{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "interactive-link",
   "metadata": {},
   "source": [
    "> **This is a saved, working copy.** Sliders here are frozen at their\n",
    "> starting value — there's no marimo runtime in plain Jupyter to drive them.\n",
    "> For the live, drag-the-sliders version of this lab (answers), see\n",
    "> [Week 2 lab (answers) — interactive](https://math4120.pages.dev/wasm/week02_lab_answers.html).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ipython-import",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:37.316245Z",
     "iopub.status.busy": "2026-11-13T23:25:37.316070Z",
     "iopub.status.idle": "2026-11-13T23:25:37.320100Z",
     "shell.execute_reply": "2026-11-13T23:25:37.319383Z"
    }
   },
   "outputs": [],
   "source": [
    "from IPython.display import Markdown, HTML\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "Hbol",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "# Week 2 lab — Nondimensionalisation — Answers\n",
    "\n",
    "**MATH4120 — Mathematical Modelling and Programming** Lancaster University, 2026–27\n",
    "\n",
    "---\n",
    "\n",
    "**This is the answers version.** Every blank below contains the completed solution, for instructors and for checking your own work.\n",
    "\n",
    "---\n",
    "\n",
    "Work through the exercises below. Press **Ctrl+Enter** (or **Shift+Enter**) to run a cell and see its output."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "MJUe",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:37.321703Z",
     "iopub.status.busy": "2026-11-13T23:25:37.321549Z",
     "iopub.status.idle": "2026-11-13T23:25:37.656077Z",
     "shell.execute_reply": "2026-11-13T23:25:37.655101Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "vblA",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## Parameters\n",
    "\n",
    "A cup of coffee cools in a room.  You can change these numbers at any point and everything below will update automatically."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "bkHC",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:37.658360Z",
     "iopub.status.busy": "2026-11-13T23:25:37.658140Z",
     "iopub.status.idle": "2026-11-13T23:25:37.661045Z",
     "shell.execute_reply": "2026-11-13T23:25:37.660354Z"
    }
   },
   "outputs": [],
   "source": [
    "k    = 0.05   # cooling rate (min⁻¹)\n",
    "T0   = 90.0   # initial temperature (°C)\n",
    "Tinf = 20.0   # ambient temperature (°C)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "lEQa",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## Exercise 1 — one time, three quantities\n",
    "\n",
    "Newton's law of cooling has analytic solution $$T(t) = T_\\infty + (T_0 - T_\\infty)\\,e^{-kt}.$$\n",
    "\n",
    "The nondimensional variables are $s = kt$ and $\\theta = (T - T_\\infty)/(T_0 - T_\\infty)$.\n",
    "\n",
    "**Task.** In the cell below, replace the three `0.0` placeholders with the correct formulas. Use `k`, `T0`, `Tinf`, `t`, and `np.exp(...)`. Run the cell.  You should get roughly $T \\approx 62$°C, $s = 0.5$, $\\theta \\approx 0.61$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "PKri",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:37.662903Z",
     "iopub.status.busy": "2026-11-13T23:25:37.662714Z",
     "iopub.status.idle": "2026-11-13T23:25:37.668503Z",
     "shell.execute_reply": "2026-11-13T23:25:37.667708Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(np.float64(62.45714617988434), 0.5, np.float64(0.6065306597126334))"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t     = 10.0\n",
    "T     = Tinf + (T0 - Tinf) * np.exp(-k * t)\n",
