Section 2.0 - Solving nonlinear equations_Fixed.ipynb

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   "source": [
    "---\n",
    "# Chapter 2: Solutions of Equations in One Variable \n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In many applications, one needs the solution to a **nonlinear equation** for which there is no closed formula.\n",
    "\n",
    "- Suppose you do not have a cube-root function, but only the operations $+$, $-$, $\\times$, $\\div$:  \n",
    "\n",
    "$$\n",
    "x^3 = a\n",
    "$$\n",
    "\n",
    "- Polynomials with degree at least five have no general algebraic solution ([Abel-Ruffini Theorem](http://en.wikipedia.org/wiki/Abel%E2%80%93Ruffini_theorem)): \n",
    "\n",
    "$$\n",
    "x^5 - 5x^4 + 5x^3 + 5x^2 - 6x - 1 = 0\n",
    "$$\n",
    "\n",
    "- Solution of Initial Value Problems (ODE's): Differential equation modelling the growth of the population with an imigration constant term $v$. \n",
    "\n",
    "$N(t)$ denotes the number in the population at time $t$ and $\\lambda$ denotes the constant birth rate of the population. \n",
    "\n",
    "$$\n",
    " \\frac{d N(t)}{dt}=  \\lambda N(t) +v, \\qquad N(t)=N_0e^{\\lambda t}+\\frac{v}{\\lambda}\\left(e^{\\lambda t}-1\\right).\n",
    "$$\n",
    "\n",
    "Suppose $N(0) = 1,000,000$ individuals initially, that $435,000$ individuals immigrate into the community in the first year, and that $N(1) = 1,564,000$ individuals are present at the end of one year. To determine the birth rate of this population, we need to find $\\lambda$ in the equation\n",
    "\n",
    "$$\n",
    "1,564,000=1,000,000 \\,e^{\\lambda }+\\frac{435,000}{\\lambda}\\left(e^{\\lambda}-1\\right).\n",
    "$$\n",
    "\n",
    "- General nonlinear equations:\n",
    "\n",
    "$$\n",
    "10\\cosh(x/4) = x\n",
    "\\qquad \\text{and} \\qquad\n",
    "2\\cosh(x/4) = x\n",
    "$$\n",
    "\n",
    "**Note:** The **hyperbolic sine**, **hyperbolic cosine**, and **hyperbolic tangent** functions are defined as\n",
    "\n",
    "$$\n",
    "\\sinh(t) = \\frac{e^t - e^{-t}}{2},\n",
    "\\qquad\n",
    "\\cosh(t) = \\frac{e^t + e^{-t}}{2},\n",
    "\\qquad\n",
    "\\tanh(t) = \\frac{e^t - e^{-t}}{e^t + e^{-t}}.\n",
    "$$\n",
    "\n",
    "Thus $\\tanh(t) = \\frac{\\sinh(t)}{\\cosh(t)}$, $\\frac{d}{dt} \\sinh(t) = \\cosh(t)$, and $\\frac{d}{dt} \\cosh(t) = \\sinh(t)$."
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem statement\n",
    "\n",
    "Given $f \\in C[a,b]$ (i.e., a *continuous* function $f \\colon [a,b] \\to \\mathbb{R}$) and we want to find $x^* \\in [a, b]$ such that\n",
    "\n",
    "$$\n",
    "f(x^*) = 0.\n",
    "$$\n",
    "\n",
    "The solution $x^*$ is called a **root** or **zero** of the function $f$. There could be exactly one root, many roots, or no roots at all."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Precompiling Roots [f2b01f46-fcfa-551c-844a-d8ac1e96c665]\n",
      "└ @ Base loading.jl:1273\n"
     ]
    }
   ],
   "source": [
    "# Plot the above functions and their roots\n",
    "using PyPlot # Package for plotting\n",
    "using Roots  # Package for finding roots of functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "N (generic function with 1 method)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N(l) = 1000MathConstants.e^l+435(MathConstants.e^l-1)/l"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a, b = 0, 1.1\n",
    "\n",
    "l = range(a, stop=b, length=1000)\n",
    "plot(l, N.(l))\n",
    "hlines(1564, a, b)\n",
    "hlines(0, a, b)\n",
    "vlines(1, 0, N(1), linestyles=\":\")\n",
    "vlines(0.100998, 0, N(0.100998), linestyles=\":\")\n",
    "xlim(a, b);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "search: \u001b[0m\u001b[1mR\u001b[22m\u001b[0m\u001b[1mo\u001b[22m\u001b[0m\u001b[1mo\u001b[22m\u001b[0m\u001b[1mt\u001b[22m\u001b[0m\u001b[1ms\u001b[22m p\u001b[0m\u001b[1mr\u001b[22m\u001b[0m\u001b[1mo\u001b[22mm\u001b[0m\u001b[1mo\u001b[22m\u001b[0m\u001b[1mt\u001b[22me_\u001b[0m\u001b[1ms\u001b[22mhape p\u001b[0m\u001b[1mr\u001b[22m\u001b[0m\u001b[1mo\u001b[22mm\u001b[0m\u001b[1mo\u001b[22m\u001b[0m\u001b[1mt\u001b[22me p\u001b[0m\u001b[1mr\u001b[22m\u001b[0m\u001b[1mo\u001b[22mm\u001b[0m\u001b[1mo\u001b[22m\u001b[0m\u001b[1mt\u001b[22me_type p\u001b[0m\u001b[1mr\u001b[22m\u001b[0m\u001b[1mo\u001b[22mm\u001b[0m\u001b[1mo\u001b[22m\u001b[0m\u001b[1mt\u001b[22me_rule Inse\u001b[0m\u001b[1mr\u001b[22mti\u001b[0m\u001b[1mo\u001b[22mnS\u001b[0m\u001b[1mo\u001b[22mr\u001b[0m\u001b[1mt\u001b[22m\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "No documentation found.\n",
       "\n",
       "No docstring found for module \\texttt{Roots}.\n",
       "\n"
      ],
      "text/markdown": [
       "No documentation found.\n",
       "\n",
       "No docstring found for module `Roots`.\n"
      ],
      "text/plain": [
       "  No documentation found.\n",
       "\n",
       "  No docstring found for module \u001b[36mRoots\u001b[39m."
