{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Homework Guidelines\n",
    "====\n",
    "\n",
    "Homework should always be done as a jupyter notebook, like this one. Problems not following guidelines will lose 25% if the issues are small (like sparsely commented code) or if serious (equations are in plain text, no work shown) the problem will not be graded and receive a 0. Read more about notebooks [here](https://jupyter-notebook.readthedocs.io/en/latest/examples/Notebook/examples_index.html). Here is an [example of a well-constructed notebook](http://nbviewer.ipython.org/github/ipython/ipython/blob/2.x/examples/Notebook/Trapezoid%20Rule.ipynb). The following guidelines for homework apply:\n",
    "\n",
    "* Work must be shown for any credit. Use common sense here. You don't need to write out very easy steps, but you also shouldn't be writing down answers to questions without any work shown. Refer to the homework solutions for examples.\n",
    "* All writing should be done in markdown. Go [here](http://daringfireball.net/projects/markdown/syntax) for a description of how to use Markdown\n",
    "* All symbolic math should be done in a Markdown cell by either enclosing an equation in the '\\$' symbol or use '\\$\\$' for longer equations that should be displayed on their own line. Go [here](http://en.wikibooks.org/wiki/LaTeX/Mathematics) to find out how to enter math, which follow the LaTeX syntax.\n",
    "* Your python code should always be well documented by lines that start with the '#' key.\n",
    "* Plots should always have labeled axes and legends when applicable\n",
    "* If asked to answer symbolically, you should plug in numbers and evaluate/simplify as far as possible while using LaTeX Equations. You should not use Python code for such problems.\n",
    "\n",
    "\n",
    "This cell is an example of Markdown. The raw markdown is shown below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Markdown Example"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Homework Guidelines\n",
    "====\n",
    "\n",
    "Homework should always be done as a jupyter notebook, like this one. Problems not following guidelines will lose 25% if the issues are small (like sparsely commented code) or if serious (equations are in plain text, no work shown) the problem will not be graded and receive a 0. Read more about notebooks [here](https://jupyter-notebook.readthedocs.io/en/latest/examples/Notebook/examples_index.html). Here is an [example of a well-constructed notebook](http://nbviewer.ipython.org/github/ipython/ipython/blob/2.x/examples/Notebook/Trapezoid%20Rule.ipynb). The following guidelines for homework apply:\n",
    "\n",
    "* Work must be shown for any credit. Use common sense here. You don't need to write out very easy steps, but you also shouldn't be writing down answers to questions without any work shown. Refer to the homework solutions for examples.\n",
    "* All writing should be done in markdown. Go [here](http://daringfireball.net/projects/markdown/syntax) for a description of how to use Markdown\n",
    "* All symbolic math should be done in a Markdown cell by either enclosing an equation in the '\\$' symbol or use '\\$\\$' for longer equations that should be displayed on their own line. Go [here](http://en.wikibooks.org/wiki/LaTeX/Mathematics) to find out how to enter math, which follow the LaTeX syntax.\n",
    "* Your python code should always be well documented by lines that start with the '#' key.\n",
    "\n",
    "\n",
    "This cell is an example of Markdown. The raw markdown is shown below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Python Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.5/site-packages/matplotlib/font_manager.py:1288: UserWarning: findfont: Font family ['Humor Sans', 'Comic Sans MS'] not found. Falling back to Bitstream Vera Sans\n",
      "  (prop.get_family(), self.defaultFamily[fontext]))\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAhAAAAFsCAYAAACdCICuAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f73f7ea5710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#This is a python example\n",
    "\n",
    "#First we enable plotting for the notbook. This statement is specific to notebooks\n",
    "#and note a part of python.\n",
    "%matplotlib inline\n",
    "\n",
    "#Now we important the libraries we need.\n",
    "#The `as` keyword allows us to shorten their names when used\n",
    "#below.\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "#make our plot look fun and cartoony\n",
    "plt.xkcd()\n",
    "\n",
    "#The `from` keyword allows us to import only certain items\n",
    "from math import pi\n",
    "\n",
    "#Create a set of points from -2pi to 2pi spaced by 0.01 and calculate the sine of them\n",
    "x = np.arange(-2*pi, 2*pi, 0.01) #notice that np refers to numpy due to the `as` statement.\n",
    "y = np.sin(x)\n",
    "\n",
    "#Make the plot and set x-limit\n",
    "plt.plot(x,y)\n",
    "plt.xlim(-2*pi, 2*pi)\n",
    "\n",
    "#show the plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Equation Example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "This is a small equation: $\\ln x^2$. This equation has sub/super scripts: $P_e(s) = b^i$ This one has a sum: $\\sum_i^N f_i(s)$. This is a big equation:\n",
    "\n",
    "$$\\frac{\\partial V(\\vec{s})}{\\partial s_j}  = \\frac{\\frac{\\partial f(\\vec{s})}{\\partial s_j} - \\frac{f(\\vec{s})}{g_j(s_j)}\\frac{\\partial g_j(s_j)}{\\partial s_j}}{\\prod_i^N g(\\vec{s})}$$"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "This is a small equation: $\\ln x^2$. This equation has sub/super scripts: $P_e(s) = b^i$ This one has a sum: $\\sum_i^N f_i(s)$. This is a big equation:\n",
    "\n",
    "$$\\frac{\\partial V(\\vec{s})}{\\partial s_j}  = \\frac{\\frac{\\partial f(\\vec{s})}{\\partial s_j} - \\frac{f(\\vec{s})}{g_j(s_j)}\\frac{\\partial g_j(s_j)}{\\partial s_j}}{\\prod_i^N g(\\vec{s})}$$"
   ]
  }
 ],
 "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}