{
 "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 lecture, see\n",
    "> [Week 1 lecture — interactive](https://math4120.pages.dev/wasm/week01_lecture.html).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ipython-import",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:27.182153Z",
     "iopub.status.busy": "2026-11-13T23:25:27.181977Z",
     "iopub.status.idle": "2026-11-13T23:25:27.186081Z",
     "shell.execute_reply": "2026-11-13T23:25:27.185314Z"
    }
   },
   "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 1: What is a mathematical model?\n",
    "## Computation lecture\n",
    "\n",
    "**MATH4120 — Mathematical Modelling and Programming** Lancaster University, 2026–27\n",
    "\n",
    "---\n",
    "\n",
    "In lectures this week we introduced the **modelling cycle** and worked through the rumour-spreading example.  Here we apply the same cycle computationally — first to a discrete population model, then to a draining tank."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "MJUe",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## 0. How this notebook works\n",
    "\n",
    "This notebook interleaves code cells (grey background) with text cells like this one, written in **Markdown**.  Markdown is how you will narrate your own solutions.\n",
    "\n",
    "| What you type | What you see |\n",
    "|---|---|\n",
    "| `**bold**` | **bold** |\n",
    "| `*italic*` | *italic* |\n",
    "| `## Heading` | a section heading |\n",
    "| `$r N$` | $r N$ (inline maths) |\n",
    "| `$$\\frac{dN}{dt} = rN$$` | $$\\frac{dN}{dt} = rN$$ |\n",
    "\n",
    "The maths uses **LaTeX** — the same notation as the printed lecture notes."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "vblA",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## 1. The modelling cycle\n",
    "\n",
    "1. **Observe** — identify the phenomenon and the question.\n",
    "2. **Simplify** — make assumptions to make the problem tractable.\n",
    "3. **Formulate** — express those assumptions as equations.\n",
    "4. **Solve** — analytically or numerically.\n",
    "5. **Interpret** — translate the output back into real-world terms.\n",
    "6. **Validate** — compare with data or known behaviour.\n",
    "7. **Refine** — relax assumptions, add complexity, repeat.\n",
    "\n",
    "The lecture notes work through the **rumour-spreading** example step by step. Here we demonstrate the cycle on two computational examples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "bkHC",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:27.187701Z",
     "iopub.status.busy": "2026-11-13T23:25:27.187548Z",
     "iopub.status.idle": "2026-11-13T23:25:27.860360Z",
     "shell.execute_reply": "2026-11-13T23:25:27.859135Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.integrate import solve_ivp"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "lEQa",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## 2. Discrete model: geometric growth\n",
    "\n",
    "An insect species breeds once per year.  Let $N_n$ be the population in year $n$. The simplest rule: each generation is a fixed multiple of the previous one,\n",
    "\n",
    "$$N_{n+1} = R\\,N_n, \\qquad N_0 \\text{ given.}$$\n",
    "\n",
    "This is a **difference equation**.  No calculus needed: given $R$ and $N_0$, the whole sequence follows by iteration.  The closed form is $N_n = R^n N_0$.\n",
    "\n",
    "- $R > 1$: unbounded growth. $\\quad R < 1$: decay to zero. $\\quad R = 1$: constant."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "PKri",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:27.862860Z",