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?Roots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1-element Array{Float64,1}:\n",
       " 0.10099792968574967"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a, b = 0,1.1\n",
    "r(l)= 1000MathConstants.e^l+435(MathConstants.e^l-1)/l-1564\n",
    "fzeros(r, a, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "p (generic function with 1 method)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p(x) = x^5 - 5x^4 + 5x^3 + 5x^2 - 6x - 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a, b = -1.25, 3.25\n",
    "\n",
    "x = range(a, stop=b, length=1000)\n",
    "plot(x, p.(x))\n",
    "hlines(0, a, b)\n",
    "xlim(a, b);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.2758341933170916"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fzero(p, a, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5-element Array{Float64,1}:\n",
       " -0.954079614623378  \n",
       " -0.15098417327497157\n",
       "  1.2758341933170914 \n",
       "  1.7907343035445205 \n",
       "  3.038495291036736  "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fzeros(p, a, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "f (generic function with 1 method)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(x) = 10cosh(x/4) - x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a, b = -10, 10\n",
    "\n",
    "x = range(a, stop=b, length=1000)\n",
    "plot(x, f.(x))\n",
    "hlines(0, a, b)\n",
    "xlim(a, b);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0-element Array{Float64,1}"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fzeros(f, a, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "g (generic function with 1 method)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g(x) = 2cosh(x/4) - x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Wq61RajQaDYKCgqBWq6FUKhsbzSwt+v0ilu27Am83BfbMGwiVs73UkYiIiIxCo9FApVKZ/Pvb5LdD+/v7IyQkBElJtY9lolAooFQqazys1UsPtEZLLxfkFmnx750XpI5DRERkcUxeXPLz85Geng5/f39Tv5XZc7SX46PHOgEANp9Ix6HLeRInIiIisiwNLi7FxcWIj49HfHw8ACAlJQXx8fFIS0tDcXExXn31VRw5cgRXr17Fvn37MHr0aHh5eWHcuHFGD2+JerTwwFN9QgAAb2w9g1JdpcSJiIiILEeDi8uJEyfQtWtXdO3aFQAwf/58dO3aFf/85z8hl8tx9uxZjBkzBm3atMG0adPQpk0bHDlyBG5ubkYPb6leGxmO5u5OSL9Rhv/suiR1HCIiIotxXxfnmkJTXdwjtX2JOZi+5jgEAdjyQhS6BTeTOhIREVGjWc3FuVS7QW19ML5bc4gi8PqPZ6Ct5AzSREREd8PiIqF/PNQeXq4OSMopxtK9l6WOQ0REZPZYXCTUzMUB792cQXrZvis4nV4ocSIiIiLzxuIisQc7+uPhTv7QG0S88sNplFfwlBEREVFdWFzMwL/GRMDLVYHLOcVYHM27jIiIiOrC4mIGmrk4YOH4jgCAlQeScTL1hsSJiIiIzBOLi5kY1t63+i6jV74/zYHpiIiIasHiYkbeHt0BfkpHXM0vxaLfE6WOQ0REZHZYXMyIysm+ei6jtYev4vAVzmVERET0VywuZmZgG29M7hkMAHjtxzMo1vKUERER0S0sLmborYfaIbCZEzIKyvDBrxekjkNERGQ2WFzMkKvCDotunjLaeCwNf1y4LnEiIiIi88DiYqaiwrwwo18ogKpTRrlFWokTERERSY/FxYz9fURbhPu5Ib9Eh9e3nIGZTeRNRETU5FhczJijvRyfTeoCBzsZ9l7MwYajaVJHIiIikhSLi5kL91Pi9ZHhAID3fz2PyznFEiciIiKSDouLBXg6qgX6tfJCeYUBL2+Og67SIHUkIiIiSbC4WACZTMAnEzvD3dke565p8NkeTsRIRES2icXFQvgqHfHhzYkYv4y5gmMpnIiRiIhsD4uLBRkZ4Y8JkYEQRWDe5nhoyiukjkRERNSkWFwszNuPdECwhzOuFZbhza1neYs0ERHZFBYXC+OqsMPnk7rATibglzNZ+P5EutSRiIiImgyLiwXqGtwMr45oCwB4e0cCkq4XSZyIiIioabC4WKi/9W+J/q2rbpGe/V0cyiv0UkciIiIyORYXCyWTCfh0Yhd4uSqQeL0I//rlvNSRiIiITI7FxYJ5uynw2eNdIAjAhqNp2Hk2S+pIREREJsXiYuH6tfbCCwPDAACvbzmD9BulEiciIiIyHRYXKzBvWBt0DXZHUXklXtoUhwo9pwQgIiLrxOJiBezlMvx3Ule4OdohLq0Qn+zmlABERGSdWFysRJCHMz56tBMAYHnMFey9eF3iRERERMbH4mJFHuzoj2l9QgAA8zaf5vUuRERkdVhcrMybD7VD5yB3qMsqMOu7U9BWcnwXIiKyHiwuVkZhJ8cXU7rC3dkeZzLUeP+XC1JHIiIiMhoWFysU2MwZix/vAgD4NjYVP8VfkzgRERGRcbC4WKnBbX0wZ0grAMCCrWdxOYfzGRERkeVjcbFiLw9tg6gwT5Tq9Hh+/SmUaCuljkRERHRfWFysmFwm4PNJXeHjpsDlnGK8te0sRFGUOhYREVGjsbhYOW83BZZO6Qa5TMD2+EysP5omdSQiIqJGY3GxAT1DPfD6yLYAgPd+TsDJ1AKJExERETUOi4uNmNm/JUZF+KFCL+KF9SeRoymXOhIREVGDsbjYCEEQ8PGEzmjt44qcIi1e2HAKukpOxkhERJaFxcWGuCrssPKp7nBztMPJ1AK890uC1JGIiIgahMXFxoR6ueDzSV0gCMD62DRsPs6LdYmIyHKwuNigIeG+mD+0DQDgH9sTEJ9eKHEiIiKie8PiYqNmDW6F4e19odMb8Py3J5FbpJU6EhER0V2xuNgomUzAJxM7I8zbBdmacszacAoVel6sS0RE5o3FxYa5OdpXXayrsMOxqzfwr1/OSx2JiIioXiwuNi7M27V6Jul1R1Kx4WiqxImIiIjqxuJCGNreF38fUTWy7ts/JeDwlTyJExEREdWOxYUAAC8OCsOYLgGoNIh4Yf0pXM0rkToSERHRHVhcCEDVyLofPdoJnYPcoS6rwIxvjkNTXiF1LCIiohpYXKiao70cq6ZGwl/liCu5JZjzXRwqeacRERGZERYXqsFH6YhVT3WHo70MMZdy8e+dF6WOREREVI3Fhe4Q0VyFTydW3Wn09aEUbDrGaQGIiMg8sLhQrR7s6I95N6cF+L/t5xCbnC9xIiIiIhYXqsdLD7TCw538UWkQ8fz6k0jOLZY6EhER2TgWF6qTIAj4+LHO6BzkjsLSCjy99jjyizmnERERSYfFherl5CDH6qe6I8jDCan5pZi57gTKK/RSxyIiIhvF4kJ35e2mwJrpPaB0tMOptEK88v1pGAyi1LGIiMgGsbjQPWnl44YVU7vDXi7g17NZ+GgXb5MmIqKmx+JC96xPmCcWPdYJALAiJpkTMhIRUZNrcHHZv38/Ro8ejYCAAAiCgO3bt9f4uSiKeOeddxAQEAAnJycMGjQICQkJRgtM0hrXNbD6Nul//pSAPxNzJE5ERES2pMHFpaSkBJ07d8bSpUtr/fmiRYvw6aefYunSpTh+/Dj8/PwwbNgwFBUV3XdYMg8vPdAKj3YLhN4gYvaGUzifqZE6EhER2QhBFMVGX2UpCAK2bduGsWPHAqg62hIQEICXX34Zr7/+OgBAq9XC19cXH330EZ577rk7XkOr1UKr/d8tthqNBkFBQVCr1VAqlY2NRiamqzRg+ppjOHwlH35KR2x9MQoB7k5SxyIiIoloNBqoVCqTf38b9RqXlJQUZGdnY/jw4dXPKRQKDBw4EIcPH651nYULF0KlUlU/goKCjBmJTMTBToYvn4xEax9XZGvK8dTXx1BYqpM6FhERWTmjFpfs7GwAgK+vb43nfX19q392uwULFkCtVlc/0tPTjRmJTEjlZI+1z/SEn9IRl3OKMeObEyjTcYwXIiIyHZPcVSQIQo0/i6J4x3O3KBQKKJXKGg+yHM3dnfDNMz2hdLTDydQCzNl4CpV6g9SxiIjIShm1uPj5+QHAHUdXcnJy7jgKQ9ajrZ8bVk/rAYWdDHsu5OCtbedwH5dOERER1cmoxSU0NBR+fn6Ijo6ufk6n0yEmJgZRUVHGfCsyMz1DPbBkclfIBGDziXR8Gn1J6khERGSFGlxciouLER8fj/j4eABVF+TGx8cjLS0NgiDg5Zdfxr///W9s27YN586dw/Tp0+Hs7IwpU6YYPTyZl+Ed/PDBuI4AgCV7L+PbI1clzUNERNbHrqErnDhxAoMHD67+8/z58wEA06ZNw9q1a/Haa6+hrKwML774IgoKCtCrVy/s3r0bbm5uxktNZmtyz2DkaLRYvOcS/rkjAZ6uCjzY0V/qWEREZCXuaxwXU2iq+8DJdERRxP9tP4cNR9PgIJdh7TM9EBXmJXUsIiIyIYscx4UIqLqr7L0xERjZwQ86vQEzvzmB0+mFUsciIiIrwOJCJiGXCfhsUhdEhXmiRKfHtDXHcOk6p30gIqL7w+JCJuNoL8fKp7qjS5A7Cksr8OTqo0jLL5U6FhERWTAWFzIpV4Ud1j7dA+F+bsgp0mLK6lhkq8uljkVERBaKxYVMzt3ZAetm9ESIpzMyCsrw5FdHcaOE8xoREVHDsbhQk/Bxc8T6Gb3gr6qa12ja18egKa+QOhYREVkYFhdqMkEezvh2Ri94uDjg7DU1nl3LSRmJiKhhWFyoSbXyccW6Z3rCTWGHY1dv4IUNJ6GtZHkhIqJ7w+JCTS6iuQpfP90DjvYy7EvMxezv4lDBGaWJiOgesLiQJHq08MDqp3rAwU6G6PPXMXdTHCpZXoiI6C5YXEgy/Vp7YeXUSDjIZdh5Nhvzvj/N8kJERPVicSFJDWrrg2VPdIO9XMDPpzPx2o9noDeY1fRZRERkRlhcSHJD2/tiyeRukMsEbI27hje2nIGB5YWIiGrB4kJmYWSEHz6f1AUyAfjhZAbe2n6O5YWIiO7A4kJm4+FOAVj8eBcIArDxWBre+TkBosjyQkRE/8PiQmZlTJfm+PixzhAEYN2RVPzrlwssL0REVI3FhczOY5GB+HB8RwDA14dS8O7P51leiIgIAIsLmanHewRj4c3ysvbwVfzjJ17zQkRELC5kxib3DMaixzpBEID1sWl4c9tZlhciIhvH4kJmbWL3IHwyoTNkArDpeDpe28JxXoiIbBmLC5m98d0CsfjxLpDLBPx4MgOv/sARdomIbBWLC1mEMV2a47+TusJOJmBb3DVOD0BEZKNYXMhiPNTJH1/8ZXqAORs5qzQRka1hcSGLMqKDH5Y/WTUx42/nsvHihlPQVuqljkVERE2ExYUszgPtfLHyqUg42MkQff46nv3mBEp1lVLHIiKiJsDiQhZpUFsfrJ3eA84OchxIysPUr45BXVYhdSwiIjIxFheyWFGtvLDh2V5QOdnjZGoBJq+MRV6xVupYRERkQiwuZNG6BjfDpr/1hperAuezNJi44ggyC8ukjkVERCbC4kIWr52/Ej883wfN3Z2QnFuCCcuPICWvROpYRERkAiwuZBVCvVzw/fN90NLLBdcKyzBh+RFczNZIHYuIiIyMxYWsRnN3J2x+rg/a+SuRV6zF4ytiEZdWIHUsIiIyIhYXsirebgpsmtkb3YLdoS6rwBOrjyLmUq7UsYiIyEhYXMjqqJzt8e2MXujf2gulOj1mrD2O7XHXpI5FRERGwOJCVslFYYevpvXAI50DUGkQ8fLmeKw+kCx1LCIiuk8sLmS1HOxk+OzxLnimbygA4P1fL2DhzgswGESJkxERUWOxuJBVk8kE/OPhdnhjVDgAYMX+ZLz6w2lOzkhEZKFYXMjqCYKA5weG4T8TOkMuE7A17hpmruP8RkRElojFhWzGY5GBWPVUJBztZdiXmIvJq47iRolO6lhERNQALC5kU4aE++K7mb3h7myP0+mFeOzLw0i/USp1LCIiukcsLmRzugU3w4/P90GAyhHJeSUYt+wQTqcXSh2LiIjuAYsL2aRWPm7Y+mLfm6Ps6vD4yiPYnZAtdSwiIroLFheyWX4qR/zwfB8MbOON8goDnlt/EmsOpUgdi4iI6sHiQjbNVWGHr6Z1x+SewRBF4N2fz+PdnxOg51gvRERmicWFbJ6dXIZ/j4uoHutlzaGreGH9SZTp9BInIyKi27G4EOF/Y70smdwVDnYy7D5/HZNWHkFukVbqaERE9BcsLkR/MbpzADY826vqdukMNcYtO4TLOUVSxyIioptYXIhu06OFB7a+EIUQT2dkFJRh3LLD2H8pV+pYREQEFheiWrX0dsXWF6IQGdIMReWVeHrtcXxz+CpEkRftEhFJicWFqA6ergp8N7MXxndrDr1BxNs7EvCPn85xgkYiIgmxuBDVQ2EnxycTOuONUeEQBGB9bBqmrzmGwlLOcUREJAUWF6K7uHXH0cqp3eHsIMehy/kYt+wwknOLpY5GRGRzWFyI7tGw9r7Y8kIUmrs7ISWvBGO/OISDSXlSxyIisiksLkQN0M5fie2z+iIypBk05ZWYtuYYvj1yVepYREQ2g8WFqIG83RTY8GwvjO9addHuP35KwIKtZ6Gt5Ei7RESmxuJC1AiO9nJ8MrEzXh9ZddHuxmNpmLwyFjmacqmjERFZNRYXokYSBAEvDArD19N7QOloh1NphXh4yUGcTC2QOhoRkdVicSG6T4Pb+mDH7H5o4+uKnCItJq08go3H0qSORURklVhciIyghZcLtr7YFyM7+KFCL2LB1rN4c9tZ6Co5WB0RkTGxuBAZiavCDl8+2Q1/H9EWggB8dzQNk1fxuhciImNicSEyIkEQMGtwK3w9rQfcHO1wMrUAo5cexKk0XvdCRGQMRi8u77zzDgRBqPHw8/Mz9tsQmbXB4VXXvbTyccV1jRaTVsTi29hUTtJIRHSfTHLEpUOHDsjKyqp+nD171hRvQ2TWQr1csH1WX4zo4Aud3oB/bD/UsBTXAAAgAElEQVSH+d+fRqmuUupoREQWyyTFxc7ODn5+ftUPb29vU7wNkdlzVdhh+ZORePPBcMhlArbFXcPYLw7hCuc5IiJqFJMUl6SkJAQEBCA0NBSTJk1CcnJynctqtVpoNJoaDyJrIggC/jYgDN892wvebgpcul6MR5YcxK9nsqSORkRkcYxeXHr16oV169Zh165dWLVqFbKzsxEVFYX8/Pxal1+4cCFUKlX1IygoyNiRiMxCr5ae+PWlfugV6oESnR6zvjuFd39O4C3TREQNIIgmvlqwpKQEYWFheO211zB//vw7fq7VaqHVaqv/rNFoEBQUBLVaDaVSacpoRJKo1Bvwn92XsDzmCgCgW7A7vniiG/xVThInIyJqPI1GA5VKZfLvb5PfDu3i4oKOHTsiKSmp1p8rFAoolcoaDyJrZieX4Y1R4Vj1VHe43Zwq4KH/HsTBpDypoxERmT2TFxetVosLFy7A39/f1G9FZFGGtffFL3P6ob2/EjdKdJj69VF8ujsRlXqeOiIiqovRi8urr76KmJgYpKSk4OjRo3jssceg0Wgwbdo0Y78VkcUL8XTB1hejMKlHEEQR+O/ey5iy6iiy1GVSRyMiMktGLy4ZGRmYPHky2rZti/Hjx8PBwQGxsbEICQkx9lsRWQVHezk+fLQTPp/UBS4Ochy7egMPfn4Aey9elzoaEZHZMfnFuQ3VVBf3EJmjq3klmL3xFM5dqxoW4Nl+oXhtZDgc7Dg7BxGZN6u5OJeI7l0LLxdseSEK06NaAABWH0zBhOWHkZZfKm0wIiIzweJCZGYUdnK880gHrJwaCZWTPU5nqPHQfw/glzOZUkcjIpIciwuRmRrewQ875/ZHZEgzFGkrMfu7OCzYehZlOr3U0YiIJMPiQmTGmrs7YdPfemPW4DAIArDxWBoeWnIA566ppY5GRCQJFhciM2cvl+HvI8Lx7TO94KtUIDm3BOOWHcLymCvQG8zq2noiIpNjcSGyEP1ae+H3uQMwsoMfKvQiPvztIp5YHYvMQo75QkS2g8WFyII0c3HAl092w6JHO8HZQY7Y5BsY+dl+/HyaF+4SkW1gcSGyMIIgYGKPIPz6Un90DnKHprwSczbGYf738Sgqr5A6HhGRSbG4EFmoUC8X/Ph8H8wZ0goyAdh66hoe/O8BnEy9IXU0IiKTYXEhsmD2chleGd4Wm5/rg8BmTki/UYYJy4/gP7sSoavkZI1EZH1YXIisQI8WHtg5tz/GdW0Ogwgs/fMyxnxxCBeyNFJHIyIyKhYXIiuhdLTH4se74Isp3dDM2R4XsjR4ZOlBfPHnZVTqefSFiKwDiwuRlXmokz92zxuIYe19UaEX8fGuRDy6/Agu5xRLHY2I6L6xuBBZIW83BVZOjcSnEzvDzdEOp9ML8dB/D+CrgykwcNA6IrJgLC5EVkoQBIzvFojd8wagf2svaCsN+Ncv5zF5VSzSb3C2aSKyTCwuRFbOX+WEdc/0xAfjIuDsIMfRlKpB6zYcTeXRFyKyOCwuRDZAEAQ80SsEv88dgJ4tPFCi0+OtbecwZXUsUvNLpI5HRHTPWFyIbEiwpzM2/a03/vFwezjayxCbfAMjPtuP1QeSOWEjEVkEFhciGyOTCZjRLxS7Xx6IqDBPlFcY8P6vFzD+y8NIzC6SOh4RUb1YXIhsVLCnMzY82wsfju8IN0XVnUcPLzmAz/Zc4qi7RGS2WFyIbJggCJjUMxjR8wdiaDsfVOhFfLYnCaOXHMTp9EKp4xER3YHFhYjgp3LEqqe6Y8nkrvB0cUDi9SKMW3YI/955AWU6vdTxiIiqsbgQEYCqoy+jOwcgev5AjOkSAIMIrNyfjGGLY/BnYo7U8YiIALC4ENFtPFwc8PmkrvhqWnc0d3dCRkEZnl5zHLM2nMJ1TbnU8YjIxrG4EFGtHmjni93zBmBm/1DIZQJ+PZuFoZ/EYN2Rq7x1mogkI4iiaFafQBqNBiqVCmq1GkqlUuo4RAQgIVONN7edq75gt3OgCv8e3xEdAlQSJyMic9FU39884kJEd9UhQIWtL0ThX2M6VN06naHGI0sP4f1fzqNEWyl1PCKyISwuRHRP5DIBU/u0wJ5XBuKhTv7QG0SsPpiCYZ/GYFdCNszs4C0RWSkWFyJqEF+lI76Y0g1rnu6BwGZOyFSX47lvT2L6muNIyeO8R0RkWiwuRNQog9v6IHreQMwaHAYHuQwxl3IxYvF+LPr9Ikp1PH1ERKbB4kJEjebkIMffR4Rj17wBGNTWGzq9Acv2XcEDn8Tg1zNZPH1EZENuFGub5H1YXIjovoV6uWDN9B5Y9VR3BDZzQpa6HLO+O4UnVh9F0nVO3Ehk7cor9JizMa5J3ovFhYiMQhAEDGvviz3zB+Lloa2hsJPh8JV8jPr8AN7/5TyKyiukjkhEJlCpN2DOxjiczlA3yfuxuBCRUTnay/Hy0DbYM38ghrf3ReXNu4+GfBKD70+kw8DB64ishiiK+OeOBESfvw57u6apFCwuRGQSQR7OWPlUd6x9ugdCvVyQW6TFaz+eweilBxGbnC91PCIygiV7L+O7o2kQBGDR+I5N8p4cOZeITE5bqce6w6n4794kFJVX3XE0soMfFjwYjhBPF4nTEVFjbD6ehte3nAUA/GtMB4zp4NEk398sLkTUZPKLtVi85xK+O5oGgwg4yGWY3rcFZg9pBaWjvdTxiOgeRZ+/jufXn4TeIGLW4DD8fUR4k31/s7gQUZNLzC7C+7+ex4GkPACAp4sD5g1rg0k9gmAn5xlsInN2ICkXM9aegE5vwGORgfj4sU4QBIHFhcWFyLqJooh9ibn416/nkZxbNeJuG19XvPlgOwxs4w1BECROSES3O5qcj2lrjqG8woBREX5YMrlr9S8bLC4sLkQ2oUJvwIbYVHz2RxIKS6tumY4K88Qbo8LRKdBd4nREdEtcWgGeXH0UJTo9Brf1xoqp3eHwlzuJWFxYXIhsSmGpDkv3Xsa6I6nQ6Q0AgIc6+ePvw9uihRcv4CWS0rlrakxZFQtNeSX6tvLEV9N6wNFeXmMZFhcWFyKblFFQik+jL2Fb3DWIImAnEzClVzDmDGkNbzeF1PGIbM65a2pM/eooCkor0D2kGdbN6AlnB7s7lmNxYXEhsmkXsjT46PeL2JeYCwBwdpBjZv+WmDmgJVwVd35oEpHxxaUVYNrXx6Apr0TnIHd8O6NnnXcAsriwuBARgMNX8vDRbxerhxP3cnXAnCGtMalnEBR28rusTUSNdfzqDTy95jiKtZXoHtIMa57uAbd6hi1gcWFxIaKbRFHEb+ey8fGuRKTkVd2B1NzdCXOGtMKjkYGw5y3UREZ1+HIeZnxzAmUVevRp6YnV07rD5S5HOllcWFyI6DYVegM2HU/H0r1JuK7RAgBCPJ3x0pDWGNu1OeQy3kJNdL/2XryOF9afgrbSgAFtvLFyauQdF+LWhsWFxYWI6lBeocf62FQsj7mCvGIdAKCltwvmDW2Dhzr6Q8YCQ9Qo359Ix4KtZ6E3iBjazgdLp3S7p9ICsLiwuBDRXZXqKvHN4VSs2H+legyYcD83vDy0DUZ08OUgdkT3SBRFLNt3BR/vSgQAPNotEB8+2rFBp2FZXFhciOgeFZVXYM2hq1h1ILl6EseI5krMfaANhrbzYYEhqofeIOLdnxOw7kgqAOCFQWF4bUTbBv+7YXFhcSGiBlKXVmDVgWSsOZSCEp0eQNURmDlDWmNkhB+vgSG6TZlOj3mb4/F7QjYEAfjnw+3xdN/QRr0WiwuLCxE10o0SHVYdSMa6w1erC0yYtwtmDW6FRzoHcCJHIgBZ6jLMXHcC565pYC8XsPjxLni4U0CjX4/FhcWFiO5TYakOaw9fxdcHU6C5eQop2MMZLw4Kw/hugTXmWSGyJfHphZi57gRyi7TwcHHAiqmR6NHC475ek8WFxYWIjKSovALfxqZi9YEU3CipugvJX+WI5weGYWL3IDg5cCA7sh0/xV/Daz+egbbSgLa+blg9rTuCPJzv+3VZXFhciMjISnWV2HgsHStiriCnqGocGA8XB0ztHYKn+oTA05VzIZH1qtQb8PGuRKzYnwwAGBLug88ndal3NNyGYHFhcSEiEymv0OOHkxlYEXMFGQVlAABHexkeiwzEs/1acjZqsjo5mnLM3hiHYyk3AAB/G9ASr48MN+oF6ywuLC5EZGKVegN+O5eNlfuTcfZa1VxIMgEYGeGHvw0IQ5cgd4kTEt2/2OR8zP4uDnnFWrgq7LDosU54sKO/0d+HxYXFhYiaiCiKOJKcjxUxyYi5lFv9fM9QDzw3oCUGt/XhaLxkcQwGESv2J+M/uxOhN4ho4+uKL5+MRJi3q0nej8WFxYWIJHAxW4OV+5OxIz4TlYaqj8dQLxdM6xOCRyMDjXY9AJEpZRaW4ZXvT+NIcj4AYFzX5vhgXAScHeqfKPF+sLiwuBCRhLLUZVhz6Co2Hk1DkbbqVmpXhR0eiwzEtKgWCOV1MGSmfj2ThQVbz0BTXgknezneHt0ej/cIMvkI0iwuLC5EZAZKtJXYeioDaw5fRXJuSfXzg9t6Y3rfUPRv5cXTSGQWNOUVeHfHeWw5lQEA6ByowmeTujZZybb44rJs2TJ8/PHHyMrKQocOHfDZZ5+hf//+d12PxYWIzJHBIOLg5TysPXwVey/mVD/f0tsFU3uHYHzXQKiceRqJpLHn/HW8tf0srmu0kAnAi4NaYe7Q1g2aJPF+WXRx2bx5M6ZOnYply5ahb9++WLFiBVavXo3z588jODi43nVZXIjI3KXklWDdkav44UQGim+eRnK0l+GhjgGY0isY3YLdObEjNYn8Yi3e/fk8dpzOBFB1Pdaixzrd9yi4jWHRxaVXr17o1q0bvvzyy+rn2rVrh7Fjx2LhwoX1rntrwzMzM1lciMislWgr8dOZ6/j+ZCaS/nIaqY2PCyZ0C8Dojr5wczTdxZBku0RRxC9nr+Oj6CsoKK2ATACm9w7CrIEt4GgvzUjQGo0GAQEBlldcdDodnJ2d8cMPP2DcuHHVz8+dOxfx8fGIiYmpsbxWq4VWq63+s0ajQVBQkDEjERGZnENAONy6jIRzeH/I7KtG4DXoylF6cT+K4n+HLuuSxAnJWth7t4DHsOfhGBQBANDlpCD/t8+hy74scbIqpi4uRv9VIC8vD3q9Hr6+vjWe9/X1RXZ29h3LL1y4EO+++66xYxARNSld5kXkZ15EwR+r4BIxBK5dRsLBKwSunYbDtdNw6PJSUXJ2L0rO/wl98Q2p45IFEhQucO/3BNy6PQRBJoehohzqw5uhObYNMFRKHa/JmOwY5u3nd0VRrPWc74IFCzB//vzqP9864sJTRURkyURRRFyGBj+czMSuC7mAVwgcBj8NzyFPo0/LZhjbyQ9D2npJdlifLEeF3oAf47KwLOYqbpRWAACGt/PG34eFIeC9kQDWSBvwplunikzN6MXFy8sLcrn8jqMrOTk5dxyFAQCFQgGF4s6JzVxcXODiwnESiMhy9Q93Rf/wAGjKK7DzTBa2nMrA8asFOHSl6uHmaIeHO/nj0W6BiAxpxgt6qQZRFLHzbDY+3nURV/NLAQBh3i5495EI9GvtJXG6O+n1+iZ5H5NdnBsZGYlly5ZVP9e+fXuMGTPmni/O5V1FRGSNruaVYOupDGw5dQ3XCsuqnw/ycMLoTgF4uFMA2vm7scTYMFEUcfhKPhbtSsTp9EIAgJerA+Y+0BqTegY36S3ODWHRdxXduh16+fLl6NOnD1auXIlVq1YhISEBISEh9a7L4kJEtsBgEBGbko8fT2bgt7PZKKv432+rYd4uGN05AKM7B5hsXhkyP6IoYt+lXCz5Iwmn0qoKi7ODHDP7t8TMAS3hqjDvO9QsurgAVQPQLVq0CFlZWYiIiMDixYsxYMCAu67H4kJEtqZUV4k/LuTglzOZ+DMxF7pKQ/XP2vsrMbpzAEZF+KEFpxmwSqIoYs+FHCzZm4QzGVWzlDvYyTC5RxBmDWkFHzdHiRPeG4svLo3F4kJEtkxTXoHohOv4+UwmDiblVU/0CABtfd0wvIMvhrf3Q0RzJU8nWbgynR5b4zKw5tBVXM4pBgA42cvxRK9g/G1AS/goLaOw3MLiwuJCRDauoESH3xOy8cuZTMQm34D+LyXGX+WI4e19MbyDH3qGepjtdQ90p8zCMqw7koqNx9KgLqu6S8jFQY6nolrg2X6h8HS984YVS8DiwuJCRFRNXVqBvYnXsTvhOmIu5aJU979rYpSOdhjQxhsDbz4s7Td1W1CpN2BfYi6+P5GOPy7mVJfQIA8nTI8KxYTugVA6WvZcVywuLC5ERLUqr9Dj0OU87E64jj0XriO/RFfj5+38ldUlJjKkGRzseDRGKldyi/HDiQxsOZWB3KL/jRLfp6Unnu7bAg+084XcSmYXZ3FhcSEiuiu9QURcWgH2X8rFvku51Rd33uLiIEefME/0bln1aOevtJovSnOVfqMUv53Lwq9nsnD6L/vD08UB47o2x8QeQWjj6yZhQtNgcWFxISJqsLxiLQ4m5SHmUi72X8q942iM0tEOPUM90bulB4uMEaXklWDP+ev45WxW9dgrACATgEFtfTCxeyCGhPta9dEvFhcWFyKi+2IwiEjI1ODwlTzEJufj+NUCFGtrzmnj5miHrsHN0DXIHV2C3dE1yB3uzg4SJbYc5RV6xCbnY19iLvYl5lSPbAtUlZVeoZ54sJM/Rnbwg7ebZV5s21AsLiwuRERGVak3ICFTg9jk/DqLDACEerlUF5kOAUqE+ynhYuaDn5laeYUe8emFOJp8A8eu5uNkagHKK/433o69XECPFh4YFeGHERF+FjP2ijGxuLC4EBGZVKXegAtZRYhPL0BcWiHi0guRkldyx3KCAIR4OKOdvxLt/JVo769EuL8bAlROkFnhaSaDQURKfgnOXVPjbIYapzMKcTpdDZ3eUGM5P6UjBod7Y1BbH/Rt5WX2I9uaGosLiwsRUZMrKNEhPqMQ8WmFOJ1RiAtZGlzXaGtd1slejhZeLmjp5YKW3i4I9XJBS29XBHs4o5mzvdkPkCeKInKKtLiSU4wrucW4kluC81kanM/U1HokyttNgV6hHlWPlp5o7eNq9tvYlFhcWFyIiMxCfrEWF7KKcCFLgwtZGpzP0uByTnGNUX1v52gvQ4DKCQHuTghwd0SAuxP8VY7wcFHAw8Wh+qF0tDPJl78oitCUV0JdWoHc4nJkFpYjS11W439T8kpqLSi38rfzV6JjcxU6NlehRwsPhHg6s6jUg8WFxYWIyGxV6A3IKChDcm4xUvJKcCW3BCl5xUjOLUFOUe1HaGpjJxPQzMUBbgo7OCvkcLa3g5ODHM4Ocjg5yGEnEyATBAgCIAgCBFSduqqoFKGt1KO8wgBtpR7aSgPKKvRQl1VAXVqBwrKKGiMN10UuExDs4YwwbxeEebuilY8rOgaq0MrbFXYcjbhBmur727ZPyBERUaPYy2UI9ao6PXQ7baUe2epyXCu8eYSjsAyZ6jJkqctRUKJDfokOBSU6lOj0qDSIyC3S1hiczZic7OXwcHFAgLsj/FVO8Hd3RICq6uhPS28XBHu4WPUtytaIxYWIiIxKYSdHiKcLQjzrn826vEKPGyU63CjRoVhbiTKdHqU6PUp1lSirqPr/eoMIURQhioBBBAyiCBGAg1yAwk4OR3sZFHZyKG7+r8rJHs1c7OHu5AB3Z3s42subZqOpybC4EBGRJBzt5TevgXGSOgpZEB4fIyIiIovB4kJEREQWg8WFiIiILAaLCxEREVkMFhciIiKyGCwuREREZDFYXIiIiMhisLgQERGRxWBxISIiIovB4kJEREQWg8WFiIiILAaLCxEREVkMFhciIiKyGGY3O7QoigAAjUYjcRIiIiK6V7e+t299j5uK2RWX/Px8AEBQUJDESYiIiKih8vPzoVKpTPb6ZldcPDw8AABpaWkm3XBzo9FoEBQUhPT0dCiVSqnjNBluN7fbFnC7ud22QK1WIzg4uPp73FTMrrjIZFWX3ahUKpva4bcolUputw3hdtsWbrdtsdXtvvU9brLXN+mrExERERkRiwsRERFZDPk777zzjtQhbieXyzFo0CDY2ZndmSyT4nZzu20Bt5vbbQu43abbbkE09X1LREREREbCU0VERERkMVhciIiIyGKwuBAREZHFYHEhIiIii8HiQkRERBZDkuLywQcfICoqCs7OznB3d691mbS0NIwePRouLi7w8vLCSy+9BJ1OV+/rFhQUYOrUqVCpVFCpVJg6dSoKCwtNsQn3bd++fRAEodbH8ePH61xv0KBBdyw/adKkJkx+/1q0aHHHNrzxxhv1riOKIt555x0EBATAyckJgwYNQkJCQhMlvn9Xr17FjBkzEBoaCicnJ4SFheHtt9++63/Tlri/ly1bhtDQUDg6OiIyMhIHDhyod/ktW7agffv2UCgUaN++PbZt29ZESY1j4cKF6NGjB9zc3ODj44OxY8ciMTGx3nXWrl1b67/98vLyJkptHO+8884d2+Dn51fvOjExMYiMjISjoyNatmyJ5cuXN1Fa46ntM0wQBMyaNavW5S11f+/fvx+jR49GQEAABEHA9u3ba/y8sZ/LDf2MuJ0kxUWn02HChAl44YUXav25Xq/HQw89hJKSEhw8eBCbNm3Cli1b8Morr9T7ulOmTEF8fDx+//13/P7774iPj8fUqVNNsQn3LSoqCllZWTUezz77LFq0aIHu3bvXu+7MmTNrrLdixYomSm087733Xo1t+L//+796l1+0aBE+/fRTLF26FMePH4efnx+GDRuGoqKiJkp8fy5evAiDwYAVK1YgISEBixcvxvLly/Hmm2/edV1L2t+bN2/Gyy+/jLfeegtxcXHo378/Ro0ahbS0tFqXP3LkCB5//HFMnToVp0+fxtSpUzFx4kQcPXq0iZM3XkxMDGbNmoXY2FhER0ejsrISw4cPR0lJSb3rKZXKOz4DHB0dmyi18XTo0KHGNpw9e7bOZVNSUvDggw+if//+iIuLw5tvvomXXnoJW7ZsacLE9+/48eM1tjk6OhoAMGHChDrXscT9XVJSgs6dO2Pp0qW1/rwxn8sN/YyolSihNWvWiCqV6o7nd+7cKcpkMvHatWvVz23cuFFUKBSiWq2u9bXOnz8vAhBjY2Ornzty5IgIQLx48aLxwxuZTqcTfXx8xPfee6/e5QYOHCjOnTu3iVKZRkhIiLh48eJ7Xt5gMIh+fn7ihx9+WP1ceXm5qFKpxOXLl5siYpNYtGiRGBoaWu8ylra/e/bsKT7//PM1ngsPDxffeOONWpefOHGiOHLkyBrPjRgxQpw0aZLJMppaTk6OCECMiYmpc5m6Pvsszdtvvy127tz5npd/7bXXxPDw8BrPPffcc2Lv3r2NHa1JzZ07VwwLCxMNBkOtP7eG/Q1A3LZtW/WfG/u53NDPiNqY5TUuR44cQUREBAICAqqfGzFiBLRaLU6ePFnnOiqVCr169ap+rnfv3lCpVDh8+LDJM9+vHTt2IC8vD9OnT7/rshs2bICXlxc6dOiAV1991WKOOvzVRx99BE9PT3Tp0gUffPBBvadMUlJSkJ2djeHDh1c/p1AoMHDgQIvYt3VRq9X3NIuqpexvnU6HkydP1thPADB8+PA699ORI0fuWH7EiBEWv18B3HXfFhcXIyQkBIGBgXj44YcRFxfXFPGMLikpCQEBAQgNDcWkSZOQnJxc57J17e8TJ06goqLC1FFNQqfTYf369XjmmWcgCEKdy1nL/r6lMZ/LjfmMqI1ZjkWcnZ0NX1/fGs81a9YMDg4OyM7OrnMdHx+fO5738fGpcx1z8tVXX2HEiBEICgqqd7knnngCoaGh8PPzw7lz57BgwQKcPn26+lClJZg7dy66deuGZs2a4dixY1iwYAFSUlKwevXqWpe/tf9u/2/C19cXqampJs9rCleuXMGSJUvwySef1LucJe3vvLw86PX6WvdTff9uG7K8uRNFEfPnz0e/fv0QERFR53Lh4eFYu3YtOnbsCI1Gg88//xx9+/bF6dOn0bp16yZMfH969eqFdevWoU2bNrh+/Tref/99REVFISEhAZ6enncsX9f+rqysRF5eHvz9/ZsqutFs374dhYWF9f7SaS37+68a87ncmM+I2hjtiEttF2nd/jhx4sQ9v15tzVUUxXobbWPWMbbG/D1kZGRg165dmDFjxl1ff+bMmRg6dCgiIiIwadIk/Pjjj9izZw9OnTplqk26Jw3Z7nnz5mHgwIHo1KkTnn32WSxfvhxfffUV8vPz632P2/djU+/b2jRmf2dmZmLkyJGYMGECnn322Xpf31z3d30aup/Mcb821uzZs3HmzBls3Lix3uV69+6NJ598Ep07d0b//v3x/fffo02bNliyZEkTJTWOUaNG4dFHH0XHjh0xdOhQ/PrrrwCAb775ps51atvftT1vKb766iuMGjWqxhmC21nL/q5NY/793u+/eaMdcZk9e/Zd73Zo0aLFPb2Wn5/fHRfnFRQUoKKi4o6m9td1rl+/fsfzubm5da5jCo35e1izZg08PT3xyCOPNPj9unXrBnt7eyQlJaFbt24NXt9Y7mf/9+7dGwBw+fLlWn9Lu3WXQnZ2do3fyHJycpp039amodudmZmJwYMHo0+fPli5cmWD389c9ndtvLy8IJfL7/jNqb795Ofn16DlzdmcOXOwY8cO7N+/H4GBgQ1aVyaToUePHkhKSjJRuqbh4uKCjh071rkdde1vOzu7Wv/tm7vU1FTs2bMHW7dubdB61rC/G/O53JjPiNoYrbh4eXnBy8vLKK/Vp08ffPDBB8jKyqr+C9m9ezcUCgUiIyPrXEetVuPYsWPo2bMnAODo0aNQq9WIiooySq570dC/B1EUsWbNGjz11FOwt7dv8PslJCSgoqJC8kOs97P/b53rrWsbbp0qiY6ORteuXQFUndUCc6IAAAROSURBVCuNiYnBRx991LjARtKQ7b527RoGDx6MyMhIrFmzBjJZww94msv+ro2DgwMiIyMRHR2NcePGVT8fHR2NMWPG1LpOnz59EB0djXnz5lU/t3v37ib9N3u/RFHEnDlzsG3bNuzbtw+hoaGNeo34+Hh07NjRBAmbjlarxYULF9C/f/9af96nTx/8/PPPNZ7bvXs3unfv3qjPP6mtWbMG/9/O/YQks0ZhAJ9LOv0VQShSQoOCcVGBbYIWCgYRKC3ahIhIy0DCaFE7c+eqTUQraVtU7oICQTdpEjULyQhKM4xWEiRFC+u5m9vwWd17yz78Mp4fzGLmfUfe4xnOHGHGjo4OweFwfOq8n5DvaupyNTXiXR9+jPc3yufzkGUZwWAQbW1tkGUZsiyjVCoBAMrlMvr6+jAyMoLj42NEo1F0dXXB5/Mpn5FKpSBJEgqFgnJsbGwMAwMDSCaTSCaT6O/vh9PprHl8nxGNRiEIAjKZzJuxQqEASZKQSqUAAOfn5wgGgzg8PEQul8POzg7MZjMsFgvK5XKtl16VRCKBpaUlyLKMbDaLjY0NGAwGjI+PV8yTJAmRSETZD4VC0Gq1iEQiSKfTcLlc0Ov1uLu