{
 "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, see\n",
    "> [Week 4 lab — interactive](https://math4120.pages.dev/wasm/week04_lab.html).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ipython-import",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:47.175474Z",
     "iopub.status.busy": "2026-11-13T23:25:47.175270Z",
     "iopub.status.idle": "2026-11-13T23:25:47.179754Z",
     "shell.execute_reply": "2026-11-13T23:25:47.179085Z"
    }
   },
   "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 4 lab — Direction fields and Euler's method\n",
    "\n",
    "**MATH4120 — Mathematical Modelling and Programming** Lancaster University, 2026–27\n",
    "\n",
    "---\n",
    "\n",
    "In the lecture you saw that an ODE $y' = f(t, y)$ is a rule that gives a slope at every point, and that a solution curve is found by following the arrows. Today you build every piece of that yourself, for a cup of coffee cooling in a room (Newton's law of cooling, from Week 2):\n",
    "\n",
    "1. write the slope rule $f$ as a Python function, and check it by hand;\n",
    "2. turn it into a direction field;\n",
    "3. trace the solution by following the arrows, and find out what goes wrong when the steps are too big;\n",
    "4. use the same tools on a problem where the room itself warms up."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "MJUe",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:47.181779Z",
     "iopub.status.busy": "2026-11-13T23:25:47.181612Z",
     "iopub.status.idle": "2026-11-13T23:25:47.523023Z",
     "shell.execute_reply": "2026-11-13T23:25:47.521932Z"
    }
   },
   "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",
    "You can change these at any point; everything below updates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "bkHC",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:47.525308Z",
     "iopub.status.busy": "2026-11-13T23:25:47.525060Z",
     "iopub.status.idle": "2026-11-13T23:25:47.528417Z",
     "shell.execute_reply": "2026-11-13T23:25:47.527654Z"
    }
   },
   "outputs": [],
   "source": [
    "k_cool  = 0.1     # cooling rate (min⁻¹)\n",
    "T0_cool = 85.0    # initial temperature of the coffee (°C)\n",
    "Tinf    = 20.0    # room temperature (°C)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "lEQa",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:47.530240Z",
     "iopub.status.busy": "2026-11-13T23:25:47.530048Z",
     "iopub.status.idle": "2026-11-13T23:25:47.535161Z",
     "shell.execute_reply": "2026-11-13T23:25:47.534508Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "marimo": {
     "config": {
      "hide_code": true
     }
    },
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [],
   "source": [
    "def draw_arrows(ax, t_grid, y_grid, rise, color=\"grey\", alpha=0.6):\n",
    "    \"\"\"Draw the arrow (1, rise) at every grid point, all the same length on screen.\"\"\"\n",
    "    fig = ax.figure\n",
    "    ax.apply_aspect()\n",
    "    box = ax.get_position()\n",
    "    t_lo, t_hi = ax.get_xlim()\n",
    "    y_lo, y_hi = ax.get_ylim()\n",
    "    t_per_inch = (t_hi - t_lo) / (fig.get_figwidth() * box.width)\n",
    "    y_per_inch = (y_hi - y_lo) / (fig.get_figheight() * box.height)\n",
    "    rise = rise * np.ones_like(t_grid)\n",
    "    # measure each arrow in inches on screen, then scale to a fixed length\n",
    "    run_in = np.ones_like(t_grid) / t_per_inch\n",
    "    rise_in = rise / y_per_inch\n",
    "    length_in = np.hypot(run_in, rise_in)\n",
    "    gap_t_in = abs(t_grid[0, 1] - t_grid[0, 0]) / t_per_inch\n",
    "    gap_y_in = abs(y_grid[1, 0] - y_grid[0, 0]) / y_per_inch\n",
    "    arrow_inches = 0.7 * min(gap_t_in, gap_y_in)\n",
    "    U = run_in / length_in * arrow_inches * t_per_inch\n",
    "    V = rise_in / length_in * arrow_inches * y_per_inch\n",
    "    ax.quiver(t_grid, y_grid, U, V, angles=\"xy\", scale_units=\"xy\", scale=1,\n",
    "              pivot=\"mid\", color=color, alpha=alpha,\n",
    "              width=0.003, headwidth=3.5, headlength=4.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "PKri",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## Exercise 1 — the slope rule\n",
    "\n",