     "iopub.status.busy": "2026-11-13T23:25:27.862492Z",
     "iopub.status.idle": "2026-11-13T23:25:27.866523Z",
     "shell.execute_reply": "2026-11-13T23:25:27.865753Z"
    }
   },
   "outputs": [],
   "source": [
    "R_slider = type('_W', (), {'value': 1.5})()  # static default\n",
    "N0_disc_slider = type('_W', (), {'value': 50})()  # static default\n",
    "n_gen_slider = type('_W', (), {'value': 15})()  # static default"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "Xref",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:27.868088Z",
     "iopub.status.busy": "2026-11-13T23:25:27.867943Z",
     "iopub.status.idle": "2026-11-13T23:25:28.080750Z",
     "shell.execute_reply": "2026-11-13T23:25:28.079786Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "marimo": {
     "config": {
      "hide_code": true
     }
    },
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R_d = R_slider.value\n",
    "N0_d = N0_disc_slider.value\n",
    "n_d = n_gen_slider.value\n",
    "\n",
    "n_disc = np.arange(n_d + 1)\n",
    "N_geom = N0_d * R_d ** n_disc\n",
    "\n",
    "fig_disc, ax_disc = plt.subplots(figsize=(8, 4))\n",
    "ax_disc.stem(n_disc, N_geom, linefmt=\"#1a5276\", markerfmt=\"C0o\", basefmt=\"k-\")\n",
    "ax_disc.set_xlabel(\"Generation $n$\", fontsize=13)\n",
    "ax_disc.set_ylabel(\"Population $N_n$\", fontsize=13)\n",
    "ax_disc.set_title(\n",
    "    f\"Geometric growth  $N_n = R^n N_0$   ($R = {R_d}$,  $N_0 = {N0_d}$)\",\n",
    "    fontsize=12,\n",
    ")\n",
    "ax_disc.grid(True, alpha=0.3)\n",
    "fig_disc.tight_layout()\n",
    "fig_disc;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "SFPL",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## 3. From discrete to continuous\n",
    "\n",
    "Suppose the time step between generations is $h$ (small).  The multiplicative factor per step is $R = e^{rh}$, where $r$ is the continuous per-capita growth rate. As $h \\to 0$ the difference equation passes to the limit\n",
    "\n",
    "$$\\frac{dN}{dt} = r N, \\qquad N(0) = N_0, \\qquad \\text{solution: } N(t) = N_0 e^{rt}.$$\n",
    "\n",
    "With $h = 1$ year and $R = e^r$, discrete and continuous are the same process sampled at different resolutions.  The exponential curve passes through each stem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "BYtC",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:28.083038Z",
     "iopub.status.busy": "2026-11-13T23:25:28.082835Z",
     "iopub.status.idle": "2026-11-13T23:25:28.290954Z",
     "shell.execute_reply": "2026-11-13T23:25:28.289875Z"
    },
    "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": [
    "R_b = R_slider.value\n",
    "N0_b = N0_disc_slider.value\n",
    "n_b = n_gen_slider.value\n",
    "\n",
    "n_both = np.arange(n_b + 1)\n",
    "N_both_disc = N0_b * R_b ** n_both\n",
    "\n",
    "r_cont = np.log(max(R_b, 1e-9))   # r such that e^r = R  (one-year steps)\n",
    "t_cont = np.linspace(0, n_b, 400)\n",
    "N_cont = N0_b * np.exp(r_cont * t_cont)\n",
    "\n",
    "fig_both, ax_both = plt.subplots(figsize=(8, 4))\n",
    "ax_both.plot(t_cont, N_cont, color=\"#1a5276\", linewidth=2.5,\n",
    "             label=rf\"Continuous: $N_0\\,e^{{rt}}$,  $r = \\ln R = {r_cont:.3f}$\")\n",
    "ax_both.stem(n_both, N_both_disc, linefmt=\"grey\", markerfmt=\"ko\", basefmt=\" \",\n",
    "             label=\"Discrete: $R^n N_0$\")\n",
    "ax_both.set_xlabel(\"Time (years)\", fontsize=13)\n",
    "ax_both.set_ylabel(\"Population\", fontsize=13)\n",
    "ax_both.set_title(\"Discrete and continuous models — same parameters, two frameworks\", fontsize=12)\n",
