{
 "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 4 lecture — interactive](https://math4120.pages.dev/wasm/week04_lecture.html).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ipython-import",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:45.154084Z",
     "iopub.status.busy": "2026-11-13T23:25:45.153926Z",
     "iopub.status.idle": "2026-11-13T23:25:45.157978Z",
     "shell.execute_reply": "2026-11-13T23:25:45.157271Z"
    }
   },
   "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: Ordinary differential equations — geometry and the discrete origin\n",
    "## Computation lecture\n",
    "\n",
    "**MATH4120 — Mathematical Modelling and Programming** Lancaster University, 2026–27\n",
    "\n",
    "---\n",
    "\n",
    "Lectures this week focused on solving ODEs by hand — separation of variables, integrating factors, and the auxiliary equation.  Here we step back and ask a more fundamental question: *what is an ODE, geometrically?*\n",
    "\n",
    "Two ideas.  First: a direction field, which turns any ODE into a picture.  Second: where the ODE comes from."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "MJUe",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:45.159944Z",
     "iopub.status.busy": "2026-11-13T23:25:45.159789Z",
     "iopub.status.idle": "2026-11-13T23:25:45.499906Z",
     "shell.execute_reply": "2026-11-13T23:25:45.498740Z"
    }
   },
   "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": [
    "## 1. Direction fields\n",
    "\n",
    "A first-order ODE $y' = f(t, y)$ looks like an equation to *solve*. Read it another way: it is a **rule that gives a slope**. Pick any point $(t, y)$ in the plane, plug it into $f$, and out comes a number: the slope that a solution curve passing through that point must have there.\n",
    "\n",
    "We will use an example from this week's lectures (integrating factor): $$y' = t - y, \\qquad\\text{so}\\qquad f(t, y) = t - y.$$\n",
    "\n",
    "### 1.1 One point, one arrow\n",
    "\n",
    "At the point $(t, y) = (2, 0.5)$ the slope is $f(2, 0.5) = 2 - 0.5 = 1.5$. In Python, $f$ is just a function of two inputs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "bkHC",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:45.502192Z",
     "iopub.status.busy": "2026-11-13T23:25:45.501726Z",
     "iopub.status.idle": "2026-11-13T23:25:45.505484Z",
     "shell.execute_reply": "2026-11-13T23:25:45.504609Z"
    }
   },
   "outputs": [],
   "source": [
    "def f_relax(t, y):\n",
    "    return t - y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "lEQa",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:45.506853Z",
     "iopub.status.busy": "2026-11-13T23:25:45.506706Z",
     "iopub.status.idle": "2026-11-13T23:25:45.510024Z",
     "shell.execute_reply": "2026-11-13T23:25:45.509217Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "slope at (2, 0.5) is 1.5\n"
     ]
    }
   ],
   "source": [
    "t_point = 2.0\n",
    "y_point = 0.5\n",
    "slope_point = f_relax(t_point, y_point)\n",
    "print(\"slope at (2, 0.5) is\", slope_point)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "PKri",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "A slope of $1.5$ means: **go 1 to the right, go 1.5 up**. That is the arrow we draw at the point, the vector $(1,\\ f(t, y))$. Move the point around and watch the arrow change. Before you move it: where do you expect the arrow to point *downhill*?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "Xref",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:45.511427Z",
     "iopub.status.busy": "2026-11-13T23:25:45.511271Z",
     "iopub.status.idle": "2026-11-13T23:25:45.513987Z",
     "shell.execute_reply": "2026-11-13T23:25:45.513228Z"
    }
   },
   "outputs": [],
   "source": [
    "t_point_slider = type('_W', (), {'value': 2.0})()  # static default\n",
    "y_point_slider = type('_W', (), {'value': 0.5})()  # static default"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "SFPL",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:45.515396Z",
     "iopub.status.busy": "2026-11-13T23:25:45.515251Z",
     "iopub.status.idle": "2026-11-13T23:25:45.757912Z",
