index.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Welcome to an example Binder"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook uses `julia`, which we have available as a kernel because we included a `Dockerfile` that installs Julia"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Do some math"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Adding"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1   2   3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Subtracting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1 - 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dividing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "3*2/12"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Do some linear algebra"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Make a matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5x5 Array{Float64,2}:\n",
       " 0.190155  0.0398036  0.717042   0.530508  0.0510607\n",
       " 0.475699  0.710277   0.0863697  0.723128  0.61855  \n",
       " 0.809481  0.349552   0.980045   0.8411    0.396291 \n",
       " 0.21775   0.849673   0.398905   0.294157  0.857497 \n",
       " 0.801216  0.260106   0.747052   0.482291  0.952977 "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M = rand(5,5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute an SVD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(\n",
       "5x5 Array{Float64,2}:\n",
       " -0.256741   0.496101    0.247033  -0.468919    0.638011\n",
       " -0.40771   -0.448952    0.607769   0.435805    0.270008\n",
       " -0.553348   0.471782    0.230678   0.0461864  -0.644889\n",
       " -0.413866  -0.571335   -0.143649  -0.674708   -0.162559\n",
       " -0.538867   0.0576566  -0.704091   0.36445     0.278802,\n",
       "\n",
       "[2.76453,1.02762,0.564152,0.443011,0.154289],\n",
       "5x5 Array{Float64,2}:\n",
       " -0.438613   0.179498  -0.128669   0.678577   -0.546238 \n",
       " -0.356315  -0.58842    0.384574  -0.387041   -0.478648 \n",
       " -0.476862   0.590254  -0.255149  -0.59126    -0.0975365\n",
       " -0.462314   0.189853   0.678432   0.186285    0.505222 \n",
       " -0.489414  -0.486928  -0.556935   0.0737671   0.455804 )"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(U,S,V)=svd(full(M))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Do some calculus!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Get the library"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "using Calculus"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Differentiate `sin`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.87758256188362"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "derivative(sin, 0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And check against `cos`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8775825618903728"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cos(0.5)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 0.3.2",
   "language": "julia",
   "name": "julia-0.3"
  },
  "language_info": {
   "name": "julia",
   "version": "0.3.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}