
+    "plot(census, ':', label='US Census')\n",
+    "plot(un, '--', label='UN DESA')\n",
+    "    \n",
+    "decorate(xlabel='Year', \n",
+    "             ylabel='World population (billion)',\n",
+    "             title='Estimated world population')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Running the quadratic model"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Here's the update function for the quadratic growth model with parameters `alpha` and `beta`."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def update_func_quad(pop, t, system):\n",
+    "    \"\"\"Update population based on a quadratic model.\n",
+    "    \n",
+    "    pop: current population in billions\n",
+    "    t: what year it is\n",
+    "    system: system object with model parameters\n",
+    "    \"\"\"\n",
+    "    net_growth = system.alpha * pop + system.beta * pop**2\n",
+    "    return pop + net_growth"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Extract the starting time and population."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "2.557628654"
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "t_0 = get_first_label(census)\n",
+    "t_end = get_last_label(census)\n",
+    "p_0 = get_first_value(census)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Initialize the system object."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>values</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>t_0</th>\n",
+       "      <td>1950.000000</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>t_end</th>\n",
+       "      <td>2016.000000</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>p_0</th>\n",
+       "      <td>2.557629</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>alpha</th>\n",
+       "      <td>0.025000</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>beta</th>\n",
+       "      <td>-0.001800</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "t_0      1950.000000\n",
+       "t_end    2016.000000\n",
+       "p_0         2.557629\n",
+       "alpha       0.025000\n",
+       "beta       -0.001800\n",
+       "dtype: float64"
+      ]
+     },
+     "execution_count": 9,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "system = System(t_0=t_0, \n",
+    "                t_end=t_end,\n",
+    "                p_0=p_0,\n",
+    "                alpha=0.025,\n",
+    "                beta=-0.0018)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Run the model and plot results."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "results = run_simulation(system, update_func_quad)\n",
+    "plot_results(census, un, results, 'Quadratic model')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Generating projections"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "To generate projections, all we have to do is change `t_end`"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {
+    "scrolled": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Saving figure to file figs/chap04-fig01.pdf\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "system.t_end = 2250\n",
+    "results = run_simulation(system, update_func_quad)\n",
+    "plot_results(census, un, results, 'World population projection')\n",
+    "savefig('figs/chap04-fig01.pdf')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The population in the model converges on the equilibrium population, `-alpha/beta`"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "13.856665141368708"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "results[system.t_end]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "13.88888888888889"
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "-system.alpha / system.beta"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Exercise:**  What happens if we start with an initial population above the carrying capacity, like 20 billion?  Run the model with initial populations between 1 and 20 billion, and plot the results on the same axes."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 46,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'p0_array = linspace(1, 25, 11)\\n\\nfor system.p_0 in p0_array:\\n    results = run_simulation(system, update_func_quad)\\n    plot(results)'"
+      ]
+     },
+     "execution_count": 46,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Solution goes here\n",
+    "\n",
+    "for i in range(20):\n",
+    "    system.p_0 = i\n",
+    "    system.t_end = 2250\n",
+    "    results = run_simulation(system, update_func_quad)\n",
+    "    plot(results)\n",
+    "    \n",
+    "\n",
+    "\"\"\"p0_array = linspace(1, 25, 11)\n",
+    "\n",
+    "for system.p_0 in p0_array:\n",
+    "    results = run_simulation(system, update_func_quad)\n",
+    "    plot(results)\"\"\"\n",
+    "    \n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Comparing projections"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We can compare the projection from our model with projections produced by people who know what they are doing."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>United States Census Bureau (2015)[28]</th>\n",