    "s     = k * t\n",
    "theta = (T - Tinf) / (T0 - Tinf)\n",
    "T, s, theta"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "Xref",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## Exercise 2 — over a range of times\n",
    "\n",
    "Now compute $T$, $s$, and $\\theta$ for every time in an array. The array `t_arr` is already defined.  Replace the three `np.zeros_like(t_arr)` placeholders with the same formulas as Exercise 1 — just using `t_arr` instead of `t`.\n",
    "\n",
    "When you run the cell, the plot below will update."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "SFPL",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:37.670145Z",
     "iopub.status.busy": "2026-11-13T23:25:37.670007Z",
     "iopub.status.idle": "2026-11-13T23:25:37.672767Z",
     "shell.execute_reply": "2026-11-13T23:25:37.672121Z"
    }
   },
   "outputs": [],
   "source": [
    "t_arr     = np.linspace(0, 30, 300)\n",
    "T_arr     = Tinf + (T0 - Tinf) * np.exp(-k * t_arr)\n",
    "s_arr     = k * t_arr\n",
    "theta_arr = (T_arr - Tinf) / (T0 - Tinf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "BYtC",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:37.674221Z",
     "iopub.status.busy": "2026-11-13T23:25:37.674089Z",
     "iopub.status.idle": "2026-11-13T23:25:38.078511Z",
     "shell.execute_reply": "2026-11-13T23:25:38.076546Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "marimo": {
     "config": {
      "hide_code": true
     }
    },
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1100x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_s_ref = np.linspace(0, max(s_arr.max(), 0.1), 300)\n",
    "\n",
    "_fig, (_ax_dim, _ax_nd) = plt.subplots(1, 2, figsize=(11, 4))\n",
    "\n",
    "_ax_dim.plot(t_arr, T_arr, color=\"#1a5276\", linewidth=2)\n",
    "_ax_dim.axhline(Tinf, color=\"grey\", linestyle=\":\", linewidth=1.5,\n",
    "                label=f\"$T_\\\\infty = {Tinf:.0f}$°C\")\n",
    "_ax_dim.set_xlabel(\"Time $t$ (min)\", fontsize=12)\n",
    "_ax_dim.set_ylabel(\"Temperature $T$ (°C)\", fontsize=12)\n",
    "_ax_dim.set_title(f\"Dimensional   ($k = {k}$)\", fontsize=12)\n",
    "_ax_dim.legend(fontsize=10)\n",
    "_ax_dim.grid(True, alpha=0.3)\n",
    "\n",
    "_ax_nd.plot(s_arr, theta_arr, color=\"#1a5276\", linewidth=2, label=\"your solution\")\n",
    "_ax_nd.plot(_s_ref, np.exp(-_s_ref), \"k--\", linewidth=1.5, label=r\"$e^{-s}$\")\n",
    "_ax_nd.set_xlabel(\"Dimensionless time $s = kt$\", fontsize=12)\n",
    "_ax_nd.set_ylabel(r\"$\\theta(s)$\", fontsize=12)\n",
    "_ax_nd.set_title(\"Nondimensional\", fontsize=12)\n",
    "_ax_nd.legend(fontsize=10)\n",
    "_ax_nd.grid(True, alpha=0.3)\n",
    "\n",
    "_fig.tight_layout()\n",
    "_fig;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "RGSE",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## Exercise 3 — numerical verification\n",
    "\n",
    "If your formulas in Exercise 2 are correct, `theta_arr` should match $e^{-s}$ evaluated at every point in `s_arr`.\n",
    "\n",
    "**Task.** Run the cell below.  The number it prints is the largest pointwise difference between your solution and the exact answer.  How small is it?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "Kclp",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:38.081468Z",
     "iopub.status.busy": "2026-11-13T23:25:38.081152Z",
     "iopub.status.idle": "2026-11-13T23:25:38.088908Z",
     "shell.execute_reply": "2026-11-13T23:25:38.087317Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(1.1102230246251565e-16)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.max(np.abs(theta_arr - np.exp(-s_arr)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "emfo",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## Observation — solution collapse\n",
