Lab 5 Differentiation_and_Richardson_Extrapolation.ipynb

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        "Make sure you remove `raise NotImplementedError()` and fill in any place that says `# YOUR CODE HERE`, as well as your `NAME`, `ID`, and `SECTION` below:"
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      "source": [
        "NAME = \"Abdullah Hasan Sajjad Rafi\"\n",
        "ID = \"19301097\"\n",
        "SECTION = \"12\""
      ]
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      "source": [
        "---"
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      "source": [
        "# Part 1: Differentiation: Forward, Backward, And Central\n",
        "---"
      ]
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      "source": [
        "## Task 1: Differentiation\n",
        "\n",
        "We have already learnt about *forward differentiation*, *backward diferentiation* and *central differentiation*. In this part of the assignment we will write methods to calculate this values and check how they perform.\n",
        "\n",
        "The equations are as follows,\n",
        "\n",
        "\\begin{align}\n",
        "\\text{forward differentiation}, f^\\prime(x) \\simeq \\frac{f(x+h)-f(x)}{h} \\tag{4.6} \\\\\n",
        "\\text{backward differentiation}, f^\\prime(x) \\simeq \\frac{f(x)-f(x-h)}{h} \\tag{4.7} \\\\\n",
        "\\text{central differentiation}, f^\\prime(x) \\simeq \\frac{f(x+h)-f(x-h)}{2h} \\tag{4.8}\n",
        "\\end{align}"
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      "source": [
        "## Importing libraries"
      ]
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      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "from numpy.polynomial import Polynomial"
      ]
    },
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      "source": [
        "Here, `forward_diff(f, h, x)`, `backward_diff(f, h, x)`, and `central_diff(f, h, x)` calculates the *forward differentiation*, *backward differentiation* and *central differentiation* respectively. finally the `error(f, f_prime, h, x)` method calculates the different values for various $h$ and returns the errors.\n",
        "\n",
        "Later we will run some code to test out performance. The first one is done for you."
      ]
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      "source": [
        "def forward_diff(f, h, x):\n",
        "    return (f(x+h) - f(x)) / h"
      ]
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      "source": [
        "def backward_diff(f, h, x):\n",
        "    # --------------------------------------------\n",
        "    \n",
        "    return (f(x) - f(x-h)) / h\n",
        "\n",
        "    # YOUR CODE HERE\n",
        "    # --------------------------------------------"
      ]
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      "source": [
        "def central_diff(f, h, x):\n",
        "    # --------------------------------------------\n",
        "    \n",
        "    return (f(x+h) - f(x-h)) / (2*h)\n",
        "\n",
        "    # YOUR CODE HERE\n",
        "    # --------------------------------------------"
      ]
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      "source": [
        "def error(f, f_prime, h, x):\n",
        "    Y_correct = f_prime(x)\n",
        "    f_error = np.array([])\n",
        "    b_error = np.array([])\n",
        "    c_error = np.array([])\n",
        "    \n",
        "    for h_i in h:\n",
        "        # for different values of h (h_i)\n",
        "        # calculate the error at the point x for  (i) forward method \n",
        "        #                                         (ii) backward method\n",
        "        #                                         (ii) central method\n",
        "        # the first one is done for you\n",
        "        f_error_h_i = forward_diff(f, h_i, x) - Y_correct\n",
        "        f_error = np.append(f_error, f_error_h_i)\n",
        "\n",
        "        # --------------------------------------------\n",
        "\n",
        "        # backward method\n",
        "        b_error_h_i = backward_diff(f, h_i, x) - Y_correct\n",
        "        b_error = np.append(b_error, b_error_h_i) \n",
        "\n",
        "        # central method\n",
        "        c_error_h_i = central_diff(f, h_i, x) - Y_correct\n",
        "        c_error = np.append(c_error, c_error_h_i)  \n",
        "\n",
        "        # YOUR CODE HERE\n",
        "        # --------------------------------------------\n",
        "        pass\n",
        "    \n",
        "    return f_error, b_error, c_error"
      ]
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      "source": [
        "## Plot1\n",
        "Polynomial and Actual Derivative Function"
      ]
    },
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        {
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            "text/plain": [
              "<matplotlib.legend.Legend at 0x7fc0075abc50>"
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          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "fig, ax = plt.subplots()\n",
        "ax.axhline(y=0, color='k')\n",
        "\n",
        "p = Polynomial([3.5, 2.0, -10.0, -4.0, 6.0, 2.0])\n",
        "data = p.linspace(domain=[-2.4, 1.5])\n",
        "ax.plot(data[0], data[1], label='Function')\n",
        "\n",
        "p_prime = p.deriv(1)\n",
        "data2 = p_prime.linspace(domain=[-2.4, 1.5])\n",
        "ax.plot(data2[0], data2[1], label='Derivative')\n",
        "\n",
        "ax.legend()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": false,
        "editable": false,
        "id": "lFKcFVDwniIv",
        "nbgrader": {
          "cell_type": "code",
          "checksum": "04304098e81e9ec18e28518a5eb177d6",
          "grade": true,
          "grade_id": "plt2_test",
          "locked": true,
          "points": 2,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "outputId": "ef583bee-859b-4c56-ba00-07feb23d9129"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7fc0075395d0>"
            ]
          },
          "metadata": {},
          "execution_count": 166
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "h = 1\n",
        "fig, bx = plt.subplots()\n",
        "bx.axhline(y=0, color='k')\n",
        "\n",
        "x = np.linspace(-2.0, 2.3, 50, endpoint=True)\n",
        "y = forward_diff(p, h, x)\n",
        "bx.plot(x, y, label='Forward; h=1')\n",
        "y = backward_diff(p, h, x)\n",
        "bx.plot(x, y, label='Backward; h=1')\n",
        "y = central_diff(p, h, x)\n",
        "bx.plot(x, y, label='Central; h=1')\n",
        "\n",
        "data2 = p_prime.linspace(domain=[-2.2, 2.4])\n",
        "bx.plot(data2[0], data2[1], label='actual')\n",
        "\n",
        "bx.legend()\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": false,
        "editable": false,
        "id": "z9sU1w9lniIv",
        "nbgrader": {
          "cell_type": "code",