+       "      <th>Population Reference Bureau (1973-2015)[15]</th>\n",
+       "      <th>United Nations Department of Economic and Social Affairs (2015)[16]</th>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Year</th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>2016</th>\n",
+       "      <td>7.334772e+09</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>7.432663e+09</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2017</th>\n",
+       "      <td>7.412779e+09</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2018</th>\n",
+       "      <td>7.490428e+09</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2019</th>\n",
+       "      <td>7.567403e+09</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2020</th>\n",
+       "      <td>7.643402e+09</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>7.758157e+09</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "      United States Census Bureau (2015)[28]  \\\n",
+       "Year                                           \n",
+       "2016                            7.334772e+09   \n",
+       "2017                            7.412779e+09   \n",
+       "2018                            7.490428e+09   \n",
+       "2019                            7.567403e+09   \n",
+       "2020                            7.643402e+09   \n",
+       "\n",
+       "      Population Reference Bureau (1973-2015)[15]  \\\n",
+       "Year                                                \n",
+       "2016                                          NaN   \n",
+       "2017                                          NaN   \n",
+       "2018                                          NaN   \n",
+       "2019                                          NaN   \n",
+       "2020                                          NaN   \n",
+       "\n",
+       "      United Nations Department of Economic and Social Affairs (2015)[16]  \n",
+       "Year                                                                       \n",
+       "2016                                       7.432663e+09                    \n",
+       "2017                                                NaN                    \n",
+       "2018                                                NaN                    \n",
+       "2019                                                NaN                    \n",
+       "2020                                       7.758157e+09                    "
+      ]
+     },
+     "execution_count": 25,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "table3 = tables[3]\n",
+    "table3.head()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "`NaN` is a special value that represents missing data, in this case because some agencies did not publish projections for some years."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "table3.columns = ['census', 'prb', 'un']"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "This function plots projections from the UN DESA and U.S. Census.  It uses `dropna` to remove the `NaN` values from each series before plotting it."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def plot_projections(table):\n",
+    "    \"\"\"Plot world population projections.\n",
+    "    \n",
+    "    table: DataFrame with columns 'un' and 'census'\n",
+    "    \"\"\"\n",
+    "    census_proj = table.census / 1e9\n",
+    "    un_proj = table.un / 1e9\n",
+    "    \n",
+    "    plot(census_proj.dropna(), 'b:', label='US Census')\n",
+    "    plot(un_proj.dropna(), 'g--', label='UN DESA')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Run the model until 2100, which is as far as the other projections go."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>values</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>t_0</th>\n",
+       "      <td>1950.000000</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>t_end</th>\n",
+       "      <td>2100.000000</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>p_0</th>\n",
+       "      <td>2.557629</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>alpha</th>\n",
+       "      <td>0.025000</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>beta</th>\n",
+       "      <td>-0.001800</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "t_0      1950.000000\n",
+       "t_end    2100.000000\n",
+       "p_0         2.557629\n",
+       "alpha       0.025000\n",
+       "beta       -0.001800\n",
+       "dtype: float64"
+      ]
+     },
+     "execution_count": 34,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "p_0 = get_first_value(census)\n",
+    "\n",
+    "system = System(t_0=t_0, \n",
+    "                t_end=2100,\n",
+    "                p_0=p_0,\n",
+    "                alpha=0.025,\n",
+    "                beta=-0.0018)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 35,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Saving figure to file figs/chap04-fig02.pdf\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "results = run_simulation(system, update_func_quad)\n",
+    "\n",
+    "plot_results(census, un, results, 'World population projections')\n",
+    "plot_projections(table3)\n",
