README updates, textbook polynomial cell, self-contained notebook

Same set of changes as che-computing-dev/LLMs:
- 03/04/05 READMEs: uv add workflow, required model caching
- 05-tool-use: add Setup section, requirements.txt
- 06-neural-networks: textbook cubic polynomial comparison cell
- 06-neural-networks: add nn_workshop_colab.ipynb (self-contained, inline data)
- vocab.md: catch up with terms from 02-05

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

06-neural-networks/nn_workshop.ipynb

@@ -93,6 +93,20 @@
     "print(f\"Parameters: 4\")"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "07673988",
+   "source": "### Comparing to a textbook polynomial\n\nMost thermodynamics textbooks tabulate $C_p$ correlations of the same cubic form, but with **fixed coefficients** drawn from a broader fit and reported in **molar** units, $C_p$ in J/(mol·K). For nitrogen, a typical reference set is:\n\n| Coefficient | Value |\n|-------------|-------|\n| $a$ | 28.883 |\n| $b$ | $-0.157 \\times 10^{-2}$ |\n| $c$ | $0.808 \\times 10^{-5}$ |\n| $d$ | $-2.871 \\times 10^{-9}$ |\n\n**Valid range: 273–1800 K.** Outside this range the textbook polynomial is being extrapolated and is not guaranteed by the original fit.\n\nTo compare with our NIST mass-basis data, we divide by the molar mass of N$_2$ (28.014 g/mol) — convenient because J/(mol·K) ÷ g/mol = kJ/(kg·K).",
+   "metadata": {}
+  },
+  {
+   "cell_type": "code",
+   "id": "f21c64a3",
+   "source": "# Reference polynomial from textbook (Cp in J/(mol·K))\n# Form: Cp = a + bT + cT^2 + dT^3\n# Valid range: 273-1800 K\n\na_ref = 28.883\nb_ref = -0.157e-2\nc_ref = 0.808e-5\nd_ref = -2.871e-9\nM_N2 = 28.014  # g/mol\n\nT_REF_MIN, T_REF_MAX = 273.0, 1800.0\n\ndef cp_ref_molar(T):\n    \"\"\"Textbook cubic in J/(mol·K).\"\"\"\n    return a_ref + b_ref * T + c_ref * T**2 + d_ref * T**3\n\ndef cp_ref(T):\n    \"\"\"Same fit converted to kJ/(kg·K) to match the NIST data.\"\"\"\n    return cp_ref_molar(T) / M_N2\n\n# Evaluate the textbook polynomial across the full plot range\nCp_ref_full = cp_ref(T_fine)\n\n# MSE on the data points that fall within the textbook's stated valid range\nin_range = (T_raw >= T_REF_MIN) & (T_raw <= T_REF_MAX)\nCp_ref_at_data = cp_ref(T_raw[in_range])\nmse_ref = np.mean((Cp_ref_at_data - Cp_raw[in_range]) ** 2)\n\n# Plot both fits across the full data range; shade the textbook's valid range\nplt.figure(figsize=(8, 5))\nplt.axvspan(T_REF_MIN, T_REF_MAX, alpha=0.07, color='green',\n            label='Textbook valid range (273–1800 K)')\nplt.plot(T_raw, Cp_raw, 'ko', markersize=6, label='NIST data')\nplt.plot(T_fine, Cp_ref_full, 'g--', linewidth=2,\n         label=f'Textbook polynomial (4 params, MSE={mse_ref:.2e})')\nplt.plot(T_fine, Cp_poly, 'b-', linewidth=2,\n         label=f'numpy.polyfit (4 params, MSE={mse_poly:.2e})')\nplt.xlabel('Temperature (K)')\nplt.ylabel('$C_p$ (kJ/kg/K)')\nplt.title('Two cubic fits: textbook coefficients vs. fit to these 35 points')\nplt.legend(fontsize=9)\nplt.show()\n\nprint(f\"Textbook polynomial MSE (within 273-1800 K, {in_range.sum()} points): {mse_ref:.6e}\")\nprint(f\"numpy.polyfit MSE (all {len(T_raw)} points):                     {mse_poly:.6e}\")\nprint()\nprint(\"Note: the textbook polynomial is plotted across the full range, but its\")\nprint(\"authors only claim validity from 273 to 1800 K (shaded band).\")\nprint(\"Beyond 1800 K, the curve is an extrapolation — useful as a teaching point\")\nprint(\"about trusting correlations only over their stated range.\")",
+   "metadata": {},
+   "execution_count": null,
+   "outputs": []
+  },
   {
    "cell_type": "markdown",
    "id": "97y7mrcekji",
@@ -425,4 +439,4 @@
  },
  "nbformat": 4,
  "nbformat_minor": 5
-}
+}