    "Newton's law of cooling is $$\\frac{\\mathrm{d}T}{\\mathrm{d}t} = -k\\,(T - T_\\infty).$$ So the slope at the point $(t, T)$ is $f(t, T) = -k\\,(T - T_\\infty)$, measured in °C per minute.\n",
    "\n",
    "**Task (a), on paper first.** With the default parameters ($k = 0.1$, $T_\\infty = 20$), work out the slope at the three points $(t, T) = (0, 85)$, $(10, 20)$ and $(5, 10)$. For each one, say in words what the coffee is doing at that moment.\n",
    "\n",
    "**Task (b).** Complete the function `f_cool` below so that it returns $f(t, T)$. Use `k_cool` and `Tinf`. Then run the cell after it and compare with your hand calculations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "Xref",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:47.536611Z",
     "iopub.status.busy": "2026-11-13T23:25:47.536460Z",
     "iopub.status.idle": "2026-11-13T23:25:47.539004Z",
     "shell.execute_reply": "2026-11-13T23:25:47.538219Z"
    }
   },
   "outputs": [],
   "source": [
    "def f_cool(t, T):\n",
    "    return 0.0    # ← replace with the right-hand side of Newton's law of cooling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "SFPL",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:47.540977Z",
     "iopub.status.busy": "2026-11-13T23:25:47.540742Z",
     "iopub.status.idle": "2026-11-13T23:25:47.543929Z",
     "shell.execute_reply": "2026-11-13T23:25:47.543280Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "slope at (t, T) = (0, 85):  0.0\n",
      "slope at (t, T) = (10, 20): 0.0\n",
      "slope at (t, T) = (5, 10):  0.0\n"
     ]
    }
   ],
   "source": [
    "print(\"slope at (t, T) = (0, 85): \", f_cool(0, 85))\n",
    "print(\"slope at (t, T) = (10, 20):\", f_cool(10, 20))\n",
    "print(\"slope at (t, T) = (5, 10): \", f_cool(5, 10))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "BYtC",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "<details><summary><b>Check your hand calculations (open after you have tried)</b></summary>\n",
    "\n",
    "\n",
    "- $(0, 85)$: $-0.1 \\times (85 - 20) = -6.5$. The coffee is losing 6.5 °C per minute.\n",
    "- $(10, 20)$: $-0.1 \\times (20 - 20) = 0$. The coffee is at room temperature, and its temperature is not changing.\n",
    "- $(5, 10)$: $-0.1 \\times (10 - 20) = +1$. A drink colder than the room warms up, by 1 °C per minute.\n",
    "\n",
    "(If Python prints `-0.0`, that is just zero.) Notice that $t$ never appears in the answer: only $T$ matters. Keep that in mind for Exercise 2.\n",
    "\n",
    "</details>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "RGSE",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## Exercise 2 — from slopes to a direction field\n",
    "\n",
    "The cell below sets up a grid of points: every 5 minutes from $t = 0$ to $60$, and every 10 °C from $T = 0$ to $90$. `t_grid` and `T_grid` are tables holding the $t$ and $T$ value of every grid point.\n",
    "\n",
    "At each grid point we want the arrow $(1,\\ f(t, T))$: run 1, rise $f$. A NumPy function works on a whole table at once, just like on a single number.\n",
    "\n",
    "**Task.** Replace `np.zeros_like(t_grid)` with the rise of the arrow at every grid point. One line is enough."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "Kclp",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:47.545745Z",
     "iopub.status.busy": "2026-11-13T23:25:47.545580Z",
     "iopub.status.idle": "2026-11-13T23:25:47.548746Z",
     "shell.execute_reply": "2026-11-13T23:25:47.547921Z"
    }
   },
   "outputs": [],
   "source": [
    "t_grid, T_grid = np.meshgrid(np.linspace(0, 60, 13), np.linspace(0, 90, 10))\n",
    "T_rise = np.zeros_like(t_grid)    # ← replace: the rise of the arrow at every grid point"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "emfo",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:47.550140Z",
     "iopub.status.busy": "2026-11-13T23:25:47.549995Z",
     "iopub.status.idle": "2026-11-13T23:25:47.750249Z",
     "shell.execute_reply": "2026-11-13T23:25:47.749302Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "marimo": {
     "config": {
      "hide_code": true
     }
    },
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 900x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_fig1, _ax1 = plt.subplots(figsize=(9, 5))\n",