+    "savefig('figs/chap04-fig02.pdf')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "People who know what they are doing expect the growth rate to decline more sharply than our model projects."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Exercises\n",
+    "\n",
+    "**Optional exercise:** The net growth rate of world population has been declining for several decades.  That observation suggests one more way to generate projections, by extrapolating observed changes in growth rate.\n",
+    "\n",
+    "The `modsim` library provides a function, `compute_rel_diff`, that computes relative differences of the elements in a sequence.  It is a wrapper for the NumPy function `ediff1d`:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 36,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "%psource compute_rel_diff"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Here's how we can use it to compute the relative differences in the `census` and `un` estimates:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "alpha_census = compute_rel_diff(census)\n",
+    "plot(alpha_census)\n",
+    "\n",
+    "alpha_un = compute_rel_diff(un)\n",
+    "plot(alpha_un)\n",
+    "\n",
+    "decorate(xlabel='Year', label='Net growth rate')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Other than a bump around 1990, net growth rate has been declining roughly linearly since 1965.  As an exercise, you can use this data to make a projection of world population until 2100.\n",
+    "\n",
+    "1. Define a function, `alpha_func`, that takes `t` as a parameter and returns an estimate of the net growth rate at time `t`, based on a linear function `alpha = intercept + slope * t`.  Choose values of `slope` and `intercept` to fit the observed net growth rates since 1965.\n",
+    "\n",
+    "2. Call your function with a range of `ts` from 1960 to 2020 and plot the results.\n",
+    "\n",
+    "3. Create a `System` object that includes `alpha_func` as a system variable.\n",
+    "\n",
+    "4. Define an update function that uses `alpha_func` to compute the net growth rate at the given time `t`.\n",
+    "\n",
+    "5. Test your update function with `t_0 = 1960` and `p_0 = census[t_0]`.\n",
+    "\n",
+    "6. Run a simulation from 1960 to 2100 with your update function, and plot the results.\n",
+    "\n",
+    "7. Compare your projections with those from the US Census and UN."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Solution goes here"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Solution goes here"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Solution goes here"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Solution goes here"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Solution goes here"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Solution goes here"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Solution goes here"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Solution goes here"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Related viewing:** You might be interested in this [video by Hans Rosling about the demographic changes we expect in this century](https://www.youtube.com/watch?v=ezVk1ahRF78)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.6.6"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/code/hiv_model.ipynb b/code/hiv_model.ipynb
new file mode 100644
index 00000000..d7895adc
--- /dev/null
+++ b/code/hiv_model.ipynb
@@ -0,0 +1,330 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# HIV Model"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Becca Suchower"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 100,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Configure Jupyter so figures appear in the notebook\n",
+    "%matplotlib inline\n",
+    "\n",
+    "# Configure Jupyter to display the assigned value after an assignment\n",
+    "%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n",
+    "\n",
+    "# import functions from the modsim.py module\n",
+    "from modsim import *\n",
+    "\n",
+    "from pandas import read_html"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 101,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def make_system():\n",
+    "    \"\"\"\n",
+    "    R = activated lymphocytes\n",
+    "    L = latently infected cells\n",
+    "    E = actively infected cells\n",
+    "    V = free virions\n",
+    "    \"\"\"\n",
+    "    init = State(R=200, L=0, E=0, V=100)\n",
+    "    \n",
+    "    t0 = 0\n",
+    "    t_end = 120  \n",
+    "    \n",
+    "    'initializes rates'\n",
+    "    'Rate is Value/Day'\n",
+    "\n",
+    "    'rate at which uninfected CD4 lymphocytes arise'\n",
+    "    gamma = 1.36 \n",
+    "\n",
+    "    'HIV independent death rate of uninfected CD4 lymphocytes'\n",
+    "    mu = 0.00136 \n",
+    "\n",
+    "    'proportion of cells activated'\n",
+    "    tau = 0.2 \n",
+    "\n",
+    "    'rate of infection of CD4 lymphocytes per virion'\n",
+    "    beta = 0.00027   \n",
+    "\n",
+    "    'proportion of cells becoming latently infected upon infection'\n",
+    "    rho = 0.1 \n",
+    "\n",