    "\n",
    "Once your formulas are correct, the right panel should show your curve sitting exactly on top of $e^{-s}$.\n",
    "\n",
    "**Now go back to the parameters cell at the top and change $k$.** Try $k = 0.1$, then $k = 2.0$.\n",
    "\n",
    "- What changes in the left panel?\n",
    "- What changes in the right panel?\n",
    "\n",
    "This is **solution collapse**: every Newton's cooling experiment, regardless of $k$, $T_0$, or $T_\\infty$, maps to the same nondimensional curve $\\theta(s) = e^{-s}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "Hstk",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## Extension — a new scenario\n",
    "\n",
    "A pan of water starts at $T_0 = 95$°C in a cold kitchen at $T_\\infty = 5$°C with cooling rate $k = 0.08$ s⁻¹.\n",
    "\n",
    "**Task.**\n",
    "1. Update the parameters cell at the top.\n",
    "2. Update $t$ in Exercise 1 to find the temperature after 20 s.\n",
    "3. Does $\\theta$ change compared to the coffee? Should it?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "nWHF",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## AI extension — feature normalisation\n",
    "\n",
    "In machine learning, before training a model you almost always *normalise* the input data.  The most common recipe is **standardisation**: subtract the mean, divide by the standard deviation, so every variable is centred at zero with spread one. Libraries like scikit-learn do this automatically with `StandardScaler`.\n",
    "\n",
    "Written in NumPy it is just two lines:\n",
    "```python\n",
    "theta_stat = (T_arr - T_arr.mean()) / T_arr.std()\n",
    "```\n",
    "\n",
    "This looks a lot like what you did in Exercise 2 — but the scales are *data-driven* (mean and std of your particular dataset) rather than *physics-motivated* ($T_0$ and $T_\\infty$).\n",
    "\n",
    "**Task.**\n",
    "1. Run the cell below.  The plot shows your physical $\\theta$ alongside the statistically standardised version.\n",
    "2. What does $\\theta_\\text{stat} = 0$ mean physically? What does $\\theta = 0$ mean physically?\n",
    "3. Which normalisation is more interpretable, and why?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "iLit",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:38.091234Z",
     "iopub.status.busy": "2026-11-13T23:25:38.091019Z",
     "iopub.status.idle": "2026-11-13T23:25:38.098613Z",
     "shell.execute_reply": "2026-11-13T23:25:38.097518Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.17920207e+00,  2.15656679e+00,  2.13404479e+00,  2.11163549e+00,\n",
       "        2.08933833e+00,  2.06715275e+00,  2.04507819e+00,  2.02311410e+00,\n",
       "        2.00125991e+00,  1.97951509e+00,  1.95787908e+00,  1.93635134e+00,\n",
       "        1.91493134e+00,  1.89361852e+00,  1.87241235e+00,  1.85131230e+00,\n",
       "        1.83031784e+00,  1.80942844e+00,  1.78864357e+00,  1.76796272e+00,\n",
       "        1.74738535e+00,  1.72691096e+00,  1.70653902e+00,  1.68626903e+00,\n",
       "        1.66610047e+00,  1.64603284e+00,  1.62606563e+00,  1.60619834e+00,\n",
       "        1.58643047e+00,  1.56676152e+00,  1.54719100e+00,  1.52771841e+00,\n",
       "        1.50834327e+00,  1.48906508e+00,  1.46988336e+00,  1.45079763e+00,\n",
       "        1.43180741e+00,  1.41291222e+00,  1.39411158e+00,  1.37540503e+00,\n",
       "        1.35679209e+00,  1.33827228e+00,  1.31984516e+00,  1.30151024e+00,\n",