    "_ax1.set_xlim(-2.5, 62.5)\n",
    "_ax1.set_ylim(-5, 95)\n",
    "_ax1.set_xlabel(r\"$t$ (min)\", fontsize=13)\n",
    "_ax1.set_ylabel(r\"$T$ (°C)\", fontsize=13)\n",
    "_ax1.set_title(\"Direction field for Newton's law of cooling\", fontsize=13)\n",
    "_ax1.grid(True, alpha=0.2)\n",
    "_fig1.tight_layout()\n",
    "draw_arrows(_ax1, t_grid, T_grid, T_rise, color=\"#922b21\", alpha=0.85)\n",
    "_ax1.plot(t_grid, T_grid, \".\", color=\"#922b21\", markersize=3)\n",
    "_fig1;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "Hstk",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "**Questions.** Answer these from the picture, then check.\n",
    "\n",
    "1. Along which horizontal line are the arrows flat? Why there?\n",
    "2. Pick one row of arrows and move along it from left to right. Do the arrows change? Which line of `f_cool` explains what you see?\n",
    "3. Compare the arrows at 80 °C with those at 30 °C. What does that tell you about how quickly very hot coffee cools compared with lukewarm coffee?\n",
    "\n",
    "<details><summary><b>Answers (open after you have answered)</b></summary>\n",
    "\n",
    "\n",
    "1. Along $T = 20$, the room temperature, because $f = -k(20 - 20) = 0$ there. A cup that is already at room temperature stays there.\n",
    "2. Every row is identical: the arrows do not depend on $t$, because `f_cool` never uses `t`. Physically, the coffee doesn't care what time it is, only how hot it is.\n",
    "3. The arrows at 80 °C are much steeper: the slope is proportional to the gap $T - T_\\infty$, so hot coffee cools fast at first and then slows down as it approaches room temperature.\n",
    "\n",
    "</details>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "nWHF",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## Exercise 3 — follow the arrows\n",
    "\n",
    "To draw a solution curve: start at $(0, T_0)$, look up the arrow there, take a step of length $h$ (in the $t$ direction) along it, look up the new arrow, and repeat.\n",
    "\n",
    "**Task.** One line inside `follow_arrows` is missing. If you are at $(t_\\text{now}, T_\\text{now})$ and the slope there is $f(t_\\text{now}, T_\\text{now})$, what is $T$ after moving $h$ to the right along the arrow? (Run 1 gives rise $f$, so run $h$ gives rise ...?)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "iLit",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:47.751945Z",
     "iopub.status.busy": "2026-11-13T23:25:47.751803Z",
     "iopub.status.idle": "2026-11-13T23:25:47.755661Z",
     "shell.execute_reply": "2026-11-13T23:25:47.754664Z"
    }
   },
   "outputs": [],
   "source": [
    "def follow_arrows(f, t_start, T_start, t_stop, h):\n",
    "    \"\"\"Start at (t_start, T_start) and repeatedly step h along the arrow.\"\"\"\n",
    "    n_steps = int(round((t_stop - t_start) / h))\n",
    "    t_values = [t_start]\n",
    "    T_values = [T_start]\n",
    "    for step in range(n_steps):\n",
    "        t_now = t_values[-1]\n",
    "        T_now = T_values[-1]\n",
    "        T_next = T_now    # ← replace: T after one step of size h along the arrow at (t_now, T_now)\n",
    "        t_values.append(t_now + h)\n",
    "        T_values.append(T_next)\n",
    "    return np.array(t_values), np.array(T_values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "ZHCJ",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:47.757407Z",
     "iopub.status.busy": "2026-11-13T23:25:47.757212Z",
     "iopub.status.idle": "2026-11-13T23:25:47.760143Z",
     "shell.execute_reply": "2026-11-13T23:25:47.759440Z"
    }
   },
   "outputs": [],
   "source": [
    "h_cool_slider = type('_W', (), {'value': 5.0})()  # static default"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "ROlb",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:47.761510Z",
     "iopub.status.busy": "2026-11-13T23:25:47.761368Z",
     "iopub.status.idle": "2026-11-13T23:25:47.763986Z",
     "shell.execute_reply": "2026-11-13T23:25:47.763267Z"
    }
   },
   "outputs": [],
   "source": [
    "t_traced, T_traced = follow_arrows(f_cool, 0.0, T0_cool, 60.0, h_cool_slider.value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "qnkX",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:47.765398Z",