+    "    'activation rate of latently infected cells'\n",
+    "    alpha = 0.036 \n",
+    "\n",
+    "    'removal rate of cell free virus'\n",
+    "    sigma = 2 \n",
+    "\n",
+    "    'removal (death) rate of actively infected CD4'\n",
+    "    delta = 0.33\n",
+    "\n",
+    "    'rate of production of virions by an actively infected cell'\n",
+    "    pi = 100 \n",
+    "\n",
+    "    dt = 0.1\n",
+    "    \n",
+    "    return System(init=init, t0=t0, t_end=t_end, gamma=gamma, mu=mu, tau=tau, beta=beta, \n",
+    "                  rho=rho, alpha=alpha, sigma=sigma, delta=delta, pi=pi, dt=dt)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 102,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def update_func(state, dt, system):\n",
+    "    unpack(system)\n",
+    "    R, L, E, V = state\n",
+    "   \n",
+    "    dr = (gamma*tau - mu*R - beta*R*V) * dt\n",
+    "    dl = (rho*beta*R*V - mu*L - alpha*L) * dt\n",
+    "    de = ((1-rho)*beta*R*V + alpha*L - delta*E) * dt\n",
+    "    dv = (pi*E - sigma*V) *dt\n",
+    "    \n",
+    "    R += dr \n",
+    "    L += dl\n",
+    "    E += de\n",
+    "    V += dv\n",
+    "    \n",
+    "    return State(R=R, L=L, E=E, V=V)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 103,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def run_simulation(system, update_func):\n",
+    "    \"\"\"Runs a simulation of the system.\n",
+    "        \n",
+    "    system: System object\n",
+    "    update_func: function that updates state\n",
+    "    \n",
+    "    returns: TimeFrame\n",
+    "    \"\"\"\n",
+    "    unpack(system)\n",
+    "    \n",
+    "    frame = TimeFrame(columns=init.index)\n",
+    "    frame.row[t0] = init\n",
+    "    \n",
+    "    for t in linrange(t0, t_end, dt):\n",
+    "        frame.row[t+dt] = update_func(frame.row[t], dt, system)\n",
+    "    \n",
+    "    return frame"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 104,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>R</th>\n",
+       "      <th>L</th>\n",
+       "      <th>E</th>\n",
+       "      <th>V</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0.0</th>\n",
+       "      <td>200</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>100</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>0.1</th>\n",
+       "      <td>199.46</td>\n",
+       "      <td>0.054</td>\n",
+       "      <td>0.486</td>\n",
+       "      <td>80</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>0.2</th>\n",
+       "      <td>199.029</td>\n",
+       "      <td>0.0968816</td>\n",
+       "      <td>0.857907</td>\n",
+       "      <td>68.86</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>0.3</th>\n",
+       "      <td>198.659</td>\n",
+       "      <td>0.133524</td>\n",
+       "      <td>1.16298</td>\n",
+       "      <td>63.6671</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>0.4</th>\n",
+       "      <td>198.318</td>\n",
+       "      <td>0.167174</td>\n",
+       "      <td>1.43243</td>\n",
+       "      <td>62.5635</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "           R          L         E        V\n",
+       "0.0      200          0         0      100\n",
+       "0.1   199.46      0.054     0.486       80\n",
+       "0.2  199.029  0.0968816  0.857907    68.86\n",
+       "0.3  198.659   0.133524   1.16298  63.6671\n",
+       "0.4  198.318   0.167174   1.43243  62.5635"
+      ]
+     },
+     "execution_count": 104,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "system = make_system()\n",
+    "results = run_simulation(system, update_func)\n",
+    "results.head()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 105,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def plot_results(R, L, E):\n",
+    "    plot(R, '--', label='R')\n",
+    "    plot(L, '-', label='L')\n",
+    "    plot(E, ':', label='E')\n",
+    "    decorate(xlabel='Days from Infection',\n",
+    "             ylabel='Number of Each Cell'\n",
+    "            )"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 106,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot_results(results.R, results.L, results.E)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 107,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def plot_v(V):\n",
+    "    plot(V, '-', label='V')\n",
+    "    decorate(xlabel='Days from Infection',\n",
+    "             ylabel='Number of Virions'\n",
+    "            )"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 108,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot_v(results.V)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.6.6"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/code/orbit_homework.ipynb b/code/orbit_homework.ipynb
new file mode 100644
index 00000000..a3c428a6
--- /dev/null
+++ b/code/orbit_homework.ipynb
@@ -0,0 +1,813 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Becca Suchower\n",
+    "\n",
+    "# Orbital Mechanics Notebook\n",
+    "\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 100,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Configure Jupyter so figures appear in the notebook\n",
