{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from ipywidgets import interact\n",
    "import ipywidgets as widgets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Functions and Summations\n",
    "\n",
    "**Warm Up**:\n",
    "\n",
    "Represent each of the following functions using symbols, tables, and graphs.\n",
    "\n",
    "1. Linear function with slope 7 and intercept of -2.\n",
    "2. Quadratic function including points:\n",
    "\n",
    "| $x$ | $y$ |\n",
    "| ---- | ----- |\n",
    "| -2 | 0 |\n",
    "| -1 | -1 |\n",
    "| 0 | 0 |\n",
    "| 1 | 1 |\n",
    "\n",
    "3. An exponential function whose terms increase as multiples of 3.\n",
    "4. A trigonometric function that passes through the point (0, 0) and completes 3 cycles by the time it reaches $x = 3\\pi$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Functions and Summations\n",
    "\n",
    "Repeat our operation above for the table shown below.  After you've completed this, compute the values for the sum column.  Can you determine a function to model this sequence?\n",
    "\n",
    "| $x$ | $y$ | sum of first n terms |\n",
    "| ---- | ----- | ------ |\n",
    "| 1 | 1 | 1 |\n",
    "| 2 | 2 | 3 |\n",
    "| 3 | 3 |  |\n",
    "| 4 | 4 |  |\n",
    "| 5  | 5 |  |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Repat for the table given below.\n",
    "\n",
    "| $x$ | $y$ | sum of first n terms |\n",
    "| ---- | ----- | ------ |\n",
    "| 1 | 1 | 1 |\n",
    "| 2 | 8 | 9 |\n",
    "| 3 | 27 |  |\n",
    "| 4 | 64 |  |\n",
    "| 5  | 125 |  |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fc4f043d950>]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f(x): return x**2\n",
    "x = np.linspace(0, 5, 1000)\n",
    "\n",
    "plt.figure(figsize = (15, 5))\n",
    "plt.subplot(121)\n",
    "plt.plot(x, f(x))\n",
    "for i in range(5):\n",
    "    plt.bar(i, f(i), width = 1, align = 'edge', color = 'orange', edgecolor = 'black', alpha = 0.5)\n",
    "\n",
    "plt.subplot(122)\n",
    "bases = [i for i in np.linspace(0, 5, 11)]\n",
    "for b in bases[:-1]:\n",
    "    plt.bar(b, f(b), width = 0.5, align = 'edge', color = 'orange', edgecolor = 'black', alpha = 0.5)\n",
    "plt.plot(x, f(x),)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# !pip install gif\n",
    "import gif\n",
    "from IPython.display import Image\n",
    "# def f(x): return x**2\n",
    "# x = np.linspace(0, 10, 1000)\n",
    "# @gif.frame\n",
    "# def plot(i):\n",
    "#     plt.plot(x, f(x), label = '$f(x)$', color = 'black')\n",
    "#     for a in range(i +1):\n",
    "#         plt.bar(a, f(a), width = 1, align = 'edge', color = 'orange', edgecolor = 'black')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# frames = []\n",
    "# for i in range(10):\n",
    "#     frame = plot(i)\n",
    "#     frames.append(frame)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# gif.save(frames, 'images/rgif.gif', duration = 500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/gif": 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      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Image('images/rgif.gif')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Riemann Sums\n",
    "\n",
    "<center>\n",
    "    <img src = 'images/riemann.png' />\n",
    "    </center>\n",
    "    \n",
    "**QUESTIONS**\n",
    "\n",
    "- Express $x_0, x_1, x_2, x_3, x_4$ in terms of $a$ and $b$\n",
    "- Express the height of each rectangle in terms of the function $f$\n",
    "- Multiply the width of each by its height and add these expressions together, call them $R(4)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problem\n",
    "\n",
    "Consider the function $f(x) = 4 - x^2$ on the interval $[-2,2]$.  \n",
    "\n",
    "- Draw a plot of the function\n",
    "- Use your formula for $R(4)$ to find an approximation for the area under the curve."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Taking it to the limit\n",
    "\n",
    "What happens if we increase the number of rectangles?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(-2,2,100)\n",
    "def f(x): return x**2\n",
    "def riemann_slider(n):\n",
    "    a = x[0]\n",
    "    b = x[-1]\n",
    "    width = (b-a)/n\n",
    "    plt.plot(x, f(x), color = 'black')\n",
    "    bases = np.array([a + width*i for i in range(n)])\n",
    "    plt.bar(bases, f(bases), width = width, align = 'edge', \n",
    "           color = 'orange', edgecolor = 'black')\n",
    "    areas = [width * height for height in f(bases)]\n",
    "    print(sum(areas))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
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       "version_major": 2,
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      "text/plain": [
       "interactive(children=(IntSlider(value=1, description='n', min=1, step=2), Output()), _dom_classes=('widget-int…"
      ]
     },
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    {
     "data": {
      "text/plain": [
       "<function __main__.riemann_slider(n)>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
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   ],
   "source": [
    "interact(riemann_slider,  n = widgets.IntSlider(1, min = 1, max = 100, step = 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example of $f(x) = x^2$\n",
    "\n",
    "<center>\n",
    "    <img src = images/r2gif.gif />\n",
    "    </center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example of $f(x) = \\sin(x)$\n",
    "\n",
    "<center>\n",
    "<img src = images/r3gif.gif />\n",
    "</center>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# x = np.linspace(-4*np.pi, 4*np.pi, 1000)\n",
    "# def f(x): return np.sin(x)\n",
    "\n",
    "# @gif.frame\n",
    "# def plot_riemann(n):\n",
    "#     a = x[0]\n",
    "#     b = x[-1]\n",
    "#     width = (b-a)/n\n",
    "#     plt.plot(x, f(x), color = 'black')\n",
    "#     bases = np.array([a + width*i for i in range(n)])\n",
    "#     plt.bar(bases, f(bases), width = width, align = 'edge', \n",
    "#            color = 'orange', edgecolor = 'black')\n",
    "#     areas = [width * height for height in f(bases)]\n",
    "#     plt.title(f'Area: {sum(areas)}')\n",
    "    \n",
    "# frames = []\n",
    "# for i in range(1, 100,10):\n",
    "#     frame = plot_riemann(i)\n",
    "#     frames.append(frame)\n",
    "    \n",
    "# gif.save(frames, 'images/r3gif.gif', duration = 200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import gif\n",
    "# from IPython.display import Image\n",
    "\n",
    "# @gif.frame\n",
    "# def plot_riemann(n):\n",
    "#     a = x[0]\n",
    "#     b = x[-1]\n",
    "#     width = (b-a)/n\n",
    "#     plt.plot(x, f(x), color = 'black')\n",
    "#     bases = np.array([a + width*i for i in range(n)])\n",
    "#     plt.bar(bases, f(bases), width = width, align = 'edge', \n",
    "#            color = 'orange', edgecolor = 'black')\n",
    "#     areas = [width * height for height in f(bases)]\n",
    "#     plt.title(f'Area: {sum(areas)}')\n",
    "    \n",
    "# frames = []\n",
    "# for i in range(1, 100,10):\n",
    "#     frame = plot_riemann(i)\n",
    "#     frames.append(frame)\n",
    "    \n",
    "# gif.save(frames, 'images/r2gif.gif', duration = 200)"
   ]
  }
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