          "checksum": "18a8931acbb2421ebd9752d28037c7ce",
          "grade": true,
          "grade_id": "plt3_test",
          "locked": true,
          "points": 2,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "outputId": "6561ea28-5c85-4fa4-c96b-2d8465427ec7"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7fc0074c2d10>"
            ]
          },
          "metadata": {},
          "execution_count": 167
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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Z933fffedU12tra3ceOONJCcnM3bsWAoKCk663Y9+9CMiIyPbLrASQpzZpoIq7E7NxKRw6q31RO+zUJ8SizKb4dBqQEHCpE45toT7KWitue6665g6dSoHDx4kJyeHZ555hrKysnPa3+nC3eFwnE+p5+XNN98kJCSEvLw8HnzwwVOOS3P77bezbNmyLq5OiJ5tXV4lXkYDmQkhbN+7mlgL9Bk7zrUyfw30Swe/0NPv5BxJuJ/CqlWrMJvN3HPPPW3LRowY0Tao1/PPP8/o0aNJS0vj6aefBqCgoICUlBTuvPNOhg0bxqWXXkpzczMLFy4kOzubW265hfT0dJqbm0lISODRRx8lIyODjz766JTD+x7vtdde47XXXjtpvaWlpVx++eUMHDiQRx55pN3Pc/Hixdx2220AzJ49my+//PKkV7VOnjz5hIHQhBBn9nWehYz+wfiYjRxe8zkAA6bNhNYGKN4MiVM67dg94iKm5zY9R25V+8Ybb68hoUN4dMypR0/ctWsXo0aNOum65cuXc+DAATZt2oTWmpkzZ5KVlUV8fDwHDhzgvffe4/XXX+eGG27g448/5gc/+AGvvPIKL7zwApmZ31xMFhYWxpYtWwCwWCynHN73mOP/0Xzbtm3b2Lp1K97e3gwePJj777+fuLg4brzxRvbt2/ed7R966CHmzp17whC+JpOJoKAgLBZL28iWQohzU91oZc+ROn5xySAAnFt20OJjJCg1HQ5+CU47DJjaacfvEeHe3Sxfvpzly5czcuRIwDV5x4EDB4iPjycxMbFtgoxRo0adsg8b4MYbb2y7fbrhfdtjxowZBAUFATB06FAKCwuJi4vjgw8+OMtnJ4ToCOsPuQYQnJAcTqOtkX77LNQNS3Cd335oNRi9IX5cpx2/3eGulDIC2UCJ1vpqpVQi8D4QBuQAt2qtrUopb+BtYBRgAW7UWhecT5Gna2F3lmHDhp1y7k+tNY8//jh33333CcsLCgrahtEF11C6zc3NpzzG8cP2nm543/b49nGPDeF7ppb7sSF8Y2Njsdvt1NbWEhYWdlbHFkJ819d5lfh7mxgRG8SmHZ/Rtxqaju9vjx8LZt9OO/7Z9Lk/AOw97v5zwJ+11slANXCHe/kdQLV7+Z/d2/U406dPp7W1tW1yDYAdO3awdu1aLrvsMt566y0aGhoAKCkpoby8/LT7CwgIaBvq92TaM7zvK6+8wiuvvHJWz+ODDz446RC+c+fOBWDmzJksWLAAgIULFzJ9+vROHalOiAvFuoMWxiSGYjIaKF7jOhkhafo10FABZbs6tb8d2hnuSqlY4CrgDfd9BUwHjjVtFwDXum9f476Pe/0M1QPTQinFokWLWLFiBUlJSQwbNozHH3+cvn37cumll3LzzTe3zVs6e/bs0wY3fDPv6bEPVL+tPcP75ubmdnir+o477sBisZCcnMyLL77Is8+6JkYpLS3lyiuvbNvu+9//PuPHj2ffvn3Exsby5ptvdmgdQvQmpTXN5Fc2MiHJ9ffqzNlOUx8jQUPTXK12gAHTOrcIrfUZv3CF9ChgKvAZEA7kHbc+Dtjlvr0LiD1u3UEg/HT7HzVqlP62PXv2fGfZhe6qq67Sra2tni6jQ8nPWfRGH2Uf1v0f/UzvKa3VDa0Nes3oIXrVD65wrVx8n9Z/itPaYT/v4wDZ+hS5esaWu1LqaqBca53Tkf9UlFJ3KaWylVLZFRUVHbnrXuuzzz7Dy8vL02UIIc5gXV4lYX28GBwVwM7tK4ioA/9x7v72Q6sh8SIweH7gsInATKVUAa4PUKcDLwHBSqljH8jGAsemACrB1ZLHvT4I1werJ9Baz9NaZ2qtMyMiIs7rSQghRHehtebrg5WMTwrDYFAUrvwUgIEXXw9V+VBT1On97dCOcNdaP661jtVaJwA3ASu11rcAq4DZ7s1uAxa7by9x38e9fqX77YMQQvR6BysaKatrZUKS61oRlb2D+iAvAgcNdQ85QKee337M+Vyh+ijwkFIqD9fpkMc+YXsTCHMvfwh47PxKFEKInmPdwUoAJiaHcbSulMQD9TRnDHKdhZa/BgKiIbzzJsY+5qwuYtJarwZWu28fAsacZJsWYE4H1CaEED3OujwLMcG+xIf6sWzpWyS0QMCUS8DphENrYNBl0AUnEMrYMkII0UEcTs36QxYmJoehlKIy60sAki6e5Tq3vbmqS/rbQcK9w6xevZp169ad1z78/f07qBohhCfsKa2jttnGhKRwHE4H/tsPUhUXhDk8/Lj+dgn3HqUjwl0I0bN97e5vn5AUxp7iLSQX2TGMcY01Rf4aCB8Egf26pBYJ9zO49tprGTVqFMOGDWsbimDZsmVkZGQwYsQIZsyYQUFBAa+99hp//vOfSU9PZ+3atdx+++0njE1zrFXe0NDAjBkzyMjIIDU1lcWLF5/0uEKInufrvEoGRvoTGejD3pUfY3JCwoxrXFPqFa7rkrNkjukRo0Ie/dOfaN3bsUP+eqcMoe8TT5xxu7feeovQ0FCam5sZPXo011xzDXfeeSdZWVkkJiZSVVVFaGgo99xzD/7+/vzyl78EOOXl+T4+PixatIjAwEAqKysZN24cM2fOlPFchOjhrHYnmwuquGl0PADN6zdgNymiJkxzjd1ua+qy/nboIeHuSS+//DKLFi0C4PDhw8ybN4/JkyeTmJgIcNYTWGiteeKJJ8jKysJgMFBSUkJZWRl9+/bt8NqFEF1na1E1LTYnE5LCqLfW03dPObWD+2Hw8XH1tytDp02pdzI9Itzb08LuDKtXr2bFihWsX78ePz8/pk6dSnp6Orm5Z34XYTKZcDqdADidTqxWKwDvvPMOFRUV5OTkYDabSUhIoKWlpVOfhxCi832dV4lBwdgBYWzetYT4Co11ljvM89dAv5HgG9xl9Uif+2nU1tYSEhKCn58fubm5bNiwgZaWFrKyssjPzwegqqoK+O6QvgkJCeTkuIbjWbJkCTabrW2fkZGRmM1mVq1aRWFhYRc/KyFEZ1i5r5yR8SEE+Zopcg85MOCS66ClDoqzu7S/HSTcT+vyyy/HbreTkpLCY489xrhx44iIiGDevHnMmjWLESNGtM2m9L3vfY9Fixa1faB65513smbNGkaMGMH69evbJua45ZZbyM7OJjU1lbfffvuUw/sKIXqO8roWdpXUMX1IJFprzBt30hTohf/QVCj8GrSjS/vboYd0y3iKt7c3n3/++UnXXXHFFSfcHzRoEDt27Dhh2YYNG9puP/eca86S8PBw1q9ff9J9Hpv8QwjRs6za55qsZ9rgSPKrDzLwQBOtE9JRBgPs/x94+XfqlHonIy13IYQ4Tytzy4kO8iElOoAdaz4moAWiZ1wFWrvCPWkamLzPvKMOJOEuhBDnodXu4KsDlUwbEolSito1q3AqiJ9xNRzdCfWlMOjyLq+rW4e7jBTcu8nPV/QGm/OrabQ6mD44EqvDSsT2w1QnRWAMDna12gEGXtrldXXbcPfx8cFisUgA9FJaaywWCz4+Pp4uRYjzsjK3HC+TgQnJYWzNXUXiESfek8a7Vh74H8SMAv/ILq+r236gGhsbS3FxMTIFX+/l4+NDbGysp8sQ4rys2lfO+AFh+HmZyF++iBFA8hU3QEOF6xTIqY97pK5uG+5ms7ntKlAhhOiO8isbya9s5PYJCQCoDVtpDDATnDoSdrwPaNf47R7QbbtlhBCiu1uZ6zoFcvqQSMrrj5K4r47GjEHuUyCXuWZdih7hkdok3IUQ4hytyi0nOdKfuFA/tq7+kIAWiJxxuWsUyLyVrg9SPTQooIS7EEKcg4ZWOxvzLUwf4vqw1LJyOQ4DJF8yC4rWg7XeI6dAHiPhLoQQ5+CrA5XYHJppgyNpdbQSnpOPZVAk5pBQ1ymQRu8um3XpZCTchRDiHKzKLSfAx0RmQgibt/6XuHIn/lOnulbuXwaJF4FXH4/VJ+EuhBBnSWvNqn3lTB4YgdlooHCpa9a1ITNvhco8qDro0S4ZkHAXQoiztru0jvL6VqYNicThdOCzcRc1ff3pMyDZ1WoHj1yVejwJdyGEOEsrc8tRCqYOjmBHwQYG5dtQk8a4Vh74H0QOhZD+Hq1Rwl0IIc7Sytxy0mKDCff3Zs/SdzE5YeDV34eWWtdE2B66cOl4Eu5CCHEWKhta2V5cw/TBrok5nF9tpLmPidDR4+HgSnDaPd7fDhLuQghxVlbvq0Br11WpeZX7GZLbSMuYYSij0XUKpG8IxI72dJkS7kIIcTZW5ZYTEeDNsH6B5Hz5Dv4tEH/l9eB0wIHlkHwJGIyeLvPM4a6U8lFKbVJKbVdK7VZK/da9PFEptVEplaeU+kAp5eVe7u2+n+den9C5T0EIIbpGi83Bqn3lXJwShcGgaFq5CrtRET3tSijZAk2WbtHfDu1rubcC07XWI4B04HKl1DjgOeDPWutkoBq4w739HUC1e/mf3dsJIUSPt3pfOU1WB1elRnOk4QhJ2yupS0/E6N8H9i0FZYTkGZ4uE2hHuGuXYzM3m91fGpgOLHQvXwBc6759jfs+7vUzlPLQyDlCCNGB/rvzKKF9vBg3IJSNa94jshYir5jpmit1zyeQONnV594NtKvPXSllVEptA8qBL4CDQI3W2u7epBiIcd+OAQ4DuNfXAmEn2eddSqlspVS2TMghhOjuWmwOVu4t47JhUZiMBmr+9zkOAyRedQMc3QFVh2DYdZ4us027wl1r7dBapwOxwBhgyPkeWGs9T2udqbXOjIiION/dCSFEp1qzv4JGq4MrhkdT21pLbE4JNSkxmEJCYPcnri6ZIVd7usw2Z3W2jNa6BlgFjAeClVLHZnKKBUrct0uAOAD3+iDA0iHVCiGEhyzdeYRgPzPjk8LYsH4hMRZN8GWXubpkdi9yjQDZ5zudFB7TnrNlIpRSwe7bvsAlwF5cIT/bvdltwGL37SXu+7jXr9Qyy7UQogdrsTn4cm85lw3ti9looHypK+4GXXMrHNkO1fndqksG2tdyjwZWKaV2AJuBL7TWnwGPAg8ppfJw9am/6d7+TSDMvfwh4LGOL1sIIbrO2gOVNLTauTIt2jV2+6aDVCaH4xXV19Vq72ZdMtCOCbK11juAkSdZfghX//u3l7cAczqkOiGE6AaW7jxCkK+ZCUlhbNzyCQlHnTTdPe2bs2QGTAW/UE+XeQK5QlUIIU6j1e5gxZ4yLh0ahdlo4PCnHwKQMuuHcGQbVBd0uy4ZkHAXQojT+upAJfXuLhmbw0bQV7uojA/Cr3+iq0vGYIIhV3m6zO+QcBdCiNP4784jBPqYmJgUzoacT0gsdeBz2Qz3WTLds0sGJNyFEOKUWu0OvthTxiVD++JlMlDwn3cBGHbDXVC6FWoKu2WXDEi4CyHEKX2dV0l9i52r0vrSaGskct1+KpPD8Yvr/02XzOArPV3mSUm4CyHEKSzdeZQAHxMTk8NZ+9V7xJc7Cb7yquPOkpnWLbtkQMJdCCFOymp3snz3US5JicLbZOTIkoU4FQy5/kdQugVqimDYtWfekYdIuAshxEl8fbCSuhY7V6ZGU9FUQdymQmpS+mGOinR3yZi75Vkyx0i4CyHESSzdcQR/bxMXDQpn7ep/EWOBiO9d5z5LZjEkTes2w/uejIS7EEJ8S6vdwfI9ZVycEom3yUjVZ0twGGDAtbe4ZlyqLYKh3bdLBiTchRDiO77cW05ts43rMmIprClgcHYZdSMGuIf3/Y+7S6Z7niVzjIS7EEJ8y8KcYqICvZmUHM76/75OeB3EzrkFHHbY9bFrKr1u3CUDEu5CCHGC8roWVu8rZ1ZGLAYF1qVf0OptJPbKWXBwJdQfgfRbPF3mGUm4CyHEcRZtLcGpYfaoWPaUbmX4znqaJo3A4OMD2/4NfmEw6HJPl3lGEu5CCOGmtWZhTjEZ8cEkRfiz7eN5+Foh+ft3QKMFcpdC2o1g8vJ0qWck4S6EEG47ims5UN7A7FFxOJwOvL/YQH2oDxETpsLOj8Bp6xFdMiDhLoQQbT7KOYy3ycBVadFk711BSl4rzksvQhkMri6Z6HToO9zTZbaLhLsQQuCaJ3XJtlIuG9aXIF8zeR/+E4OGoTf/xDVP6tGdMPIHni6z3STchRACWLG3jLoWO3MyY2m0NjAX2y0AAB4NSURBVBKxeieVCSEEDkqBre+A0RuGX+/pMttNwl0IIXCd2x4d5MOEpHCyvniLuDIngddfC/ZW2PmhaxyZbjoC5MlIuAshLnhHa1vI2l/BrIwYjAaFZeEHWM2KYTfeA/uWQnN1j+qSAQl3IYRoO7f9+oxY9hZvJSXHQv2kVEyBga4umcAY13R6PYiEuxDiguY6t/0wmf1DGBDhz6b3XsLPCoPm/hTqSuHgl5B+MxiMni71rEi4CyEuaNsO13CwopHZo2JptDUStDybuih/IsZNhu3vgXa6wr2HkXAXQlzQPsopxsds4Mq0aFZkzWfwYQd+181EgatLpv9ECB3g6TLPmoS7EOKC1WJz8On2Ui4f1pcAbxPlH76PwwBDbr4bijZA1cEe90HqMRLuQogL1pLtpdS32LkhM47dpVtJ21RJ/ZghmCMjXVekevnD0Gs8XeY5OWO4K6XilFKrlFJ7lFK7lVIPuJeHKqW+UEodcH8PcS9XSqmXlVJ5SqkdSqmMzn4SQghxtrTWzP+6gEFR/oxPCmPTey8R2AzJP7oPmmtg1yIYdh149fF0qeekPS13O/ALrfVQYBxwr1JqKPAY8KXWeiDwpfs+wBXAQPfXXcCrHV61EEKcp80F1ew5UsftExJpsDUQ8Xk2dVEBhE+aBlv/DbZGGHOnp8s8Z2cMd631Ea31FvftemAvEANcAyxwb7YAODah4DXA29plAxCslIru8MqFEOI8zF+XT5CvmWtH9uPLL14nucSJ/42zUWjY9A/XB6nRIzxd5jk7qz53pVQCMBLYCERprY+4Vx0Foty3Y4DDxz2s2L3s2/u6SymVrZTKrqioOMuyhRDi3JXUNPO/3WXcNDoOX7ORuvc/xGpWDPmB+4rUmiIYe4+nyzwv7Q53pZQ/8DHwc6113fHrtNYa0GdzYK31PK11ptY6MyIi4mweKoQQ5+XfGwrRWnPr+P5sP/Q1aVtraZg2CmNgIGx4FYLjXWPJ9GDtCnellBlXsL+jtf6Pe3HZse4W9/dy9/ISIO64h8e6lwkhhMe12By8t6mIS4f2JTbEj50LXsbbDsPufMg1tG/h1zDmrh53Req3tedsGQW8CezVWr943KolwG3u27cBi49bPtd91sw4oPa47hshhPCoT7aWUNNk4/aJCVQ3VRH7xS4sSeEEp46EDa+BuQ+MvNXTZZ43Uzu2mQjcCuxUSm1zL3sCeBb4UCl1B1AI3OBetxS4EsgDmoAfdmjFQghxjrTWzF9XwJC+AYxNDGXhW48yvFqjHvohNJTDroWQcRv4Bnu61PN2xnDXWn8FritxT2LGSbbXwL3nWZcQQnS4DYeqyD1az3PXp9LiaMH84TLqQrwZc91c+OoFcFh7/Aepx8gVqkKIC8b8dfkE+5m5Jj2G5cteZXChDe/vX4/CAZvfgIGXQniyp8vsEBLuQogLwuGqJr7YU8b3x8RjMmrq/vUurd4Ght/+AOz6DzRWwLifeLrMDiPhLoS4IPx7QyFKKW4d15+V2R+RvrMR21VTMAUEwIa/Q8QQGDDN02V2GAl3IUSv12S1896mIi4f1pfoIB8K/vkqBg1pP30citbD0R2uvnZ1qo8Xex4JdyFEr7cwp5i6Fju3TUhgfd5KMtZV0DB+GN6xca5Wu28IpN3o6TI7lIS7EKJXa7U7eHX1QTL7hzA6IYSd856nTyukPPArqMqH3P/CqNvBy8/TpXYoCXchRK/2YXYxR2pbeODigew5spW0LwupGZFA4IiRkPUCGL1gzN2eLrPDSbgLIXotq93Jq6vyyIgPZlJyOBvm/YngJhj4wGNgOeiaI3XUDyGw9w1cK+EuhOi1FuYUU1rbwgMXD+JwdQEDl+6malAUYeMnw9r/B0YzTPq5p8vsFBLuQoheyWp38rdVeaTHBTN5YDhr3vwdEXWQcN9DqKpDsP19yPwRBPT1dKmdQsJdCNEr/WdLMSU1zTxw8UAsjRX0+2Qj1fHB9Lvke+6+djNM7J2tdpBwF0L0QjaHk1dW5TEiNoipgyJY/sav6WfRRN7zU1erfcf7kHkHBESdeWc9lIS7EKLXWbSlhOJqV6u9tPYw0R+spSouiKRrb4E1/wdGb5j4gKfL7FQS7kKIXuVYqz0tNohpgyNZ/vfH6FutiXvwYVerfeeHMLp3t9pBwl0I0ct8srWEoqomfjZ9IAfK95L0yVaqB0QQd8UsyLowWu0g4S6E6EXs7lb78JhAZqREsupvTxBRB0m//BXKkgc7P4IxPwb/SE+X2ukk3IUQvcbibaUUWlyt9q1FGxi+dB+1KTFETrvU1ddu8oEJvb/VDhLuQoheotnq4IXl+0iNCeLilEg2/uVJQhtg8GO/RVUecE2hN/rH4B/h6VK7hIS7EKJXeG3NQY7UtvDU94ayduenjP2ylLpxKYSMnQjLf+Wa+HrCzzxdZpeRcBdC9HglNc38I+sgV6dFkxEfxKE/P4uXHVKf+j/Y/z84sBymPHLBtNpBwl0I0Qs8+3kuWsPjV6awbPUbjN5YQ9PVF+EXHw/LHoew5F4z8XV7mTxdgBBCnI/NBVV8ur2Un80YSHiAgcaXX8PmbWDko8/Axleh6iDc8jGYvDxdapeSlrsQosdyOjW//XQ30UE+3DNlAJ998EdSc1tQt16P2cvmOkNm0OUw8GJPl9rlJNyFED3WwpxidpXU8dgVQ6huLCH4bx9TG+5L2n2/ghW/AYcVLvuTp8v0CAl3IUSPVN9i4//+l8uo/iF8Ly2az5+7l34WJ/2e/DWG8h2uiTjG3wthSZ4u1SOkz10I0SO9siqPygYrb90+mlU5Cxn134NUj04m5dJr4I0ZEBANF/3S02V6jLTchRA9Tn5lI299lc/sUbEkRhopfe4ZjFox8g8vw/Z3oXQLXPxb8Pb3dKkeI+EuhOhRtNb8/rM9eBkNPHLZYN57+zEyd7VgunU2vlGhrr722DGQdoOnS/WoM4a7UuotpVS5UmrXcctClVJfKKUOuL+HuJcrpdTLSqk8pdQOpVRGZxYvhLjwfLylhJW55Tx4ySBKq7Yx+PWVNPQNZMgDT8DKP0JjJVz5f6CUp0v1qPa03OcDl39r2WPAl1rrgcCX7vsAVwAD3V93Aa92TJlCCAGlNc389tPdjEkI5QfjY8n+wy+IrIUBz/4/DKUbYdM/YMxd0G+kp0v1uDOGu9Y6C6j61uJrgAXu2wuAa49b/rZ22QAEK6WiO6pYIcSFS2vNox/vwO7QPD8njcWLn2P8V1U0fu8iwtJT4ZOfuq5Evfg3ni61WzjXPvcorfUR9+2jwLEpTWKAw8dtV+xe9h1KqbuUUtlKqeyKiopzLEMIcaF4d1MRaw9U8sSVQ1AcJfTP79MY4sPIp1+Ezx+D+iNw3Tzw8vN0qd3CeX+gqrXWgD6Hx83TWmdqrTMjIi6cwXyEEGevyNLEH/+7l0nJ4Xx/TByrnr6H2Eon0b95GuPhVa4zZC76BcSO8nSp3ca5hnvZse4W9/dy9/ISIO647WLdy4QQ4pw4nZqHF27HqBTPzU7jPwt/T+aKYqouHUXcxInw6c8hegRMftjTpXYr5xruS4Db3LdvAxYft3yu+6yZcUDtcd03Qghx1uavK2BjfhW/vnoo5VVb6Pv/PqA+0o9xf3wVPn0AWuvhun9ccAODnckZr1BVSr0HTAXClVLFwNPAs8CHSqk7gELg2AmlS4ErgTygCfhhJ9QshLhAHKxo4LlluUwfEsmlqQEsue1nZDRA37+/gjFvCez7L1z6R4hM8XSp3c4Zw11r/f1TrJpxkm01cO/5FiWEEDaHk198uB0fs5FnrhvO2y/N5ZLtTTjvuIHw5Bj4+xzoPwnG/dTTpXZLMraMEKJb+v1ne9h2uIZXbh7JVxv/wUX/3kV9Siyj738U3p0FaLj272CQC+1PRsJdCNHtfLC5iLfXF3LX5AEkhpRS+tN5OH28SH/t36gVv4Ki9TDrDQjp7+lSuy0JdyFEt7KlqJpff7KbiwaG85Op/Vh6+wzSLZrweS/iVfQpZL8FEx+AtDmeLrVbk/czQohuo7yuhXv+lUPfIB9evimdT567g4wdjTjuuIGoOG/4/FEYeCnMeNrTpXZ7Eu5CiG6h1e7gnn/nUN9iZ97cUSz76NeM+XA3ltFJpP7wdvhwLoQOgOvfAIPR0+V2e9ItI4TwOK01Ty/ezZaiGv5+Swb7d/+bQX/+lNrYIMa/9Cbqg1ngtMNN74FPkKfL7REk3IUQHvfOxiLe33yYe6clEWDYiv3Jv4KXmfS33sf4xS+gfA/cshDCkz1dao8h4S6E8Kg1+yv4zZLdTBscwaUpDRT+6GES6xSx8+fhd/B92Pupa5Lr5O9cWiNOQ8JdCOEx6/IquevtbAZFBfDLy4LYc/cNDC1xEvz8Hwhx7oDVz8CIm+VCpXMg4S6E8IjNBVXcsSCb/mF+vHxzEuvvn0nmASvmx+4nJqoa/vswDL4KvvfSBT+r0rmQcBdCdLmtRdX88J+biQ72Yd7c4WQ9ci2jtzVi//ENpAz3hc9+DoOugDnzZUCwcySnQgohutSuklrmvrWJMH8v/v6DwWQ9fA2jv66kYfYMhk8b4Ar2gZfBDQsk2M+DtNyFEF0m92gdP3hzI4E+Zl66uT/rH7mOcRtrabzhEjKvHYNach8kXww3vA0mb0+X26NJuAshukTu0TpueX0jPiYjL9wQxdaHb2DclkasN1/NqJkZqE9+AgOmwo3vgNnH0+X2eBLuQohOtyq3nPvf20ofbyN/nOlL0c9vZtx+K/qHc0i7KAq1+KeQOBm+/54EeweRcBdCdBqtNW99XcAf/7uHlOhAHpzURNMDdzG81IHpl3czMOIALH8JhlwNs14Hs6+nS+41JNyFEJ3C5nDy9JLdvLuxiEuHRjErZgfGe1+gfz0E/P5h4ms/gK0bYPIjMPVxGZe9g0m4CyE6XG2TjZ++m8PXeRbumhJH1KFXiHxwLQ5vE5HP/5K+uc9DYwXMfguGX+/pcnslCXchRIc6VNHAjxdkc7i6iSeuCsXxwX1MWFFBTVIE6Y/8CN+vHgOfYPjRMug30tPl9loS7kKIDuF0at5eX8Czy3LxNRt5dEIpEb97hEGHHTRfMoaxl/bFsOoBiMmEm96BgL6eLrlXk3AXQpy3IksTDy/czsb8KqYMDmZC9ZukP7EeEwb8HryJlJZFkPMJZN7hGgRMzojpdBLuQohz5nRq3tlUxDNL92JUigfGWYj519Ok7m6kOimcoTcMwy//RQhJgNs+dZ3uKLqEhLsQ4pwUVzfx6Mc7+DrPwtgkB5OK32L80/vwciiabprI+IANqPz3YexPYMavwauPp0u+oEi4CyHOSlWjlVdX5/H2+kJMRht3Rq8g498rSCjT1A7pS8oVfelz5CPwSnZ9aBo/ztMlX5Ak3IUQ7VLXYuONtfm8ufYQzTYr10RtZ+zq/zAit4X6UB/63BTPENaiKvbCpIdgyiNyUZIHSbgLIU6r2erg7fUFvLrmIDXNDVwetoEp61aQvqiZFm8DrZfEkBmyFYOxBEbfDZMeBP9IT5d9wZNwFx7hcGqarHasdicOmw1HUzNWazOtzQ1Ym+pw2hoxOu2Y0JgNCpNRYTKAl9mMj18fvP2CMPr6o3x8UUYzGMyuUQRlUocOk1/ZyIfZh/ko+zDVzeXMZDkTt21hWL6dFm8D9dOiSA/bjZd3OYz6kau1Hhjt6bKFW6eEu1LqcuAlwAi8obV+tjOOIzzP5nBSXt/K0doWjlY3YCkuoq40j5aKw1Bdim91Kd6NNfg1N+HbYsPHase71YmP1Ym3DbxsYHKeuE+j+wvACbS6v07GqcBqAqsZrF4auxfYvBQOb4XTx4D2MWLo4413QB/8Q4LwD48gOKIfoTGJ+ET0RwX0hT6R4Bsil78DLTYHy3Yd5f3NRWw4VE4/tnODZR1jdhYRVaNpCDRhn2AmrW8RRj8LjLgFLvoFBMd5unTxLR0e7kopI/A34BKgGNislFqitd7T0ccSnc/ucHKktoUCSyMFlY0UH9xPTf42jOX5BFpKiKivJKKhkbB6G/0bNQP0d/fR5AVNvtDso7F6Q30fqPY2oL2MaLMJbTbiNJvQJhPKbEYbvcBoQisDTsCpFU4Ah0Y7NNphx2mzgc2Gstkx2hyYrHZMNgcmqwNvqxOfWo1vuQP/ZgfeditQDxwF9lEH1OH6p9Dgp2nuAzY/jdPfgCnAC5/QAIIiwwmLSSAyYRje4YmuFmlgP9eVlb3s3UGLzcHmgiq+2FPGoq2F+FpzmFa9kTmHihhaaAegIt6Md6qFIdENqPgxMPIhGDYLfAI9XL04FaX1Sf4az2eHSo0HfqO1vsx9/3EArfUzp3pMQECAHjVqVIfWIc6OU5mw+YZi8w3D5htKuNlGDFXEtVhIqK8gtq6OqGobvrZvHuNQUBUIDQEaa4ATp6/G7qWxmqAFRaPDSE2rieomL6qtZmptJurtJhy6c8NRo3CafHCYfHGYfDD4mPAzg5/ZSbBqJYxmQuzNhNiaCWppJbDZSmCjg+AGjZ/1u/ur94P6AE1rH42jjxO7j8Zm0liVgQaHgeoWM+Wt3pS3mqlo9cLq7N7vADRg8wmlOTiRluD+OEJMDG3axcjKXEaWHmXgEVcmVAdpTAOaGRZTT4tZ8b+yUJYdDaOoSS5A6i7WrFmTo7XOPNm6zuiWiQEOH3e/GBj77Y2UUncBdwF4e8uMK13Jbu6DtU8kVr8oDD6BxBotDGg9QlJtKYkV+4irsuJl/2b7ykCoDdEU9XVg8HfgMGtalKK21UxlozfFzd6U1HtTX909PsJRaIz2Zoz2ZteCBnDgarvXc/wvpxcabxxmPxwh/tii/DF5mwn0dhBKC+G6kb62OsJbGglraiak1kZosRPfb/0DsBsc1AQ00eT+J+fw1di9NTYDNCtFvcNETbMRS6sPFa1mLFZzl/0D0IDDKwCrXwStfuE4gvwJ9W5ikLWIwTUbGZS3jAFlTnxsri4uS6STxowWBkY2oJUXOTUBvJsXzs5a/07/pyw6Vme03GcDl2utf+y+fyswVmt936kek5mZqbOzszu0DuFiaWhl2+Eath+uYXfBERr3fUW/it0MrC5moKWG6Cp720S6dX5QGa6xhdjxDXYSGRNKfNIwwvqnQ+RQiEyBwNgLrm/a7nBS0dBKaU0zJVVNHC4pwlK4m5YjhzBXHiao9iihDbWENrYS0mAnpF5j/Nafld0Atf7Q2Edj9dM4fRXOPiYM/t6YA/3xDQkhIDSSwIgY/MKi8Q2NxjewLz59IjD4hoBXwHded601rXYnloZWDtfUUFhdydGKI9SUldJSfgRbZSFeVYcJa6gmvKGJiFobMRbd9o/bbtTUhmtUuI3IiFYSkqMwD5nimg0pcbLrcwjRrSmlurTlXgIc/+lKrHuZ6GRWu5NdpbVsK6pha1E1xXtzCCvdREr1IYZUVnJJpbXtw8sqf6iKdHIoyU5wqJO4hBgGJWVijBkJ/dIhIkUmJ3YzGQ1EB/kSHeTLqP6hMDIWmHDCNi02B2V1LRytbSGvuoHSwv1UF+/HVl6Et6UY/7oKAhvqCGxsJqDGTkCpE/9mBwaagCagHNh3wjsMqxFavMBuBIfR9f34Br/BCUYHmBzgbYPhVkg7SVvNbtQ0BEBrgJPqFAd9wr1JSIgjbPgoDDGpEDUUwgfJOem9TGe03E3AfmAGrlDfDNystd59qsdIy/3cVDdaySmsJruwmq2HjtC8bw2Dq3Yx1FJMSlkdQU2un22zF5RFaewRdgJDW0mIjyB+4FhUbCbEjna1yo3do0ult7PanVQ1WrE0tlLf2EJ12VFqjhbRVFlCa/URVN0RvBpqMbU2YWxtxmxtxWCzYnTYMTo0Bq1RgAENCpwmUEYDRi8TJl8vvPv44BvYB9/gAILCIoiIS8ErfgAqMBr8o8A39IJ759WbdWnLXWttV0rdB/wP1xltb50u2EX7FVc3sbmgik35VWzbX0CfwixSq/cytOIIV5Q1t73drgiGingHteFWYiJg+KA0MhInQNwY6JcBvsGefSIXMC+Tgb5BPvQN8gGCYGAUMMLTZYleqFOaa1rrpcDSztj3hUJrzcGKRjblV7Ep38LuffuIKP2KtKr9TCgv45ZyK0btOmPlaCQUDbUTGNHKoJg+pAwaD/HjIW4sRA0Dg/HMBxRC9CryXrybcDg1uUfr3GFexb7c7cSXb2C4JY8ryiq4u9LVLLca4WhfTWGGjfCwFob0j2T4wEkQPwH6T4Dg+F53HrYQ4uxJuHtIi83BzpJaNuVXsTm/kuL9m0iqyGa4JZ85R6uJrnEA7v7yaE1BopWo8FaGDujPiKRJ0H889J8oY3gIIU5Kwr2LVDVa2VpUzeaCarIPltCUl8WQ6t0MqyzmrrI6QhpcH342+EBFPydFQ6zEhltJHTiIjMRJriCPHyunpwkh2kXCvRPYHE72Ha1nS1E1WwqryDuQQ3BJDoNrDjG0opzLy1rxdn/4WRUINf0cNEdY6R+pGTVkJIaEia4xsGNGgZefZ5+MEKJH6tnhXpwN+VmQMMk1i7rR3OUltNod7D/awO7SWnYWV5F3cDvGwmwSqw8xuLqM2eVNhLlb5XYDlEdqjqTYCQ5rJbl/GCmDx0JsputMlqjh8uGnEKJD9Ohw/3rJKxSu/xrvsJfpG+ZkcHwq4YlTof8kiMlwDQHbQVpsDgotTRysaGB/WTUHC/fQmL8Dv6P76V93hP41NXyv0kpQ0zePqQzRNEY7sIXZiI7yZvDgFFITx7hmf4/NBL/QDqtPCCGO16PD/WCRD6OyTRi062nsDTxEWeghrMGvYwpy4h3sh294GIH94giOHkhY5BCCI4Zh7hMBZl+02RerE5paHTTZHByprSPfUkZpWTE1R4poKS9BVR/Fu7qMwDoLoU2NhNfZmFjj5LKWb+qwmqA6VFMX76AlxE5EdCADBg8jJTEDokdA3zQIiPLQqySEuBD16HCPue23vDYoD+eB7QQVbyXeUkB8nYXk4ma87UbAhmuY16NoNlNshv3eru4Rh/tSbuV0Xb5tcoKP1XUJ9/CTHMtmdI0M2BKgqUl20hTiRWBEIHFJAwkbOBIVORjCB7pmefdA95AQQhyvR4f7jJQoZqREARMBqG+xUVzdTLGlkYr8w7SUFeGsLERZjmJsKMOrqRJzcz0mhx2T04nR6UQZNK0GwKCp9TZi9vXGx9+XPsGB+IUEERAaTki/eHzjBqMC+0FAX9cZK3IuuRCiG+vR4f5tAT5mUqLNpEQHwvBoYIynSxJCCI+QEYSEEKIXknAXQoheSMJdCCF6IQl3IYTohSTchRCiF5JwF0KIXkjCXQgheiEJdyGE6IU6fILscypCqQqgsIsPGw5UdvExuyt5LU4kr8eJ5PX4Rnd7LfprrSNOtqJbhLsnKKWyTzVr+IVGXosTyetxInk9vtGTXgvplhFCiF5Iwl0IIXqhCznc53m6gG5EXosTyetxInk9vtFjXosLts9dCCF6swu55S6EEL2WhLsQQvRCF3S4K6WeV0rlKqV2KKUWKaWCPV2Tpyil5iildiulnEqpHnGqV2dQSl2ulNqnlMpTSj3m6Xo8SSn1llKqXCm1y9O1eJpSKk4ptUoptcf9d/KAp2s6kws63IEvgOFa6zRgP/C4h+vxpF3ALCDL04V4ilLKCPwNuAIYCnxfKTXUs1V51Hzgck8X0U3YgV9orYcC44B7u/vvxgUd7lrr5Vpru/vuBiDWk/V4ktZ6r9Z6n6fr8LAxQJ7W+pDW2gq8D1zj4Zo8RmudBVR5uo7uQGt9RGu9xX27HtgLxHi2qtO7oMP9W34EfO7pIoRHxQCHj7tfTDf/AxZdTymVAIwENnq2ktPrVRNkn4xSagXQ9ySrfqW1Xuze5le43na905W1dbX2vBZCiP/fzh2iVBSEYRh+36BJd6DBIK5BbGoQEcFmEQSrweQyTAaLUQRBg2AQF2CwWMQNXDdgsP6Ge4PFq8mRud/Tzkz5mPBxOP9wvqfOANfAUVW9t84zTvflXlXr4/bVfWALWKvOL/3/dBbBGzD/5XlutBaBOsWw2C+q6qZ1np9M9GcZdQM4Brar6qN1nmjuCVhUF9RpYBe4bZwp/gFV4Bx4raqT1nl+Y6LLHTgFZoEH9Vk9ax2oFXVHHQDLwJ163zrTXxsN1w+Be4YDs6uqemmbqh31EngEltSBetA6U0MrwB6wOuqKZ3Wzdahx8vuBiIgOTfqbe0REl1LuEREdSrlHRHQo5R4R0aGUe0REh1LuEREdSrlHRHToE9YPAsF2FzVCAAAAAElFTkSuQmCC\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "h = 0.1\n",
        "fig, bx = plt.subplots()\n",
        "bx.axhline(y=0, color='k')\n",
        "\n",
        "x = np.linspace(-2.2, 2.3, 50, endpoint=True)\n",
        "y = forward_diff(p, h, x)\n",
        "bx.plot(x, y, label='Forward; h=0.1')\n",
        "y = backward_diff(p, h, x)\n",
        "bx.plot(x, y, label='Backward; h=0.1')\n",
        "y = central_diff(p, h, x)\n",
        "bx.plot(x, y, label='Central; h=0.1')\n",
        "\n",
        "data2 = p_prime.linspace(domain=[-2.2, 2.3])\n",
        "bx.plot(data2[0], data2[1], label='actual')\n",
        "\n",
        "bx.legend()\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": false,
        "editable": false,
        "id": "QAiVfHxCniIw",
        "nbgrader": {
          "cell_type": "code",
          "checksum": "a68d54e8ab1303582d48ca0a484c013d",
          "grade": true,
          "grade_id": "plt4_test",
          "locked": true,
          "points": 2,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "outputId": "9c5ffca3-4e1d-4fd4-f8a7-967a36aefc9c"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7fc007430750>"
            ]
          },
          "metadata": {},
          "execution_count": 168
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "h = 0.01\n",
        "fig, bx = plt.subplots()\n",
        "bx.axhline(y=0, color='k')\n",
        "\n",
        "x = np.linspace(-2.2, 2.3, 50, endpoint=True)\n",
        "y = forward_diff(p, h, x)\n",
        "bx.plot(x, y, label='Forward; h=0.01')\n",
        "y = backward_diff(p, h, x)\n",
        "bx.plot(x, y, label='Backward; h=0.01')\n",
        "y = central_diff(p, h, x)\n",
        "bx.plot(x, y, label='Central; h=0.01')\n",
        "\n",
        "data2 = p_prime.linspace(domain=[-2.2, 1.8])\n",
        "bx.plot(data2[0], data2[1], label='actual')\n",
        "\n",
        "bx.legend()\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": false,
        "editable": false,
        "id": "-ZUdiK_sniIw",
        "nbgrader": {
          "cell_type": "code",
          "checksum": "4d802ba0cb9f6582992226c4898ab0af",
          "grade": true,
          "grade_id": "plt5_test",
          "locked": true,
          "points": 2,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "outputId": "e61714d0-c130-4860-e45a-5f086ee01907"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7fc0073e0a10>"
            ]
          },
          "metadata": {},
          "execution_count": 169
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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vttVaM2fOHB544IGzxqelpeHn52d/7u3tTXl5+UWXX7M98qXaKAshoLiimpf+t49FOzLpGRLEZ/fG0b1D422jUFdy9c5VGDVqFJWVlfYvPgHYtWsXQUFBfPTRR5SUlACQlZXFyZMnL7mswMDAi3bJhNq3URbCE20+nMe4tzewZGcmD1/Xha/+7xoJ/Mtw6z19Z1FKsXTpUh599FFef/11/P39MRgMvP3227Rs2ZIhQ4YA0Lx5c/7zn/9c8gqcM99re+ZE7rlq20ZZCE9SUW1m7sqDfPjjUQzBTVn04FD6R3pGG4W6ktbKQtapcCu7Mwt5bGESqSdLuHNwJHNuiKZpE9l/relSrZUve3hHKeWvlNqqlEpWSu1VSr1oGx+llNqilEpVSi1QSjWxjfezPU+1TTfUWNYc2/iDSik5IymEqLVqs4V3Vqcw8e8bKakw8ck9A3n55t4S+FeoNmurEhiltS5RSvkCPyqlvgVmAm9prb9QSv0D+A3wvu3naa11F6XUNOB1YKpSqicwDegFdARWK6W6aa3NDvhcQohG5HBuCTMXJJGcWciEuI68NL63R99VWxeX3dPXViW2p762hwZGAWcuYfkYuNk2PMH2HNv00cp6V8QE4AutdaXW+iiQCgy8mqJd+ZCUu5F1KVyZxaKZv/EoN7yzgfT8Mv52W1/emdZXAr8OavV3kVLKG9gBdAHeAw4DBVprk22WTCDUNhwKZABorU1KqUIg2Db+pxqLrfmamu91P3A/QERExHm1+Pv7k5eXR3BwsNxhV0daa/Ly8vD3l1vThes5XlDOrMXJbEzN47rubXn9lhjaBcnval3VKvRth2DilFItgaVAtKMK0lrPA+aB9UTuudPDwsLIzMwkNzfXUSV4FH9/f8LCwpxdhhB2WmuW/pzFC8v3YrZoXp3Uh2kDpI1CfbmiMyBa6wKl1FpgCNBSKeVj29sPA7Jss2UB4UCmUsoHaAHk1Rh/Rs3X1Jqvry9RUVFX+jIhhBvIK6nkmaV7+G5vNvGRrXhjSiyRwc0u/0JRa7W5eqetbQ8fpVQAMBbYD6wFbrXNNh1YZhtebnuObfoabT1wvByYZru6JwroCmytrw8ihHBvq/flkPD2BtYcOMlT10ez4IEhEvgOUJs9/RDgY9txfS9godb6a6XUPuALpdQrwM/Ah7b5PwQ+VUqlAvlYr9hBa71XKbUQ2AeYgP+TK3eEEMUV1bzy9X4WbM+gR0gQ/7l3INEdgpxdVqPldjdnCSEaj5+O5PHEomSOF5Tz4IjO/H5MV/x85Dsk6upSN2fJXQ1CiAZXUW3mjcSD/OvHo0S0bsqiB4fQP7K1s8vyCBL6QogGtSerkMcWJJFysoQ7Bkcw5/oeNPOTKGoosqaFEA3CZLbw/rrDvPN9Cq2bNWH+3QMY2b2ds8vyOBL6QgiHO5JbwsyFySRlFHBTbEdentCLlk2bOLssjyShL4RwGItF858t6fxpxX78fLz566/7Mj62o7PL8mgS+kIIhzhRWM7sxbvYkHKKEd3a8udbY2gvbRScTkJfCFGvtNYsSzrOc8v2YDJr/jixN7cNjJA2Ci5CQl8IUW/yS6t49qvdrNidTf/IVrwxORZDG7mr1pVI6Ash6sX3+3N4csluCsureHJcNPcP74S3l+zduxoJfSFEnZRUmnjl6318sS2D6A6BfHLPQHp2lDYKrkpCXwhx1bYezefxRUlknra2UXhsrLRRcHUS+kKIK1ZRbeatVYeYt+EI4a2asvCBIQwwSBsFdyChL4S4InuPFzJzQTIHc4q5bVAEz9wgbRTcifxLCSFqxWS28M/1R3h79SFaNW3Cv2cM4LpoaaPgbiT0hRCXdfRUKTMXJvHzsQJujAnhlQm9adVM2ii4Iwl9IcRFaa35z0/p/GnFAXy9lbRRaAQk9IUQF5RdWMGsxclsSDnFsK5tmHtrLB1aSBsFdyehL4Q4i9aa5cnHee6rPVSbNS/f3Js7BkkbhcZCQl8IYXe6tIpnl+3hm10n6BvRkjenxBElbRQaFQl9IQQAaw+cZPaSXRSUVTEroTsPDO+Ej7eXs8sS9UxCXwgPV1pp4pVv9vP51mN0bx/I/LsH0KtjC2eXJRxEQl8ID7YtLZ/HFyaTcbqMB4Z34rGx3fD3lTYKjZmEvhAeqNJk5s1Vh5i3/ghhrQJYcP8QBkZJGwVPIKEvhIfZd7yImQuTOJBdzK8HhvPMjT1pLm0UPIb8SwvhIcwWzT/XH+atVYdoEdCEj2bEMyq6vbPLEg1MQl8ID5B2qpTHFyWzI/00N/TpwCs396G1tFHwSBL6QjRiWms+23KMP36zH19vxTvT4hgf21FutPJgEvpCNFI5RRXMXryLHw7lcm2XNsydHENIiwBnlyWcTEJfiEbof8nHefarPVSazLw0oRd3DIrES76vViChL0SjUlBWxXPL9vK/5OPEhbfkzSmxdGrb3NllCRcioS9EI7Hu4ElmL95FfmkVTxi78eCIztJGQZxHQl8IN1daaeJPK/bz2ZZjdGvfnI9mDKB3qLRREBcmoS+EG9uRns/Mhckcyy/j/uGdmCltFMRlSOgL4YYqTWbeXp3CP384TMeWAXxx32AGdQp2dlnCDUjoC+Fm9p8o4rEF1jYKU+PDefZXPQj093V2WcJNSOgL4SbMFs0HG47wZuIhggJ8+Ndd8YzpKW0UxJWR0BfCDaTnlfL4wmS2p59mXK8O/HFib4Kb+zm7LOGGJPSFcGFaaz7fmsEr3+zD20vx1tRYbo4LlTYK4qpJ6Avhok4WVTB7yS7WHczlmi7BzL01lo4tpY2CqJvL3rmhlApXSq1VSu1TSu1VSv3eNr61UmqVUirF9rOVbbxSSv1VKZWqlNqllOpXY1nTbfOnKKWmO+5jCeHevt51HOPb6/npSB4vju/Fp/cMksAX9aI2e/om4HGt9U6lVCCwQym1CpgBfK+1fk0p9RTwFPAkcD3Q1fYYBLwPDFJKtQZeAOIBbVvOcq316fr+UEK4q4KyKp5ftpflyceJtbVR6CxtFEQ9umzoa61PACdsw8VKqf1AKDABGGmb7WNgHdbQnwB8orXWwE9KqZZKqRDbvKu01vkAtg3HOODzevw8Qrit9YdymbU4mbySKmaO7cZvR0obBVH/ruiYvlLKAPQFtgDtbRsEgGzgzLVjoUBGjZdl2sZdbPy573E/cD9ARETElZQnhFsqqzLx6ooDfPpTOl3aNedfdw2gT5i0URCOUevQV0o1B5YAj2qti2pePaC11kopXR8Faa3nAfMA4uPj62WZQriqHemneXxhEun5Zdx7bRRPJHSXNgrCoWoV+kopX6yB/5nW+kvb6BylVIjW+oTt8M1J2/gsILzGy8Ns47L45XDQmfHrrr50IdxXlcnCO98f4v11hwlpEcB/7x3MkM7SRkE4Xm2u3lHAh8B+rfWbNSYtB85cgTMdWFZj/F22q3gGA4W2w0ArAaNSqpXtSh+jbZwQHuVAdhET3tvIe2sPc0u/ML57dJgEvmgwtdnTvwa4E9itlEqyjXsaeA1YqJT6DZAOTLFNWwHcAKQCZcDdAFrrfKXUy8A223wvnTmpK4QnMFs0/9pwhDdsbRQ+uCuesdJGQTQwZb3IxjXFx8fr7du3O7sMIersWF4Zjy9KYlvaaRJ6tedPE/tIGwXhMEqpHVrr+AtNkztyhXAgrTULtmXw8tf78FKKNybHMqmftFEQziOhL4SDnCyu4Kklu1lz4CRDOwczd3IsoXJXrXAyCX0hHGDF7hM8s3Q3ZVVmXripJ9OHGPDykr17cWlmi5mdJ3eSmJZIZFAkd/S8o97fQ0JfiHpUWFbNC8v38FXScWLCWvDmlFi6tAt0dlnChZ0J+pVpK/n+2PecKj+Fv7c/06KnOeT9JPSFqCcbUnKZtWgXuSWVPDqmK/93XRd8pY2CuACzxcyOnB0kpieyOn01eRV5+Hv7MyxsGEaDkeGhw2nq29Qh7y2hL0QdlVWZeO3bA3yyOZ3ObZsx766hxIS1dHZZwsWcCfqVaStZfWw1+RX5BPgEMCzUGvTDQoc5LOhrktAXog52HjvN4wuTOXqqlHuuiWL2OGmjIH5hspise/RpiecFfYIhgWtDr22QoK9JQl+Iq1BlsvDumhTeW5tqbaNw3yCGdm7j7LKECzBZTGzP2U5iWiLfH/veHvTDw4ZjjDQyLGwYAT7Ou4pLQl+IK3Qop5jHFiSx93gRt/YP4/mbehLk7+vssoQTmSwmtmVvIzE9kTXH1tiDfkTYCIwGI9eGXuvUoK9JQl+IWjJbNB/9eJS5iQcJ9PPhn3f2J6FXB2eXJZzEZDGxNXsriWnWoD9deZoAnwBGho3EaDByTeg1LhP0NUnoC1ELGfllPL4oma1H8xnbsz2vTupDG2mj4HFqBv33x76noLKApj5NGRE+goTIBK4JvQZ/H39nl3lJEvpCXILWmkXbM3nxf3tRSjH31hhu7R8mbRQ8SLWlmm0nrIduzgt6QwLXdHT9oK9JQl+IizhZXMHTX+5m9f6TDO7Umr9MjiWsVcNeaSGco9pSzdYTW+1BX1hZSDPfZvZj9O4W9DVJ6AtxAd/uPsHTS3dTWmXmuV/15O6h0kahsau2VLPlxBbrMfqMNfagHxk+EmOk9Ri9n7f7H9KT0BeihsLyal5cvpcvf86iT6i1jULX9tJGobGqNlfz04mf7FfdFFUV0dy3uT3oh4YObRRBX5OEvhA2P6acYtbiZE4WV/L70V15eJS0UWiMqs3VbD6xmcS0RNZmrLUH/XXh12E0GBnacShNvJs4u0yHkdAXHq+8yszr3x1g/qY0OrVtxpcPDSU2XNooNCZngn5l2krWZqyluKqYQN9Arou4DmOkkSEdhzTqoK9JQl94tKSMAmYuTOJIbikzhhp4clw0AU2kjUJjcKmgTzAkMDhksMcEfU0S+sIjVZstvLsmlffWptIu0I/P7h3ENV2kjYK7qzJXsfn4ZhLTE1l7bC3F1cUENgnkunDPDvqaJPSFx0nJKeaxhUnsySpiUr9QXripFy0CpI2Cu6oyV7Hp+CYS0xJZl7HOHvSjIkZhNBgZEjIEX2/59z1DQl94DItF89HGo/x55UGa+/nwjzv6Ma53iLPLEleh0lzJpqxNJKZbg76kuoSgJkGMjhyNMdLI4JDBEvQXIaEvPEJGfhlPLEpmy9F8xvRox6uTYmgb2LguxWvszgT9yvSVrMtYR2l1KUFNghgbORajwcigDoMk6GtBQl80alprFu3I5KX/7QPgz7fGMFnaKLiNSnMlG7M22vfoS6tLaeHXAmOkkQRDAgNDBuLrJUF/JST0RaOVW1zJnC93s3p/DoOirG0UwltLGwVXV2mu5MesH0lMS+SHzB/sQZ9gSMAYaZSgryMJfdEofbcnm2eW7qa40sSzN/bgnmuipI2CC6swVbAxayMr01fyQ8YPlJnKaOnXknGGcRgjjQwIGSBBX08k9EWjUlRRzYvL97FkZya9Ogbx+dQ4ukkbBZdUYao4a4/+TNBfH3U9RoORAR0k6B1BQl80GptST/HEomRyiit5ZFQXHh7VlSY+0kbBlZSbys8K+nJTOa38WnFDpxuse/QdBuDjJbHkSLJ2hdurqLa2Ufj3xjSi2jRj8YND6BvRytllCZszQb8ybSXrM9dTbiqntX9rftXpVxgNRuLbx0vQNyBZ08KtJdvaKBzOLWX6kEieur6HtFFwAeWmcjZkbiAxPfG8oE8wJNC/fX8JeieRtS7cUrXZwt/WpPK3tam0be7Hp78ZyLCubZ1dlkcrqy5jQ9YGEtMS2ZC1wR70N3W6CaPBKEHvIuRfQLid1JPFPLYgmd1ZhUzsG8ofxksbBWcpqy5jfdZ6EtMS+THrR3vQj+88HmOkNei9veQvL1cioS/chsWimb8pjde/O0DTJt78/fZ+3NBH2ig0tLLqMtZnricxPZENmRuoMFcQ7B/M+M7jSTAk0K9dPwl6FyahL9xCVkE5TyxMZvORPEZHt+PVW/rQLtA9v6PUHZVVl/FD5g/2PfoKcwVtAtpwc5ebMRqMEvRuREJfuDStNUt2ZvHi8r1YtOb1W/owJT5c2ig0gJpBvyFrA5XmSnvQJxgS6NuurwS9G5LQFy7rVEklT2sMGTsAABXESURBVH+5m8R9OQw0WNsoRARLGwVHKq0u5YeMH0hMt+7RV5oraRvQlkldJ2GMNErQNwIS+sIlJe7NZs6XuymuMPH0DdH85tpOeEsbBYcorS5lXcY6EtMS2Xh8oz3ob+l6C0aDNei9lNzk1lhI6AuXUlRRzUv/28fiHZn0DAniv/fF0b2DtFGobyVVJazLtAV91kaqLFW0C2jHrd1uxRhpJK5dnAR9IyWhL1zGpsOnmLVoFycKy3n4ui48MlraKNSnkqoS1masJTE9kU1Zm6xB37QdU7pPwWgwEts2VoLeA0joC6erqDYzd+VBPvzxqLWNwkND6SdtFOpFcVWx9dBNunWPvtpSTfum7ZnSfQoJhgRi2sZI0HuYy4a+Uuoj4FfASa11b9u41sACwACkAVO01qeV9ZKKd4AbgDJghtZ6p+0104FnbYt9RWv9cf1+FOGOdmcW8tjCJFJPlnDXkEieuj6apk1kX6Qu7EFvO0Z/Juindp8qQS9qtac/H/gb8EmNcU8B32utX1NKPWV7/iRwPdDV9hgEvA8Msm0kXgDiAQ3sUEot11qfrq8PItxLtdnC39ce5t01KbRp7scn9wxkeDdpo3C1iqqK7EG/6fgmqi3VdGjWgWnR0zBGGiXohd1lQ19rvV4pZThn9ARgpG34Y2Ad1tCfAHyitdbAT0qplkqpENu8q7TW+QBKqVXAOODzOn8C4XYO55Ywc0ESyZmFTIjryEvje9OiqbRRuFJFVUWsPWY7Rn98EyaLiZBmIfw6+tcYDUb6tOkjQS/Oc7V/R7fXWp+wDWcD7W3DoUBGjfkybeMuNv48Sqn7gfsBIiIirrI84YosFs0nm9N49dsDBDTx5m+39eVXMR2dXZZbKawstJ6MTUtk84nN9qC/Pfp2e9DLjWviUup88FRrrZVSuj6KsS1vHjAPID4+vt6WK5zreEE5sxYnszE1j+u6t+X1W2JoFyRtFGqjsLKQNcfWkJieyE8nfsJkMdGxWUfu6HEHxkgjvdv0lqAXtXa1oZ+jlArRWp+wHb45aRufBYTXmC/MNi6LXw4HnRm/7irfW7gRrTVLf87ihWV7MWvNq5P6MG2AtFG4nLOC/vhPmLSJ0Oah3NnjTowGI72Ce8k6FFflakN/OTAdeM32c1mN8Q8rpb7AeiK30LZhWAn8SSl15jo8IzDn6ssW7iCvpJJnlu7hu73ZDDC04o3JcdJG4RLOBP3K9JVsOb7ll6DveScJhgR6BveUoBd1VptLNj/HupfeRimVifUqnNeAhUqp3wDpwBTb7CuwXq6ZivWSzbsBtNb5SqmXgW22+V46c1JXNE6r9uUw58tdFJWbmHN9NPcOkzYKF1JQUcCajDUkpiWy5USNoO91JwmREvSi/inrhTauKT4+Xm/fvt3ZZYgrUFxRzctf72Ph9kx6hATx1tRYojsEObssl1JQUcD3x74nMT2RrSe2YtImwpqHYTQYMRqM9GwtQS/qRim1Q2sdf6FpcheMqDc/HcnjiUXJHC8o57cjO/P7MV3x85GOjACnK05bgz4tka3ZWzFrM+GB4UzvNR2jwUiP1j0k6EWDkNAXdVZRbeaNxIP868ejRLRuyqIHh9A/srWzy3K6CwV9RGAEd/e+G2OkkejW0RL0osFJ6Is62ZNVyGMLkkg5WcIdgyOYc30Pmvl57q9VfkW+Pei3ZW87K+gTDAl0b9Vdgl44lef+7xR1YjJbeH/dYd75PoXWzZow/+4BjOzeztllOUV+RT6r01eTmJ7I9uztmLWZyKBI7ul9D0aDUYJeuBQJfXHFDueWMHNhMskZBYyP7chLE3rRsmkTZ5fVoPLK837Zo8/ZhkVbMAQZuKf3PSQYEujWqpsEvXBJEvqi1iwWzac/pfPqt/vx8/Hm3V/35aZYz2mjcKr8FN+nW6+62Z6z3R709/a5F2OkUYJeuAUJfVErxwvKmb14Fz+mnmKkrY1Cew9oo3Cq/JT90M2OnB1YtIWoFlHc1+c+jAYjXVt2laAXbkVCX1yS1pplScd5btkeTGbNHyf25raBEY066GoG/fbs7Wg0nVp04v6Y+zFGGunSskuj/vyicZPQFxeVX1rFs1/tZsXubPpHtuKNybEY2jRzdlkOcar8FKvSV5GYZt2jPxP0D8Q+QEJkAl1adXF2iULUCwl9cUHf78/hySW7KSyv4slx0dw/vPG1Ucgty7UGfXoiO3N2otF0btGZB2MftO7RS9CLRkhCX5ylpNLEK1/v44ttGUR3COSTewbSs2PjaaNwsuykfY/+55M/o9F0admFh2Ifwmgw0rllZ2eXKIRDSegLuy1H8nh8UTJZBeU8OKIzj41tHG0UckpzWH1s9flBH/cQCZEJdGrZydklCtFgJPQFFdVm3lx1iA82HCG8VVMWPjCEAQb3bqMgQS/EhUnoe7g9WYXMXJjEoZwSbhsUwTM3uG8bhezSbPtVNz+f/BmArq268tu432I0GOnUQoJeCPf83y3qzGS28M/1R3h79SFaNW3Cv+8ewHVu2EYhuzTbfow+KTcJgG6tuvFw3MMYDUaiWkQ5uUIhXIuEvgc6eqqUmQuT+PlYATfGhPDKhN60auY+bRSyS7NJTEskMT2R5NxkALq36s7v+v4OY6QRQwuDcwsUwoVJ6HsQrTX/+SmdP604gK+34q+/7st4N2mjcKLkBInp1qDflbsLgOjW0TzS9xHGRo6VoBeiliT0PUR2YQWzFiezIeUUw7q2Ye6tsXRo4dptFI6XHLcfutl1yhr0PVr34Pf9fs/YyLFEBkU6uUIh3I+EfiOntWZ58nGe+2oP1WbNyzf35o5BrttG4VJBb4w0EhEU4eQKhXBvEvqN2OnSKp79ag/f7D5B34iWvDkljigXbKOQVZLFqjTrnbG7T+0Gfgn6hMgEwoPCnVyhEI2HhH4jteaAtY1CQVkVsxK688DwTvh4ezm7LLuskizrydi0RPbk7QGgZ3BPHu33KMZIowS9EA4iod/IlFaaeOWb/Xy+9Rjd2wcy/+4B9OrYwtllAZBZnGk9GZuWyN68vQD0Cu7FY/0fY2zkWMIDJeiFcDQJ/UZkW1o+jy9MJuN0GQ+M6MTMsd2c3kYhozjDfnnlvrx9APQO7s3M/jMZGzmWsMAwp9YnhKeR0G8EKk3WNgrz1h8hrFUAC+4fwsAo57VRyCjKYGX6ShLTEtmfvx+APm368Hj/xxlrGEto81Cn1SaEp5PQd3P7jhcxc2ESB7KL+fXAcJ65sSfNndBGQYJeCPcgoe+mzBbNP9cf5q1Vh2gR0ISPZsQzKrp9g9ZwrOiY/Rj9maCPaRPDE/FPMDZyLB2bu8eNX0J4Egl9N5R2qpTHFyWzI/00N/TpwCs396F1A7VRSC9Ktx+jP5B/AICYttagN0YaCWke0iB1CCGujoS+G9Fa89mWY/zxm/34eivemRbH+NiODr/RKq0wzb5Hf/D0QQBi28YyK34WYyPHStAL4UYk9N1EdmEFs5fsYv2hXIZ1bcOfb40hpEWAw97vaOFR+x79odOHAIhrG8fsAbMZGzmWDs06OOy9hRCOI6HvBs60Uag0mXl5Qi/uGBzpkL17CXohGj8JfRdWUGZto/D1rhPEhbfkzSmxdGrbvF7f40jhEXvQp5xOAaBvu748OeBJxkSOkaAXopGR0HdR6w6eZPbiXeSXVvGEsRsPjuhcb20UjhQcsV9emVqQikLRt11fnhr4FGMixtC+WcNeBSSEaDgS+i4kr6SSpIwCvtuTzaIdmXRr35yPZgygd2jd2ygcLjhs36M/N+jHRo6lXVP3+9YsIcSVk9B3kopqM3uPF5GUUWB7nCYjvxwAHy/FfcOieNzYHX/fq2+jkHo61X7VzeHCwygU/dr3Y87AOYyJHCNBL4QHktBvABaL5mheKUnHCuwhv/9EESaLBqBjC3/iIlpy5+BI4sJb0Ts0iKZNru6fJvV0qv3QzZHCIygU/dv35+nopxkTMYa2TdvW50cTQrgZCX0HyC+tIinjNEnHCvg5o4DkjAKKKkwANGviTUxYS+4b3om48Jb0DW9Ju6Cr/wYrrTWpBb/s0dcM+mnR0yTohRBnkdCvo0qT7TBNjb34Y/llAHgp6NY+kBtjQogLb0lceCu6tGuOt1fdLrfUWpNSkGI/Rn+08Cheyov+7fvz6+hfMyZyDG0C2tTHxxNCNDIS+legsLyaAyeK2H+iiP0nitmfbR2uNlsP03QI8icuvCW3DYogLrwlfUJb0Kyemp9prTl0+pB9jz6tKA0v5UV8+3huj76d0ZGjJeiFEJcloX8BFosmPb/MFu6/hHxWQbl9ntbNmhDdIZB7ro2ir20vvr6/aPxM0K9MW8mq9FX2oB/QfgB39ryTURGjJOiFEFekwUNfKTUOeAfwBv6ltX6toWs4Q2tNTlElh3KKOZRTTEpOCYdOFnMwu5iyKjMA3l6KTm2a0S+yFbcPjqBHSBA9Q4JoF+hXr3fFmi1mSqpLKKku4VT5KX7I+OHsoO9gDfrREaMJDgiut/cVQniWBg19pZQ38B4wFsgEtimllmut9znyfc0WzfGCclJPlpB6soTDuSWknCwhJafYfoIVILhZE7q2b86U+HB6hgTRIySIru2bX/aySZPFRElVCcXVxZRUWYO7uKr4l5/njDszb2lVqf01Zaays5YpQS+EcASltW64N1NqCPAHrXWC7fkcAK31qxeaPzAwUPfv3/+K38erhR9BfXzI9QomzzsYc5NmoLwADcqCMlfgbSrFx1SMl6kUL3MJ3uYyFNWgQHtr8Lb+1D6/DNvH1Rz21eBbi6JMoKoUqkrhVe1lH1bV6rxhryovfHJ88Kp0nS8yF0K4jx9++GGH1jr+QtMa+vBOKJBR43kmMKjmDEqp+4H7Afz8/K7qTdq3rWBP13zgGL5cOpMttofpzIAGZVIoswIzKHON4WqFqlBnTzedHdpeVV4XDnOLY9sfCyFEbbjciVyt9TxgHkB8fLxet27dFS+jvDSP3LQN+BamowqPoQoyUKfT8CrIwNtUgRcaLw0+ygufwFC8W0Xg1doArQzQ0gAtw6FFGASGgJdzv1hcCCGu1KXONzZ06GcB4TWeh9nG1auAZsFE9Lr5/AkWC5TkQP4ROH0UTqfD6TQoSIeUVdZpNSlvCAr9ZSPQIgxahNsetud+9dv1UgghHKmhQ38b0FUpFYU17KcBtzXYu3t5QVCI9WG45vzpVWVQcAwKM6Eww/bIhIIMSN8MRVmgzWe/xq8FBLaH5u0hsMMvPwNDzh7nFwgO/oYrIYS4nAYNfa21SSn1MLAS6yWbH2mt9zZkDZfUpCm0i7Y+LsRihuITv2wICo9Bcbb1UZIDGVutP00V57/Wt+k5G4YQ28aiQ42fHSCglWwchBAO06BX71yp+Ph4vX37dmeXcWW0hopC24YgG4pzzv9ZfMK6cagqOf/13k2sGwXfAOuwt6/tZ83hC4270uErfJ2Xj2yMhHATSimXuXqn8VMKAlpaHxf7i+GMyhJr+NfcQBSfgNJcqC4HczWYq2yPatu4qhrjz5lurgJzpeM+W31uROp1A3buBkpOvgtxMRL6zuTX3PoI7lx/y9TaehjqvI1BXYav8HWmKusG7dzplgsszxGUVx03Lg7YEJ077GV77iX3YoiGJaHf2CgF3j7WB02dXc2laQ0WU8NsiC62jOpy6+G4y81rMV3+81wN5X0VGx1HbpQuMV0O7zUKEvrCeZSyBYsv0MzZ1VyaxXLhv1QcOnzOuKqSy89rqgQcdJ7Oy9EbpXo8vCcbqIuS0BeiNry8wMsPfK7uLvEGVe+H96rAfKG/yC7xuurCWszrqPNPqh43Lg7+q8oJ558k9IVobLy8wSvAegWYK3OJ80+VUFlci8N71Y5ZB5c6/9RtHCT8sd7fUkJfCOEc7nb+qUHOM9UYDurokI8ioS+EEJejFPg0sT7cnFwvJoQQHkRCXwghPIiEvhBCeBAJfSGE8CAS+kII4UEk9IUQwoNI6AshhAeR0BdCCA/i0l+iopTKBdKv8uVtgFP1WI4juVOt4F71ulOtIPU6kjvVCnWrN1Jr3fZCE1w69OtCKbX9Yt8c42rcqVZwr3rdqVaQeh3JnWoFx9Urh3eEEMKDSOgLIYQHacyhP8/ZBVwBd6oV3Kted6oVpF5HcqdawUH1Ntpj+kIIIc7XmPf0hRBCnENCXwghPIhbh75SapxS6qBSKlUp9dQFpvsppRbYpm9RShkavsqz6rlcvTOUUrlKqSTb415n1Gmr5SOl1Eml1J6LTFdKqb/aPssupVS/hq7xnHouV+9IpVRhjXX7fEPXWKOWcKXUWqXUPqXUXqXU7y8wj0us31rW6krr1l8ptVUplWyr98ULzOMyuVDLeus3F7TWbvkAvIHDQCegCZAM9Dxnnt8C/7ANTwMWuHi9M4C/OXvd2moZDvQD9lxk+g3At4ACBgNbXLzekcDXzl6vtlpCgH624UDg0AV+F1xi/dayVldatwpobhv2BbYAg8+Zx5VyoTb11msuuPOe/kAgVWt9RGtdBXwBTDhnngnAx7bhxcBopZRqwBprqk29LkNrvR7Iv8QsE4BPtNVPQEulVEjDVHe+WtTrMrTWJ7TWO23DxcB+IPSc2Vxi/dayVpdhW18ltqe+tse5V6u4TC7Ust565c6hHwpk1Hieyfm/jPZ5tNYmoBAIbpDqzlebegFusf05v1gpFd4wpV2V2n4eVzLE9mf0t0qpXs4uBsB2aKEv1j28mlxu/V6iVnChdauU8lZKJQEngVVa64uuWxfIhdrUC/WYC+4c+o3R/wCD1joGWMUveyOi7nZi7UcSC7wLfOXkelBKNQeWAI9qrYucXc+lXKZWl1q3Wmuz1joOCAMGKqV6O7Oey6lFvfWaC+4c+llAzS1emG3cBedRSvkALYC8BqnufJetV2udp7WutD39F9C/gWq7GrVZ/y5Da1105s9orfUKwFcp1cZZ9SilfLGG6Gda6y8vMIvLrN/L1epq6/YMrXUBsBYYd84kV8oFu4vVW9+54M6hvw3oqpSKUko1wXpCZvk58ywHptuGbwXWaNuZESe4bL3nHLMdj/X4qataDtxlu8pkMFCotT7h7KIuRinV4cxxW6XUQKy/+075j26r40Ngv9b6zYvM5hLrtza1uti6bauUamkbDgDGAgfOmc1lcqE29dZ3LvjU5cXOpLU2KaUeBlZivTLmI631XqXUS8B2rfVyrL+snyqlUrGe5Jvm4vU+opQaD5hs9c5wVr1Kqc+xXpXRRimVCbyA9SQTWut/ACuwXmGSCpQBdzunUqta1Hsr8JBSygSUA9OcuANwDXAnsNt2LBfgaSACXG791qZWV1q3IcDHSilvrBufhVrrr101F6hdvfWaC9KGQQghPIg7H94RQghxhST0hRDCg0joCyGEB5HQF0IIDyKhL4QQHkRCXwghPIiEvhBCeJD/B0K9zX4b+f1nAAAAAElFTkSuQmCC\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "fig, bx = plt.subplots()\n",
        "bx.axhline(y=0, color='k')\n",
        "\n",
        "h = np.array([3.5, 0.55, 0.3, .17, 0.1, 0.055, 0.03, 0.017, 0.01])\n",
        "err = error(p, p_prime, h, 2.0)\n",
        "\n",
        "bx.plot(h, err[0], label='Forward')\n",
        "bx.plot(h, err[1], label='Backward')\n",
        "bx.plot(h, err[2], label='Central')\n",
        "bx.legend()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "id": "Gs3FQ6gGniIw",
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "c9e5886e4a1a0dcc11d7e19c14146fe9",
          "grade": false,
          "grade_id": "cell-1c9064b8444721b5",
          "locked": true,
          "schema_version": 3,
          "solution": false,
          "task": false
        }
      },
      "source": [
        "## Part 2: Richardson Extrapolation\n",
        "---"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "id": "VCFJEL7RniIw",
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "446cd2f0472413299f074ff754675ef8",
          "grade": false,
          "grade_id": "cell-188a9d297b8ffc8e",
          "locked": true,
          "schema_version": 3,
          "solution": false,
          "task": false
        }
      },
      "source": [
        "## Instructions\n",
        "\n",
        "\n",
        "Today's assignment is to:\n",
        "1. Implement Richardson Extrapolation method using Python\n",
        "\n",
        "## Richardson Extrapolation:\n",
        "We used central difference method to calculate derivatives of functions last task. In this task we will use Richardson extrapolation to get a more accurate result.\n",
        "Let,\n",
        "$$ D_h = \\frac{f(x_1+h) -f(x_1-h)}{2h}\\tag{5.1}$$ \n",
        "\n",
        "\n",
        "General Taylor Series formula:\n",
        "$$ f(x) = f(x_1) + f'(x_1)(x - x_1) + \\frac{f''(x_1)}{2}(x - x_1)^2+... $$\n",
        "Using Taylor's theorem to expand we get,\n",
        "\n",
        "\\begin{align}\n",
