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   "source": [
    "# Revision notes and plans"
   ]
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    "## Recent changes\n",
    "\n",
    "- **2023-11-12:** Slight revisions and corrections to\n",
    "{doc}`main/derivatives-and-the-method-of-undetermined-coefficents`,\n",
    "\n",
    "- Added notes on rounding errors, illustrated for IEEE-64 machine arithmetic, in\n",
    "{doc}`main/machine-numbers-rounding-error-and-error-propagation-python`.\n",
    "\n",
    "- Added a draft section {doc}`main/piecewise-polynomial-approximation-and-splines`,\n",
    "based on notes by Stephen Roberts.\n",
    "\n",
    "- Added a draft section {doc}`main/polynomial-collocation-chebychev`,\n",
    "based on notes by Stephen Roberts.\n",
    "\n",
    "- Added first drafts of some sections on multi-step methods:\n",
    "leapfrog, Adams-Bashforth methods and Adams-Moulton methods.\n",
    "\n",
    "- Filled in several incomplete sections on ODE's.\n",
    "\n",
    "- Better labelling of graphs and improved examples on ODE's.\n",
    "\n",
    "- Brought over some revisions from the Julia edition; more to come (see TO DO list)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "268f99f4-7dbc-4538-b0bb-9e0bf0afd371",
   "metadata": {},
   "source": [
    "## To Do"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "146ddd15-4ad2-46bc-98c4-eeb316d402fd",
   "metadata": {},
   "source": [
    "### Content improvements\n",
    "\n",
    "- Add derivation of the formula for the matrix norm $\\| A \\|_\\infty$\n",
    "\n",
    "- Add a derivation of the error bound\n",
    "$\\displaystyle\n",
    "Rel(x_a) := \\frac{\\|x - x_a\\|}{\\| x \\|} \\leq \\|A\\|\\|A^{-1}\\|\\frac{\\|r\\|}{\\|b\\|}\n",
    "$\n",
    "\n",
    "- Expand some sections that are only stubs or very brief; in particular those on\n",
    "  1) Mimimization\n",
    "  2) Multi-step methods for ODEs and determining their stability.\n",
    "\n",
    "- Continue to port updates from the Julia version from {doc}`main/minimization-1D` onwards.\n",
    "\n",
    "- Add more exercises."
   ]
  },
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   "cell_type": "markdown",
   "id": "939ec27b-bad1-4680-b6a8-a5adf33927b9",
   "metadata": {},
   "source": [
    "### Formating and style improvements\n",
    "\n",
    "- **camelCase** everything (e.g. change from *numerical_methods* to *numericalMethods*),\n",
    "except where an underscore is used to indicate a subscript. (For one thing that harmonises with Julia style.)\n",
    "\n",
    "- When using `<br>`, it should appear on its own line, not at end-of-line. (For PDF output; HTML output is more forgiving.)\n",
    "This is relevant to some pseudo-code appearence in the PDF; e.g in {doc}`main/ODE-IVP-1-basics-and-Euler-python`:\n",
    "\n",
    "- Get frontmatter not numbered as a chapter."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "05aedcac-a779-4cc0-a40a-77132f6e85fc",
   "metadata": {},
   "source": [
    "### MyST markdown tips\n",
    "\n",
    "- See https://jupyterbook.org/en/stable/content/myst.html\n",
    "\n",
    "- Move to MyST Markdown notation `{doc}`, `{ref}`, `{eq}` and so on.\n",
    "\n",
    "- To number equations for referencing, use MyST-Markdown-augmented `$$...$$` notation, as with `$$2+2=4$$ (eq-obvious)`\n",
    "\n",
    "- If the top-level section atop a file is labelled as with <c>(section-label)=</c> then the usage\n",
    "`{ref}<section-label>`\n",
    "can be used instead of\n",
    "`{doc}<file-base-name>`\n",
    "this is posibly useful if the file name can have suffix either \"-python\" or \"-julia\" but I want to use the same cross-reference text."
   ]
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