    "ax_both.legend(fontsize=11)\n",
    "ax_both.grid(True, alpha=0.3)\n",
    "fig_both.tight_layout()\n",
    "fig_both;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "RGSE",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## 4. A different model: the draining tank\n",
    "\n",
    "Not every model gives exponential behaviour.  We now apply the full modelling cycle, live and from scratch, to a tank of water draining under gravity through a hole in the bottom.\n",
    "\n",
    "**Observe.**  Water flows out through a small hole at the bottom of the tank.  The flow is fast when the tank is full and slows to a trickle as the water level drops. We want to predict the depth $h(t)$ at any time — and in particular, how long the tank takes to drain completely.\n",
    "\n",
    "**Simplify.**\n",
    "- The tank is a vertical cylinder with constant cross-sectional area $A$.\n",
    "- The hole at the bottom has area $a$, much smaller than $A$ ($a \\ll A$).\n",
    "- The water surface stays flat and horizontal — no swirling, sloshing, or waves.\n",
    "- The speed of the water leaving the hole depends only on the current depth $h$.\n",
    "\n",
    "**Formulate.**  Let $h(t)$ be the water depth at time $t$.  We need two ingredients.\n",
    "\n",
    "*Conservation of volume.*  The volume of water in the tank is $V = A\\,h$ (area times depth).  Water only leaves through the hole, at some volumetric outflow rate $Q$ (units m³/s — the volume leaving per second).  So the volume falls exactly as fast as water leaves: $$\\frac{dV}{dt} = -Q \\qquad\\Longrightarrow\\qquad A\\,\\frac{dh}{dt} = -Q.$$\n",
    "\n",
    "*Torricelli's law.*  $Q$ itself is (exit speed) × (hole area): $Q = a\\,v$, where $v$ is the speed of the water jetting out of the hole.  Energy conservation (the same idea as a falling object trading height for speed) gives $v = \\sqrt{2gh}$ — a deeper column of water drives the jet out faster.  So $Q = a\\sqrt{2gh}$.\n",
    "\n",
    "Putting the two together: $$\\boxed{\\frac{dh}{dt} = -\\frac{a}{A}\\sqrt{2g\\,h}.}$$\n",
    "\n",
    "**Dimensional check.**  $[a/A] = 1$ (a ratio of two areas is dimensionless), and $\\bigl[\\sqrt{2gh}\\bigr] = \\mathrm{m\\,s^{-1}}$.  So the right-hand side has dimensions $\\mathrm{m\\,s^{-1}}$ — matching $[\\dot{h}]$. ✓\n",
    "\n",
    "**Solve.**  This ODE separates.  With initial depth $h(0) = h_0$, the exact solution is $$h(t) = h_0\\!\\left(1 - \\frac{t}{t_\\mathrm{drain}}\\right)^{\\!2}, \\qquad t_\\mathrm{drain} = \\frac{A}{a}\\sqrt{\\frac{2h_0}{g}},$$ valid until the tank empties at $t = t_\\mathrm{drain}$.  Below: numerical (`solve_ivp`) and analytic solutions overlaid."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "Kclp",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:28.292971Z",
     "iopub.status.busy": "2026-11-13T23:25:28.292762Z",
     "iopub.status.idle": "2026-11-13T23:25:28.296560Z",
     "shell.execute_reply": "2026-11-13T23:25:28.295553Z"
    }
   },
   "outputs": [],
   "source": [
    "h0_slider = type('_W', (), {'value': 2.0})()  # static default\n",
    "ratio_slider = type('_W', (), {'value': 0.005})()  # static default\n",
    "steps_slider = type('_W', (), {'value': 10})()  # static default"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "emfo",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:28.298499Z",
     "iopub.status.busy": "2026-11-13T23:25:28.298292Z",
     "iopub.status.idle": "2026-11-13T23:25:28.566611Z",
     "shell.execute_reply": "2026-11-13T23:25:28.565713Z"
    },
    "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": [