        "f(x_1+h) &= f(x_1) + f^{\\prime}(x_1)h + \\frac{f^{\\prime \\prime}(x_1)}{2}h^2 + \\frac{f^{\\prime \\prime \\prime}(x_1)}{3!}h^3 + \\frac{f^{(4)}(x_1)}{4!}h^4 + \\frac{f^{(5)}(x_1)}{5!}h^5 + O(h^6)\\tag{5.2} \\\\\n",
        "f(x_1-h) &= f(x_1) - f^{\\prime}(x_1)h + \\frac{f^{\\prime \\prime}(x_1)}{2}h^2 - \\frac{f^{\\prime \\prime \\prime}(x_1)}{3!}h^3 + \\frac{f^{(4)}(x_1)}{4!}h^4 - \\frac{f^{(5)}(x_1)}{5!}h^5 + O(h^6)\\tag{5.3}\n",
        "\\end{align}\n",
        "Subtracting $5.3$ from $5.2$ we get,\n",
        "$$ f(x_1+h) - f(x_1-h) = 2f^{\\prime}(x_1)h + 2\\frac{f^{\\prime \\prime \\prime}(x_1)}{3!}h^3 + 2\\frac{f^{(5)}(x_1)}{5!}h^5 + O(h^7)\\tag{5.4}$$\n",
        "So,\n",
        "\\begin{align}\n",
        "D_h &= \\frac{f(x_1+h) - f(x_1-h)}{2h} \\\\\n",
        "&= \\frac{1}{2h} \\left( 2f^{\\prime}(x_1)h + 2\\frac{f^{\\prime \\prime \\prime}(x_1)}{3!}h^3 + 2\\frac{f^{(5)}(x_1)}{5!}h^5 + O(h^7) \\right) \\\\\n",
        "&= f^{\\prime}(x_1) + \\frac{f^{\\prime \\prime \\prime}(x_1)}{6}h^2 + \\frac{f^{(5)}(x_1)}{120}h^4 + O(h^6) \\tag{5.5}\n",
        "\\end{align}\n",
        "We get our derivative $f'(x)$ plus some error terms of order $>= 2$ Now, we want to bring our error order down to 4.\n",
        "\n",
        "If we use $h, \\text{and} \\frac{h}{2}$ as step size in $5.5$, we get,\n",
        "\\begin{align}\n",
        "D_h &= f^{\\prime}(x_1) + f^{\\prime \\prime \\prime}(x_1)\\frac{h^2}{6} + f^{(5)}(x_1) \\frac{h^4}{120} + O(h^6) \\tag{5.6} \\\\\n",
        "D_{h/2} &= f^{\\prime}(x_1) + f^{\\prime \\prime \\prime}(x_1)\\frac{h^2}{2^2 . 6} + f^{(5)}(x_1) \\frac{h^4}{2^4 . 120} + O(h^6) \\tag{5.7}\n",
        "\\end{align}\n",
        "Multiplying $5.7$ by $4$ and subtracting from $5.6$ we get,\n",
        "\\begin{align}\n",
        "D_h - 4D_{h/2} &= -3f^{\\prime}(x) + f^{(5)}(x_1) \\frac{h^4}{160} + O(h^6)\\\\ \n",
        "\\Longrightarrow D^{(1)}_h = \\frac{4D_{h/2} - D_h}{3} &= f^{\\prime}(x) - f^{(5)}(x_1) \\frac{h^4}{480} + O(h^6) \\tag{5.8}\n",
        "\\end{align}\n",
        "Let's calculate the derivative using $5.8$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "id": "EwMxR-plniIx",
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "5225e4115f21bdcc7141c237dfe0d0d2",
          "grade": false,
          "grade_id": "cell-03b32275bf20e854",
          "locked": true,
          "schema_version": 3,
          "solution": false,
          "task": false
        }
      },
      "source": [
        "## 1. Let's create a function named `dh(f, h, x)`\n",
        "function `dh(f, h, x)` takes three parameters as input: a function `f`, a value `h`, and a set of values `x`. It returns the derivatives of the function at each elements of array `x` using the Central Difference method. This calculates equation $(5.1)$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": false,
        "id": "F6BRYPykniIx",
        "nbgrader": {
          "cell_type": "code",
          "checksum": "ab90e121daa8121cebfdad5227aee5fa",
          "grade": false,
          "grade_id": "cell-69d7eccf1727ad43",
          "locked": false,
          "schema_version": 3,
          "solution": true,
          "task": false
        }
      },
      "outputs": [],
      "source": [
        "def dh(f, h, x):\n",
        "    '''\n",
        "    Input:\n",
        "        f: np.polynomial.Polynonimial type data. \n",
        "        h: floating point data.\n",
        "        x: np.array type data.\n",
        "    Output:\n",
        "        return np.array type data of slope at each point x.\n",
        "    '''\n",
        "    # --------------------------------------------\n",
        "    \n",
        "    return (f(x+h) - f(x-h)) / (2*h)\n",
        "    \n",
        "    # YOUR CODE HERE\n",
        "    # --------------------------------------------"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "id": "QNCZ1QxyniIy",
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "36b3dddc8be0efb9a97fb5768d9d8ced",
          "grade": false,
          "grade_id": "cell-0c13cf39da895e01",
          "locked": true,
          "schema_version": 3,
          "solution": false,
          "task": false
        }
      },
      "source": [
        "## 2. Let's create another funtion `dh1(f, h, x)`.\n",
        "`dh1(f, h, x)` takes the same type of values as `dh(f, h, x)` as input. It calculates the derivative using previously defined `dh(f, h, x)` function and using equation $5.8$ and returns the values."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": false,
        "id": "tM6YOR3hniIy",
        "nbgrader": {
          "cell_type": "code",
          "checksum": "6ae95f8d4c68cb8306001ca5f9752220",
          "grade": false,
          "grade_id": "cell-ed364c63e8c23e35",
          "locked": false,
          "schema_version": 3,
          "solution": true,
          "task": false
        }
      },
      "outputs": [],
      "source": [
        "def dh1(f, h, x):\n",
        "    '''\n",
        "    Input:\n",
        "        f: np.polynomial.Polynonimial type data. \n",
        "        h: floating point data.\n",
        "        x: np.array type data.\n",
        "    Output:\n",
        "        return np.array type data of slope at each point x.\n",
        "    '''\n",
        "    # --------------------------------------------\n",
        "\n",
        "    return  ( (4*(dh(f, h/2, x)))  -  dh(f, h, x) )  / (3)\n",
        "    \n",
        "    # YOUR CODE HERE\n",
        "    # --------------------------------------------"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "id": "Zt4qjdMVniIy",
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "7d794eaafc49abd1e798a85026114d67",
          "grade": false,
          "grade_id": "cell-4eb597d5a4be4420",
          "locked": true,
          "schema_version": 3,
          "solution": false,
          "task": false
        }
      },
      "source": [
        "## 3. Now let's create the `error(f, hs, x_i)` function\n",
        "The `error(f, hs, x_i)` function takes a function `f` as input. It also takes a list of different values of h as `hs` and a specific value as `x_i` as input. It calculates the derivatives as point `x_i` using both functions described in **B** and **C**, i.e. `dh` and `dh1`."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": false,
        "id": "0JyAd9TcniIy",
        "nbgrader": {
          "cell_type": "code",
          "checksum": "57af2549c86921869eab0881ae72fd42",
          "grade": false,
          "grade_id": "cell-4aef4fe1b49d44da",
          "locked": false,
          "schema_version": 3,
          "solution": true,
          "task": false
        }
      },
      "outputs": [],
      "source": [
        "def error(f, hs, x_i):  #Using the functions we wrote dh() my c_diff  and dh1() which is my first order c diff, we find the error through appending their diffrences with Y_actual ny f(x)\n",
        "    '''\n",
        "    Input:\n",
        "        f  : np.polynomial.Polynonimial type data. \n",
        "        hs : np.array type data. list of h.\n",