     "iopub.status.busy": "2026-11-13T23:25:47.765260Z",
     "iopub.status.idle": "2026-11-13T23:25:47.993152Z",
     "shell.execute_reply": "2026-11-13T23:25:47.992338Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "marimo": {
     "config": {
      "hide_code": true
     }
    },
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_h = h_cool_slider.value\n",
    "_t_exact = np.linspace(0, 60, 400)\n",
    "_T_exact = Tinf + (T0_cool - Tinf) * np.exp(-k_cool * _t_exact)\n",
    "_y_lo = min(-5.0, T_traced.min() - 5)\n",
    "_y_hi = max(95.0, T_traced.max() + 5)\n",
    "\n",
    "_fig2, _ax2 = plt.subplots(figsize=(9, 5))\n",
    "_ax2.set_xlim(-2.5, 62.5)\n",
    "_ax2.set_ylim(_y_lo, _y_hi)\n",
    "_ax2.set_xlabel(r\"$t$ (min)\", fontsize=13)\n",
    "_ax2.set_ylabel(r\"$T$ (°C)\", fontsize=13)\n",
    "_ax2.set_title(rf\"Following the arrows with step $h = {_h:g}$ min\", fontsize=13)\n",
    "_ax2.grid(True, alpha=0.2)\n",
    "_fig2.tight_layout()\n",
    "_tg2, _Tg2 = np.meshgrid(np.linspace(0, 60, 13), np.linspace(_y_lo + 5, _y_hi - 5, 10))\n",
    "draw_arrows(_ax2, _tg2, _Tg2, f_cool(_tg2, _Tg2), alpha=0.45)\n",
    "\n",
    "_ax2.plot(_t_exact, _T_exact, \"k--\", linewidth=1.5,\n",
    "          label=r\"Week 2 formula $T_\\infty + (T_0 - T_\\infty)e^{-kt}$\")\n",
    "_ax2.plot(t_traced, T_traced, \"o-\", color=\"#1a5276\", linewidth=2.0,\n",
    "          markersize=6, label=\"following the arrows\")\n",
    "_ax2.axhline(Tinf, color=\"tomato\", linestyle=\":\", linewidth=1.5,\n",
    "             label=rf\"room, $T_\\infty = {Tinf:g}$ °C\")\n",
    "_ax2.legend(fontsize=10, loc=\"best\", framealpha=0.9)\n",
    "_fig2;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "TqIu",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
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     "md_prefix": "r"
    }
   },
   "source": [
    "**Questions.** Use the slider.\n",
    "\n",
    "1. With $h = 0.5$, how does the traced curve compare with the Week 2 formula (dashed)? What happens as you increase $h$ to 5?\n",
    "2. Set $h = 10$. The very first step lands *exactly* on room temperature and stays there. Explain why, using the slope at the starting point from Exercise 1.\n",
    "3. Set $h = 15$. The coffee becomes colder than the room, which is physically impossible. What went wrong? Then try $h = 25$.\n",
    "\n",
    "<details><summary><b>Answers (open after you have answered)</b></summary>\n",
    "\n",
    "\n",
    "1. With small $h$ the dots sit on the dashed curve. As $h$ grows the dots fall below it: each step follows the arrow at the *start* of the step, which is steeper than the curve further on, so every step cools a bit too much.\n",
    "2. The slope at $(0, 85)$ is $-6.5$ °C/min. Following it for 10 minutes gives $85 + 10 \\times (-6.5) = 20$, exactly room temperature, where the slope is 0, so it never moves again.\n",
    "3. With $h = 15$ the first step is $85 + 15 \\times (-6.5) = -12.5$ °C. The arrow at the start is only correct *at the start*; following it blindly for 15 minutes overshoots the room temperature. The next step overshoots back the other way, by less, so it still settles down. With $h = 25$ each overshoot is bigger than the last and the steps blow up. Small steps are not just more accurate, they can be the difference between a sensible answer and nonsense. Chapter 6 comes back to this.\n",
    "\n",
    "</details>\n",
    "\n",
    "**Try it.** Change `T0_cool` to `5.0` (a cold drink in a warm room). Does the picture still make sense?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "Vxnm",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## Exercise 4 — a room that warms up\n",
    "\n",
    "Now the heating comes on. The room starts at 15 °C and warms by 0.25 °C every minute, so the room temperature is $15 + 0.25\\,t$. The coffee follows Newton's law with this moving target: $$\\frac{\\mathrm{d}T}{\\mathrm{d}t} = -k\\,\\bigl(T - (15 + 0.25\\,t)\\bigr).$$\n",
    "\n",
    "**Predict first.** Before you write any code:\n",
    "\n",
    "1. Will every row of arrows still look the same? Why or why not?\n",
    "2. Where will the arrows be flat now?\n",