+    "%matplotlib inline\n",
+    "\n",
+    "# Configure Jupyter to display the assigned value after an assignment\n",
+    "%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n",
+    "\n",
+    "# import functions from the modsim.py module\n",
+    "from modsim import *"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "\n",
+    "Here's a question from the web site [Ask an Astronomer](http://curious.astro.cornell.edu/about-us/39-our-solar-system/the-earth/other-catastrophes/57-how-long-would-it-take-the-earth-to-fall-into-the-sun-intermediate):\n",
+    "\n",
+    "\"If the Earth suddenly stopped orbiting the Sun, I know eventually it would be pulled in by the Sun's gravity and hit it. How long would it take the Earth to hit the Sun? I imagine it would go slowly at first and then pick up speed.\"\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 101,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "year"
+      ],
+      "text/latex": [
+       "$year$"
+      ],
+      "text/plain": [
+       "<Unit('year')>"
+      ]
+     },
+     "execution_count": 101,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# Here are the units we'll need\n",
+    "\n",
+    "s = UNITS.second\n",
+    "N = UNITS.newton\n",
+    "kg = UNITS.kilogram\n",
+    "m = UNITS.meter\n",
+    "y = UNITS.year"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 102,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>values</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>x</th>\n",
+       "      <td>147000000000.0 meter</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>y</th>\n",
+       "      <td>0 meter</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>vx</th>\n",
+       "      <td>0.0 meter / second</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>vy</th>\n",
+       "      <td>30330.0 meter / second</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "x       147000000000.0 meter\n",
+       "y                    0 meter\n",
+       "vx        0.0 meter / second\n",
+       "vy    30330.0 meter / second\n",
+       "dtype: object"
+      ]
+     },
+     "execution_count": 102,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# And an inition condition (with everything in SI units)\n",
+    "\n",
+    "x = 147e9 * m\n",
+    "y = 0 * m\n",
+    "vx = 0 * m/s\n",
+    "vy = 30330 * m/s\n",
+    "\n",
+    "init = State(x = x,\n",
+    "             y = y,\n",
+    "             vx = vx,\n",
+    "             vy = vy)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 103,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>values</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>init</th>\n",
+       "      <td>x       147000000000.0 meter\n",
+       "y                ...</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>G</th>\n",
+       "      <td>6.674e-11 meter ** 2 * newton / kilogram ** 2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>m1</th>\n",
+       "      <td>1.989e+30 kilogram</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>r_final</th>\n",
+       "      <td>701879000.0 meter</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>m2</th>\n",
+       "      <td>5.972e+24 kilogram</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>t_0</th>\n",
+       "      <td>0 second</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>t_end</th>\n",
+       "      <td>31536000 second</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>dt</th>\n",
+       "      <td>0.1 second</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "init       x       147000000000.0 meter\n",
+       "y                ...\n",
+       "G              6.674e-11 meter ** 2 * newton / kilogram ** 2\n",
+       "m1                                        1.989e+30 kilogram\n",
+       "r_final                                    701879000.0 meter\n",
+       "m2                                        5.972e+24 kilogram\n",
+       "t_0                                                 0 second\n",
+       "t_end                                        31536000 second\n",
+       "dt                                                0.1 second\n",
+       "dtype: object"
+      ]
+     },
+     "execution_count": 103,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# Making a system object\n",
+    "\n",
+    "r_earth = 6.371e6 * m\n",
+    "r_sun = 695.508e6 * m\n",
+    "\n",
+    "system = System(init=init,\n",
+    "                G=6.674e-11 * N / kg**2 * m**2,\n",
+    "                m1=1.989e30 * kg,\n",
+    "                r_final=r_sun + r_earth,\n",
+    "                m2=5.972e24 * kg,\n",
+    "                t_0=0 * s,\n",
+    "                t_end=60*60*24*365 * s,\n",
+    "                dt=0.1 * s)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 104,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Here's a function that computes the force of gravity\n",
+    "\n",
+    "def universal_gravitation(state, system):\n",
+    "    \"\"\"Computes gravitational force.\n",
+    "    \n",
+    "    state: State object with distance r\n",