7q3UIVbm+vkZvby/sdjsKhQJubm6U7cVPyPf6+jrUajXC4TAymQz8fj9aW1txeXkJAPB4PBVvD+zv76OhoQGhUAinp6cIhUJQqVQVbwd+d9PT09BqtYjH4xV5fXh4UOa8jntxcRG7u7u4uLiALMuYmpqCSqVScl8v5ubmEI/Hkc1mcXBwAKfTCY1Go+R7YWEBHo9HmZ/NZtHS0oLZ2VlkMhmEw2Go1WpsbW39qRCq9vT0BKPRiPn5+TdjPyXfpVJJuT8LgqDU7nw+D+Bjddlut2N5eVnZ/78a8RF/pHHxer0QBOHNFovFlDn5fB4OhwPNzc3Q6XTw+Xx4fHxUxmOxGARBQC6XU44Vi0W43W5oNBpoNBq43W7c3t7WMLLPc7lcGB4efncsl8tVfC9XV1ewWq3Q6XQQRRE9PT2YmZlBsVis4Yq/5ujoCENDQ9BqtWhqaoIkSQgEAri/v6+YJwgC1tbWlP3n52cEAgF0dnaisbERVqsV6XS6xquv3tra2rvX/K+/HX5KvldWVmAymSCKIgYHByteC7bZbPB6vRXzNzc3IUkS1Go1zGYztre3a7zir/m3vP56/b6O2+/3w2g0QhRFtLe3Y3R0FIlEovaL/6LJyUno9Xqo1WoYDAZMTEzg5OREGfd6vbDZbBXnxONxWCwWiKKI7u5urK6u1njVv8fe3h4EQcDZ2dmbsZ+S75f77OvtJbaP1GWTyYRAIFBx7L9qxEf8BfzzZBQRERHRN/ct/8eFiIiI6D1sXIiIiKhusHEhIiKiusHGhYiIiOoGGxciIiKqG2xciIiIqG6wcSEiIqK6wcaFiIiI6gYbFyIiIqobbFyIiIiobrBxISIiorrxN4RfkRAKXjxXAAAAAElFTkSuQmCC",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a, b = -10, 10\n",
    "\n",
    "x = range(a, stop=b, length=1000)\n",
    "plot(x, g.(x))\n",
    "hlines(0, a, b)\n",
    "xlim(a, b);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Float64,1}:\n",
       " 2.357551053877402\n",
       " 8.507199570713025"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fzeros(g, a, b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Iterative methods\n",
    "\n",
    "Often there is no closed formula for a root $x^*$ of the function $f$. Instead of using a formula to compute a root $x^*$, we will start with an **initial guess** $x_0$ and generate a **sequence of iterates**\n",
    "\n",
    "$$ x_1, x_2, x_3, \\ldots, x_k, \\ldots $$\n",
    "\n",
    "that we hope **converges** to $x^*$; i.e.,\n",
    "\n",
    "$$\\lim_{k \\to \\infty} x_k = x^*.$$\n",
    "\n",
    "**Note:** Different initial guesses $x_0$ may generate sequences of iterates that converge to different roots. We will see how to deal with this issue."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## When to stop\n",
    "\n",
    "Since the sequence of iterates is infinite, we must decide when we are close enough to a root $x^*$. However, we do not know $x^*$, so how can we decide when we are close enough?\n",
    "\n",
    "Some options are to stop when:\n",
    "\n",
    "1. The function value is small:\n",
    "\n",
    "  $$\\left|f(x_k)\\right| < \\mathtt{ftol}.$$\n",
    "  \n",
    "  A problem with this test is that $\\left|f(x_k)\\right|$ may be very small although $x_k$ is still very far from a root.\n",
    "    \n",
    "2. Consecutive iterates are very close to each other:\n",
    "\n",
    "   $$\\left|x_k - x_{k-1}\\right| < \\mathtt{atol}.$$\n",
    "   \n",
    "   A problem with this test is that `atol` must take into account the magnitude of the iterates.\n",
    "\n",
    "3. Consecutive iterates are *relatively* close to each other:\n",
    "\n",
    "   $$\\left|x_k - x_{k-1}\\right| < \\mathtt{rtol} \\left|x_k\\right|.$$\n",
    "   \n",
    "   Usually this is more robust than the above absolute test.\n",
    "  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Julia 1.3.1",
   "language": "julia",
   "name": "julia-1.3"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.3.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}