        "        x_i: floating point data. single value of x.\n",
        "    Output:\n",
        "        return two np.array type data of errors by two methods..\n",
        "    '''\n",
        "    f_prime = f.deriv(1)   #first order derivitive f^1(x)\n",
        "    Y_actual = f_prime(x_i)  \n",
        "\n",
        "    diff_error = []\n",
        "    diff2_error = []\n",
        "\n",
        "    for h in hs: #where h is my loop counter iterating through hs\n",
        "        # for each values of hs calculate the error using both methods\n",
        "        # and append those values into diff_error and diff2_error list.\n",
        "\n",
        "        # --------------------------------------------\n",
        "        \n",
        "        diff_error_h_i =   Y_actual - dh(f, h, x_i)\n",
        "        diff_error.append(diff_error_h_i)  \n",
        "\n",
        "        diff2_error_h_i =   Y_actual  - dh1(f, h, x_i)\n",
        "        diff2_error.append(diff2_error_h_i)  \n",
        "\n",
        "        # YOUR CODE HERE\n",
        "        # --------------------------------------------\n",
        "        \n",
        "    print(pd.DataFrame({\"h\": hs, \"Diff\": diff_error, \"Diff2\": diff2_error}))\n",
        "\n",
        "    return diff_error, diff2_error"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "id": "4mkvTZcqniIz",
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "e1e6e88bb67c3769e422424e3b101ce3",
          "grade": false,
          "grade_id": "cell-ed3e46dc9c1804fd",
          "locked": true,
          "schema_version": 3,
          "solution": false,
          "task": false
        }
      },
      "source": [
        "## 4. Finally let's run some tests\n",
        "function to draw the actual function.\n",
        "\n",
        "### Draw the polynomial and it's actual derivative function"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": false,
        "editable": false,
        "id": "AGdx3IhxniIz",
        "nbgrader": {
          "cell_type": "code",
          "checksum": "98c555e4aede6188c8531178d3013480",
          "grade": false,
          "grade_id": "cell-0da2679376673916",
          "locked": true,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "outputId": "d0e5ad68-6619-436c-8fda-ac46eec090af"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7fc0072f1b90>"
            ]
          },
          "metadata": {},
          "execution_count": 173
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "def draw_graph(f, ax, domain=[-10, 10], label=None):\n",
        "    data = f.linspace(domain=domain)\n",
        "    ax.plot(data[0], data[1], label=label)\n",
        "\n",
        "fig, ax = plt.subplots()\n",
        "ax.axhline(y=0, color='k')\n",
        "\n",
        "p = Polynomial([3.0, 4.0, -14.0, -14.0, 3.0, 1.5])\n",
        "p_prime = p.deriv(1)\n",
        "draw_graph(p, ax, [-2.4, 1.5], 'Function')\n",
        "draw_graph(p_prime, ax, [-2.4, 1.5], 'Derivative')\n",
        "\n",
        "ax.legend()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "id": "EgK7NagOniIz",
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "ebcddecf0623331e7f7147da731c67a8",
          "grade": false,
          "grade_id": "cell-d291e8def1fd93fe",
          "locked": true,
          "schema_version": 3,
          "solution": false,
          "task": false
        }
      },
      "source": [
        "### Draw the actual derivative and richardson derivative using `h=1` and `h=0.1` as step size."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": false,
        "editable": false,
        "id": "qlx3Y_e3niIz",
        "nbgrader": {
          "cell_type": "code",
          "checksum": "fae4bb70108b896682a6950fc66b0f1a",
          "grade": true,
          "grade_id": "cell-a55ea4a66a38f4e1",
          "locked": true,
          "points": 6,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "outputId": "851465d3-d72f-440d-bfdc-42c56b32304e"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7fc0072bfc90>"
            ]
          },
          "metadata": {},
          "execution_count": 174
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "fig, ax = plt.subplots()\n",
        "ax.axhline(y=0, color='k')\n",
        "\n",
        "draw_graph(p_prime, ax, [-2.4, 1.5], 'actual')\n",
        "\n",
        "h = 1\n",
        "x = np.linspace(-2.4, 1.5, 50, endpoint=True)\n",
        "y = dh1(p, h, x)\n",
        "ax.plot(x, y, label='Richardson; h=1')\n",
        "\n",
        "h = 0.1\n",
        "x = np.linspace(-2.4, 1.5, 50, endpoint=True)\n",
        "y = dh1(p, h, x)\n",
        "ax.plot(x, y, label='Richardson; h=0.1')\n",
        "\n",
        "ax.legend()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "id": "KShe_FjPniIz",
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "efabbb55aa021747d9bbdd2c0bfda2be",
          "grade": false,
          "grade_id": "cell-aa732ac513c32594",
          "locked": true,
          "schema_version": 3,
          "solution": false,
          "task": false
        }
      },
      "source": [
        "### Draw error-vs-h cuve"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": false,
        "editable": false,
        "id": "tjnPCoD5niI0",
        "nbgrader": {
          "cell_type": "code",
          "checksum": "c3e2d5ef6eb54fa473d58d8ec6af67f3",
          "grade": true,
          "grade_id": "cell-47f9daf2fe2b2d07",
          "locked": true,
          "points": 6,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 468
        },
        "outputId": "61ad16a2-ddfd-4b15-c5a8-bbe179c160db"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "       h         Diff         Diff2\n",
            "0  3.500 -1082.593750  5.627344e+01\n",
            "1  0.550   -21.312259  3.431484e-02\n",
            "2  0.300    -6.312150  3.037500e-03\n",
            "3  0.170    -2.024253  3.132038e-04\n",
            "4  0.100    -0.700150  3.750000e-05\n",
            "5  0.055    -0.211764  3.431485e-06\n",
            "6  0.030    -0.063001  3.037501e-07\n",
            "7  0.017    -0.020230  3.131795e-08\n",
            "8  0.010    -0.007000  3.746014e-09\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7fc0071fbcd0>"
            ]
          },
          "metadata": {},
          "execution_count": 175
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "fig, ax = plt.subplots()\n",
        "ax.axhline(y=0, color='k')\n",
        "hs = np.array([3.5, 0.55, 0.3, .17, 0.1, 0.055, 0.03, 0.017, 0.01])\n",
        "e1, e2 = error(p, hs, 2.0)\n",
        "ax.plot(hs, e1, label='e1')\n",
        "ax.plot(hs, e2, label='e2')\n",
        "\n",
        "ax.legend()\n"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "name": "19301097_Abdullah_Hasan_Sajjad_Rafi_12_Differentiation_and_Richardson_Extrapolation.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "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": "3.9.1"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}