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    "# CDS: Numerical Methods Assignments\n",
    "\n",
    "- See lecture notes and documentation on Brightspace for Python and Jupyter basics. If you are stuck, try to google or get in touch via Discord.\n",
    "\n",
    "- Solutions must be submitted via the Jupyter Hub.\n",
    "\n",
    "- Make sure you fill in any place that says `YOUR CODE HERE` or \"YOUR ANSWER HERE\".\n",
    "\n",
    "## Submission\n",
    "\n",
    "1. Name all team members in the the cell below\n",
    "2. make sure everything runs as expected\n",
    "3. **restart the kernel** (in the menubar, select Kernel$\\rightarrow$Restart)\n",
    "4. **run all cells** (in the menubar, select Cell$\\rightarrow$Run All)\n",
    "5. Check all outputs (Out[\\*]) for errors and **resolve them if necessary**\n",
    "6. submit your solutions  **in time (before the deadline)**"
   ]
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   "source": [
    "## Runge's Phenomenom\n",
    "\n",
    "Use your own Lagrange interpolation routine to interpolate the function \n",
    "\n",
    "$$f(x) = \\frac{1}{1+25x^2}$$ \n",
    "\n",
    "between $x=-1$ and $x=+1$, using the $x_k$ below. Plot the results and briefly discuss their differences."
   ]
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   "source": [
    "# Import packages here ...\n",
    "\n",
    "# YOUR CODE HERE\n",
    "raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "source": [
    "# Paste your Lagrange interpolation routine here ...\n",
    "\n",
    "# YOUR CODE HERE\n",
    "raise NotImplementedError()"
   ]
  },
  {
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   "metadata": {
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   "source": [
    "### Task 1\n",
    "\n",
    "Use equidistant $x_k = \\frac{2k}{n} - 1$ with $k \\in \\{0, 1, \\dots, n  \\}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "8eb435d8d318786d191583d6f3fcd737",
     "grade": true,
     "grade_id": "cell-943d2b180794f480",
     "locked": false,
     "points": 4,
     "schema_version": 3,
     "solution": true,
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    }
   },
   "outputs": [],
   "source": [
    "# YOUR CODE HERE\n",
    "raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
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     "locked": true,
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   },
   "source": [
    "### Task 2\n",
    "\n",
    "Use Chebychev nodes $x_k = \\operatorname{cos}\\left(\\frac{2k-1}{2n}\\pi \\right)$ with $k \\in \\{1, \\dots, n  \\}$."
   ]
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   "cell_type": "code",
   "execution_count": null,
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     "cell_type": "code",
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     "grade": true,
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     "locked": false,
     "points": 4,
     "schema_version": 3,
     "solution": true,
     "task": false
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   },
   "outputs": [],
   "source": [
    "# YOUR CODE HERE\n",
    "raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
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     "grade": false,
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     "locked": true,
     "schema_version": 3,
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     "task": false
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   },
   "source": [
    "### Task 3\n",
    "\n",
    "Use $n$ randomly chosen points $x_k$."
   ]
  },
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   "execution_count": null,
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     "points": 4,
     "schema_version": 3,
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   "outputs": [],
   "source": [
    "# YOUR CODE HERE\n",
    "raise NotImplementedError()"
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  }
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