       "        1.28326708e+00,  1.26511521e+00,  1.24705417e+00,  1.22908352e+00,\n",
       "        1.21120279e+00,  1.19341154e+00,  1.17570932e+00,  1.15809568e+00,\n",
       "        1.14057019e+00,  1.12313240e+00,  1.10578186e+00,  1.08851816e+00,\n",
       "        1.07134084e+00,  1.05424948e+00,  1.03724365e+00,  1.02032292e+00,\n",
       "        1.00348686e+00,  9.86735058e-01,  9.70067081e-01,  9.53482512e-01,\n",
       "        9.36980936e-01,  9.20561936e-01,  9.04225099e-01,  8.87970014e-01,\n",
       "        8.71796273e-01,  8.55703467e-01,  8.39691192e-01,  8.23759046e-01,\n",
       "        8.07906626e-01,  7.92133534e-01,  7.76439374e-01,  7.60823749e-01,\n",
       "        7.45286268e-01,  7.29826538e-01,  7.14444172e-01,  6.99138781e-01,\n",
       "        6.83909981e-01,  6.68757389e-01,  6.53680622e-01,  6.38679302e-01,\n",
       "        6.23753051e-01,  6.08901493e-01,  5.94124255e-01,  5.79420964e-01,\n",
       "        5.64791252e-01,  5.50234748e-01,  5.35751088e-01,  5.21339906e-01,\n",
       "        5.07000840e-01,  4.92733529e-01,  4.78537614e-01,  4.64412737e-01,\n",
       "        4.50358544e-01,  4.36374680e-01,  4.22460793e-01,  4.08616534e-01,\n",
       "        3.94841554e-01,  3.81135506e-01,  3.67498045e-01,  3.53928828e-01,\n",
       "        3.40427514e-01,  3.26993762e-01,  3.13627235e-01,  3.00327597e-01,\n",
       "        2.87094512e-01,  2.73927647e-01,  2.60826671e-01,  2.47791255e-01,\n",
       "        2.34821070e-01,  2.21915790e-01,  2.09075090e-01,  1.96298647e-01,\n",
       "        1.83586140e-01,  1.70937247e-01,  1.58351652e-01,  1.45829037e-01,\n",
       "        1.33369088e-01,  1.20971490e-01,  1.08635931e-01,  9.63621017e-02,\n",
       "        8.41496925e-02,  7.19983961e-02,  5.99079067e-02,  4.78779201e-02,\n",
       "        3.59081335e-02,  2.39982456e-02,  1.21479566e-02,  3.56968416e-04,\n",
       "       -1.13750158e-02, -2.30482913e-02, -3.46631518e-02, -4.62198898e-02,\n",
       "       -5.77187960e-02, -6.91601598e-02, -8.05442692e-02, -9.18714107e-02,\n",
       "       -1.03141869e-01, -1.14355929e-01, -1.25513871e-01, -1.36615978e-01,\n",
       "       -1.47662528e-01, -1.58653799e-01, -1.69590068e-01, -1.80471610e-01,\n",
       "       -1.91298699e-01, -2.02071607e-01, -2.12790607e-01, -2.23455966e-01,\n",
       "       -2.34067955e-01, -2.44626839e-01, -2.55132886e-01, -2.65586358e-01,\n",
       "       -2.75987519e-01, -2.86336631e-01, -2.96633955e-01, -3.06879749e-01,\n",
       "       -3.17074272e-01, -3.27217780e-01, -3.37310527e-01, -3.47352770e-01,\n",
       "       -3.57344759e-01, -3.67286746e-01, -3.77178983e-01, -3.87021717e-01,\n",
       "       -3.96815196e-01, -4.06559667e-01, -4.16255376e-01, -4.25902565e-01,\n",
       "       -4.35501479e-01, -4.45052358e-01, -4.54555443e-01, -4.64010972e-01,\n",
       "       -4.73419185e-01, -4.82780318e-01, -4.92094606e-01, -5.01362284e-01,\n",
       "       -5.10583585e-01, -5.19758741e-01, -5.28887983e-01, -5.37971541e-01,\n",
       "       -5.47009644e-01, -5.56002518e-01, -5.64950390e-01, -5.73853486e-01,\n",
       "       -5.82712030e-01, -5.91526244e-01, -6.00296350e-01, -6.09022569e-01,\n",
       "       -6.17705121e-01, -6.26344223e-01, -6.34940095e-01, -6.43492951e-01,\n",
       "       -6.52003007e-01, -6.60470478e-01, -6.68895576e-01, -6.77278514e-01,\n",
       "       -6.85619502e-01, -6.93918750e-01, -7.02176468e-01, -7.10392863e-01,\n",
       "       -7.18568141e-01, -7.26702510e-01, -7.34796172e-01, -7.42849333e-01,\n",
       "       -7.50862194e-01, -7.58834957e-01, -7.66767824e-01, -7.74660993e-01,\n",