    "h0_tank = h0_slider.value\n",
    "aA = ratio_slider.value\n",
    "n_steps_tank = steps_slider.value\n",
    "g = 9.81\n",
    "\n",
    "c_tank = aA * np.sqrt(2 * g)          # shorthand: (a/A) sqrt(2g)\n",
    "t_drain = 2 * np.sqrt(h0_tank) / c_tank\n",
    "\n",
    "t_eval_tank = np.linspace(0, t_drain * 1.05, 400)\n",
    "h_exact = h0_tank * np.maximum(1 - t_eval_tank / t_drain, 0.0) ** 2\n",
    "\n",
    "def tank_ode(t, h):\n",
    "    return [-c_tank * np.sqrt(max(h[0], 0.0))]\n",
    "\n",
    "sol_tank = solve_ivp(\n",
    "    tank_ode, [0, t_drain * 1.05], [h0_tank],\n",
    "    t_eval=t_eval_tank, max_step=t_drain * 1.05 / n_steps_tank,\n",
    ")\n",
    "\n",
    "fig_tank, ax_tank = plt.subplots(figsize=(8, 4))\n",
    "ax_tank.plot(t_eval_tank, h_exact, color=\"#1a5276\", linewidth=2.5,\n",
    "             label=r\"Analytic: $h_0\\!\\left(1 - t/t_\\mathrm{drain}\\right)^2$\")\n",
    "ax_tank.plot(sol_tank.t, sol_tank.y[0], color=\"tomato\", linewidth=2, linestyle=\"--\",\n",
    "             label=f\"solve_ivp (RK45, ≤{n_steps_tank} steps)\")\n",
    "ax_tank.axvline(t_drain, color=\"grey\", linestyle=\":\", linewidth=1.5)\n",
    "ax_tank.text(\n",
    "    t_drain * 0.76, h0_tank * 0.55,\n",
    "    f\"$t_\\\\mathrm{{drain}} = {t_drain:.1f}\\\\,\\\\mathrm{{s}}$\",\n",
    "    fontsize=11, color=\"grey\",\n",
    ")\n",
    "ax_tank.set_xlabel(\"Time $t$ (s)\", fontsize=13)\n",
    "ax_tank.set_ylabel(\"Depth $h(t)$ (m)\", fontsize=13)\n",
    "ax_tank.set_title(\n",
    "    f\"Draining tank   ($h_0 = {h0_tank}\\\\,\\\\mathrm{{m}}$,  $a/A = {aA}$)\",\n",
    "    fontsize=13,\n",
    ")\n",
    "ax_tank.legend(fontsize=11)\n",
    "ax_tank.grid(True, alpha=0.3)\n",
    "fig_tank.tight_layout()\n",
    "fig_tank;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "Hstk",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "**Interpret.**  The curve is concave up: draining is fastest at the start and slows to a trickle near the end.  This is qualitatively different from the exponential curves we saw earlier — there is a *finite* drain time, not an ever-approaching asymptote.\n",
    "\n",
    "The drain time scales as $\\sqrt{h_0}$: doubling $h_0$ multiplies $t_\\mathrm{drain}$ by $\\sqrt{2} \\approx 1.41$, not by 2.\n",
    "\n",
    "**Validate.**  Two limiting cases we can check by hand, without any further maths:\n",
    "- As the hole shrinks ($a \\to 0$), $t_\\mathrm{drain} \\to \\infty$ — a vanishingly small hole never empties the tank.  Sensible.\n",
    "- As the hole grows to fill the whole base ($a \\to A$), $t_\\mathrm{drain} \\to \\sqrt{2h_0/g}$ — exactly the time for an object to *fall* height $h_0$ under gravity.  Also sensible: with no tank wall left to constrain it, the water just free-falls.\n",
    "\n",
    "Both extremes agree with physical intuition, which gives us some confidence the model captures the right behaviour in between too.\n",
    "\n",
    "**Refine.**  Real tanks lose some efficiency at the hole due to viscosity. Engineers account for this with a discharge coefficient $C_d \\approx 0.6$, replacing $Q = a\\sqrt{2gh}$ with $Q = C_d\\,a\\sqrt{2gh}$.  The model structure is unchanged; only the constant $c = (a/A)\\sqrt{2g}$ picks up a factor of $C_d$."
   ]
  }
 ],
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   "codemirror_mode": {
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   "pygments_lexer": "ipython3",
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   "app_config": {
    "app_title": "Week 1 — What is a mathematical model?",
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