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   "source": [
    "# PDE first exercise"
   ]
  },
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   "metadata": {},
   "source": [
    "In this first exercise, we will focus our work on to finite differences and plotting tool."
   ]
  },
  {
   "attachments": {},
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   "metadata": {},
   "source": [
    "First we import our mandatory module"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np # for our mathematics\n",
    "import matplotlib.pyplot as plt # for plotting"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will use the following equation as our reference function and solution:\n",
    "\n",
    "$$ f = sin(20x)+exp(-100x)+100*x^2$$"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this exercise you have to:\n",
    "1. make a function to compute $f$\n",
    "2. make a function which computes the first derivative of $f$ with respect to $x$\n",
    "3. plot the function and its derivatives for $0\\le x \\le 1$ in a subplot (i.e one plot for $f$ and one plot for its derivative)\n",
    "\n",
    "Using a simple `for` loop:\n",
    "\n",
    "4. make a function to compute the first derivative of $f$ using a backward difference\n",
    "5. make a function to compute the first derivative of $f$ using a forward difference\n",
    "6. make a function to compute the first derivative of $f$ using a centered difference\n",
    "7. compute the error commited by the different the finite differences and plot them in a subplot\n",
    "\n",
    "Finally, replicate the question 4. without using a `for` loop"
   ]
  },
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   "metadata": {},
   "source": []
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