    "\n",
    "**Task.** Complete `f_room` below. `room_temp(t)` is already written for you. The plot then reuses your arrows and your `follow_arrows` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "DnEU",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:47.994841Z",
     "iopub.status.busy": "2026-11-13T23:25:47.994703Z",
     "iopub.status.idle": "2026-11-13T23:25:47.997862Z",
     "shell.execute_reply": "2026-11-13T23:25:47.996954Z"
    }
   },
   "outputs": [],
   "source": [
    "def room_temp(t):\n",
    "    return 15 + 0.25 * t    # the heating is on: +0.25 °C per minute\n",
    "\n",
    "def f_room(t, T):\n",
    "    return 0.0    # ← replace with the slope for the warming room"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "ulZA",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:47.999647Z",
     "iopub.status.busy": "2026-11-13T23:25:47.999496Z",
     "iopub.status.idle": "2026-11-13T23:25:48.297980Z",
     "shell.execute_reply": "2026-11-13T23:25:48.297104Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "marimo": {
     "config": {
      "hide_code": true
     }
    },
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 900x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_fig3, _ax3 = plt.subplots(figsize=(9, 5))\n",
    "_ax3.set_xlim(-3.75, 93.75)\n",
    "_ax3.set_ylim(-5, 95)\n",
    "_ax3.set_xlabel(r\"$t$ (min)\", fontsize=13)\n",
    "_ax3.set_ylabel(r\"$T$ (°C)\", fontsize=13)\n",
    "_ax3.set_title(\"Coffee in a warming room\", fontsize=13)\n",
    "_ax3.grid(True, alpha=0.2)\n",
    "_fig3.tight_layout()\n",
    "_tg3, _Tg3 = np.meshgrid(np.linspace(0, 90, 13), np.linspace(0, 90, 10))\n",
    "draw_arrows(_ax3, _tg3, _Tg3, f_room(_tg3, _Tg3), alpha=0.45)\n",
    "\n",
    "_t_room = np.linspace(0, 90, 100)\n",
    "_ax3.plot(_t_room, room_temp(_t_room), \":\", color=\"tomato\", linewidth=2.0,\n",
    "          label=\"room temperature\")\n",
    "_starts = [T0_cool, 50.0, 5.0]\n",
    "_colours = [\"#1a5276\", \"#1e8449\", \"#7d3c98\"]\n",
    "for _T_start, _col in zip(_starts, _colours):\n",
    "    _t_r, _T_r = follow_arrows(f_room, 0.0, _T_start, 90.0, 0.5)\n",
    "    _ax3.plot(_t_r, _T_r, color=_col, linewidth=2.0,\n",
    "              label=rf\"coffee starting at {_T_start:g} °C\")\n",
    "_ax3.legend(fontsize=10, loc=\"best\", framealpha=0.9)\n",
    "_fig3;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ecfG",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
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   "source": [
    "**Questions.**\n",
    "\n",
    "3. Does the coffee ever catch up with the room temperature? Look at the curves after about 45 minutes: is the coffee above or below the room, and by roughly how much?\n",
    "4. Explain that gap. *Hint:* once the coffee has settled into following the room, it must warm at the same rate as the room, 0.25 °C per minute. What does $f_\\text{room} = 0.25$ tell you about $T - (15 + 0.25t)$?\n",
    "5. Change `k_cool` to `0.05` (a better-insulated mug). Predict the new gap, then check.\n",
    "\n",
    "<details><summary><b>Answers (open after you have answered)</b></summary>\n",
    "\n",
    "\n",
    "1. No. The rows differ, because `f_room` now uses `t`: the same temperature means something different early on (cold room) and later (warm room).\n",
    "2. On the room-temperature line $T = 15 + 0.25t$, where $T - \\text{room} = 0$. It is now a sloping line, not a horizontal one.\n",
    "3. It never catches up. All three curves end up running parallel to the room line, about 2.5 °C *below* it.\n",
    "4. Setting $-k\\,(T - \\text{room}) = 0.25$ gives $T - \\text{room} = -0.25/k = -2.5$ °C for $k = 0.1$. The coffee has to be cooler than the room for heat to flow *into* it at the rate the room is warming.\n",
    "5. $-0.25/0.05 = -5$ °C: a better-insulated mug lags further behind.\n",
    "\n",
    "This is the lecture's $y' = t - y$ in disguise: the curves funnel onto a line that runs parallel to the line of flat arrows, a little way behind it. You could also solve it with an integrating factor, but the picture gets you the answer without any integrals.\n",
    "\n",
    "</details>"
   ]
  }
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