       "       -7.82514664e-01, -7.90329033e-01, -7.98104299e-01, -8.05840655e-01,\n",
       "       -8.13538298e-01, -8.21197420e-01, -8.28818215e-01, -8.36400874e-01,\n",
       "       -8.43945588e-01, -8.51452548e-01, -8.58921941e-01, -8.66353957e-01,\n",
       "       -8.73748781e-01, -8.81106600e-01, -8.88427600e-01, -8.95711965e-01,\n",
       "       -9.02959877e-01, -9.10171519e-01, -9.17347073e-01, -9.24486720e-01,\n",
       "       -9.31590639e-01, -9.38659008e-01, -9.45692007e-01, -9.52689811e-01,\n",
       "       -9.59652597e-01, -9.66580540e-01, -9.73473814e-01, -9.80332594e-01,\n",
       "       -9.87157051e-01, -9.93947357e-01, -1.00070368e+00, -1.00742620e+00,\n",
       "       -1.01411508e+00, -1.02077048e+00, -1.02739258e+00, -1.03398154e+00,\n",
       "       -1.04053753e+00, -1.04706071e+00, -1.05355125e+00, -1.06000931e+00,\n",
       "       -1.06643505e+00, -1.07282864e+00, -1.07919023e+00, -1.08551999e+00,\n",
       "       -1.09181807e+00, -1.09808464e+00, -1.10431985e+00, -1.11052385e+00,\n",
       "       -1.11669681e+00, -1.12283888e+00, -1.12895021e+00, -1.13503096e+00,\n",
       "       -1.14108128e+00, -1.14710133e+00, -1.15309125e+00, -1.15905119e+00,\n",
       "       -1.16498131e+00, -1.17088176e+00, -1.17675268e+00, -1.18259422e+00,\n",
       "       -1.18840652e+00, -1.19418975e+00, -1.19994403e+00, -1.20566951e+00,\n",
       "       -1.21136635e+00, -1.21703468e+00, -1.22267464e+00, -1.22828638e+00,\n",
       "       -1.23387003e+00, -1.23942575e+00, -1.24495366e+00, -1.25045391e+00,\n",
       "       -1.25592664e+00, -1.26137198e+00, -1.26679007e+00, -1.27218105e+00,\n",
       "       -1.27754505e+00, -1.28288221e+00, -1.28819266e+00, -1.29347654e+00,\n",
       "       -1.29873397e+00, -1.30396510e+00, -1.30917005e+00, -1.31434895e+00,\n",
       "       -1.31950193e+00, -1.32462913e+00, -1.32973068e+00, -1.33480669e+00])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_stat = (T_arr - T_arr.mean()) / T_arr.std()\n",
    "theta_stat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ZHCJ",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:38.100788Z",
     "iopub.status.busy": "2026-11-13T23:25:38.100538Z",
     "iopub.status.idle": "2026-11-13T23:25:38.297710Z",
     "shell.execute_reply": "2026-11-13T23:25:38.296678Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "marimo": {
     "config": {
      "hide_code": true
     }
    },
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_fig, _ax = plt.subplots(figsize=(8, 4))\n",
    "_ax.plot(s_arr, theta_arr,  color=\"#1a5276\", linewidth=2,\n",
    "         label=r\"Physical: $\\theta = (T - T_\\infty)/(T_0 - T_\\infty)$\")\n",
    "_ax.plot(s_arr, theta_stat, color=\"tomato\",  linewidth=2, linestyle=\"--\",\n",
    "         label=r\"Statistical: $(T - \\bar T)/\\sigma_T$\")\n",
    "_ax.plot(np.linspace(0, s_arr.max(), 300),\n",
    "         np.exp(-np.linspace(0, s_arr.max(), 300)),\n",
    "         \"k:\", linewidth=1.5, label=r\"$e^{-s}$\")\n",
    "_ax.axhline(0, color=\"grey\", linewidth=0.8, alpha=0.5)\n",
    "_ax.set_xlabel(\"Dimensionless time $s = kt$\", fontsize=12)\n",
    "_ax.set_ylabel(\"Normalised temperature\", fontsize=12)\n",
    "_ax.set_title(\"Physical vs statistical normalisation\", fontsize=12)\n",
    "_ax.legend(fontsize=10)\n",
    "_ax.grid(True, alpha=0.3)\n",
    "_fig;"
   ]
  }
 ],
 "metadata": {
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.13.3"
  },
  "marimo": {
   "app_config": {
    "app_title": "Week 2 Lab (Answers) — Nondimensionalisation",
    "width": "medium"
   },
   "marimo_version": "0.25.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