+    "    system: System object with m1, m2, and G\n",
+    "    \"\"\"\n",
+    "    x, y, vx, vy = state\n",
+    "    unpack(system)\n",
+    "    \n",
+    "    r = Vector(x, y) * m\n",
+    "    \n",
+    "    force = G * m1 * m2 / r.mag**2\n",
+    "    f_vector = -r.hat() * force\n",
+    "    return f_vector"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 105,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "[-3.6686486e+22 -0.0000000e+00] newton/meter<sup>2</sup>"
+      ],
+      "text/latex": [
+       "$[-3.6686486e+22 -0.0000000e+00] \\frac{newton}{meter^{2}}$"
+      ],
+      "text/plain": [
+       "<Quantity([-3.6686486e+22 -0.0000000e+00], 'newton / meter ** 2')>"
+      ]
+     },
+     "execution_count": 105,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "universal_gravitation(init, system)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 106,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# The slope function\n",
+    "\n",
+    "def slope_func(state, t, system):\n",
+    "    \"\"\"Compute derivatives of the state.\n",
+    "    \n",
+    "    state: position, velocity\n",
+    "    t: time\n",
+    "    system: System object containing `g`\n",
+    "    \n",
+    "    returns: derivatives of y and v\n",
+    "    \"\"\"\n",
+    "    x, y, vx, vy = state\n",
+    "    unpack(system)    \n",
+    "        \n",
+    "    f_vector = universal_gravitation(state, system)\n",
+    "  \n",
+    "    v = Vector(vx, vy)\n",
+    "    dxdt = vx\n",
+    "    dydt = vy\n",
+    "    \n",
+    "    dvdt = f_vector / m2\n",
+    "    dvxdt = dvdt.x\n",
+    "    dvydt = dvdt.y\n",
+    "    \n",
+    "    return dxdt, dydt, dvxdt, dvydt"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 107,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(<Quantity(0.0, 'meter / second')>,\n",
+       " <Quantity(30330.0, 'meter / second')>,\n",
+       " <Quantity(-0.006143082049146188, 'newton / kilogram / meter ** 2')>,\n",
+       " <Quantity(-0.0, 'newton / kilogram / meter ** 2')>)"
+      ]
+     },
+     "execution_count": 107,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# Always test the slope function!\n",
+    "\n",
+    "slope_func(init, 0, system)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 108,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
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+       " 31441297.2972973  31472864.86486486 31504432.43243243 31536000.        ], 'second')>"
+      ]
+     },
+     "execution_count": 108,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "timesteps = linspace(system.t_0, system.t_end, 1000)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 109,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>values</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>sol</th>\n",
+       "      <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>t_events</th>\n",
+       "      <td>[]</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>nfev</th>\n",
+       "      <td>152</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>njev</th>\n",
+       "      <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>nlu</th>\n",
+       "      <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>status</th>\n",
+       "      <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>message</th>\n",
+       "      <td>The solver successfully reached the end of the...</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>success</th>\n",
+       "      <td>True</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "sol                                                      None\n",
+       "t_events                                                   []\n",
+       "nfev                                                      152\n",
+       "njev                                                        0\n",
+       "nlu                                                         0\n",
+       "status                                                      0\n",
+       "message     The solver successfully reached the end of the...\n",
+       "success                                                  True\n",
+       "dtype: object"
+      ]
+     },
+     "execution_count": 109,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# Run simulation\n",
+    "\n",
+    "results, details = run_ode_solver(system, slope_func, t_eval = timesteps)\n",
+    "details\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 110,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "#Plot x and y vs time\n",
+    "results.index /= 60*60*24\n",
+    "plot(results.x, label='x')\n",
+    "plot(results.y, label='y')\n",
+    "\n",
+    "decorate(xlabel='Time (s)',\n",
+    "         ylabel='Position (m)')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 111,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x155f4834710>]"
+      ]
+     },
+     "execution_count": 111,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "#Plot trajectory\n",
+    "plot(results.x, results.y, label='trajectory')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.6.6"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}