     "shell.execute_reply": "2026-11-13T23:25:45.757121Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "marimo": {
     "config": {
      "hide_code": true
     }
    },
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_t0 = t_point_slider.value\n",
    "_y0 = y_point_slider.value\n",
    "_f0 = f_relax(_t0, _y0)\n",
    "\n",
    "_fig1, _ax1 = plt.subplots(figsize=(8, 5))\n",
    "\n",
    "# run: 1 to the right\n",
    "_ax1.plot([_t0, _t0 + 1], [_y0, _y0], \"--\", color=\"#1a5276\", linewidth=1.5)\n",
    "_ax1.text(_t0 + 0.5, _y0 - 0.12, \"run = 1\", ha=\"center\", va=\"top\",\n",
    "          fontsize=12, color=\"#1a5276\")\n",
    "# rise: f(t, y) up (or down)\n",
    "_ax1.plot([_t0 + 1, _t0 + 1], [_y0, _y0 + _f0], \"--\", color=\"#1e8449\",\n",
    "          linewidth=1.5)\n",
    "_ax1.text(_t0 + 1.08, _y0 + _f0 / 2, rf\"rise = $f$ = {_f0:g}\",\n",
    "          ha=\"left\", va=\"center\", fontsize=12, color=\"#1e8449\")\n",
    "# the arrow itself\n",
    "_ax1.annotate(\"\", xy=(_t0 + 1, _y0 + _f0), xytext=(_t0, _y0),\n",
    "              arrowprops=dict(arrowstyle=\"-|>\", color=\"#922b21\", lw=2.5,\n",
    "                              mutation_scale=20))\n",
    "_ax1.plot(_t0, _y0, \"o\", color=\"#922b21\", markersize=9, zorder=5)\n",
    "\n",
    "_ax1.set_xlim(-0.3, 4.6)\n",
    "_ax1.set_ylim(-0.5, 3.5)\n",
    "_ax1.set_aspect(\"equal\")\n",
    "_ax1.set_xlabel(r\"$t$\", fontsize=13)\n",
    "_ax1.set_ylabel(r\"$y$\", fontsize=13)\n",
    "_ax1.set_title(\n",
    "    rf\"At $(t, y) = ({_t0:g}, {_y0:g})$:   \"\n",
    "    rf\"$f = t - y = {_t0:g} - {_y0:g} = {_f0:g}$\",\n",
    "    fontsize=13,\n",
    ")\n",
    "_ax1.grid(True, alpha=0.3)\n",
    "_fig1.tight_layout()\n",
    "_fig1;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "BYtC",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "### 1.2 Many points, many arrows\n",
    "\n",
    "Now do the same at lots of points. Here are the slopes at the 16 whole-number points with $t$ and $y$ between 0 and 3, laid out like the plane (large $y$ at the top):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "RGSE",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:45.759839Z",
     "iopub.status.busy": "2026-11-13T23:25:45.759690Z",
     "iopub.status.idle": "2026-11-13T23:25:45.763198Z",
     "shell.execute_reply": "2026-11-13T23:25:45.762389Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         t = 0   t = 1   t = 2   t = 3\n",
      "y = 3       -3      -2      -1       0  \n",
      "y = 2       -2      -1       0       1  \n",
      "y = 1       -1       0       1       2  \n",
      "y = 0        0       1       2       3  \n"
     ]
    }
   ],
   "source": [
    "print(\"         t = 0   t = 1   t = 2   t = 3\")\n",
    "for y_row in [3, 2, 1, 0]:\n",
    "    table_line = \"y = \" + str(y_row) + \"   \"\n",
    "    for t_col in [0, 1, 2, 3]:\n",
    "        table_line = table_line + f\"{f_relax(t_col, y_row):6}  \"\n",
    "    print(table_line)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "Kclp",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "**Question.** Find the zeros in the table. What line do they lie on? What does a zero slope look like as an arrow?\n",
    "\n",
    "Below, every one of those numbers becomes an arrow. Start with 4 points per side (the table above), then drag the slider up. One thing changes: a slope of $3$ gives an arrow three times taller than a slope of $1$, and a slope of $50$ would fill the whole picture. So when we draw a field we **give every arrow the same length and keep only its direction**. The slope is still exactly $f(t, y)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "emfo",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:45.764723Z",
     "iopub.status.busy": "2026-11-13T23:25:45.764548Z",
     "iopub.status.idle": "2026-11-13T23:25:45.770341Z",
     "shell.execute_reply": "2026-11-13T23:25:45.769569Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "marimo": {
     "config": {
      "hide_code": true
     }
    },
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [],
   "source": [
    "def draw_arrows(ax, f, t_min, t_max, y_min, y_max, n_t, n_y,\n",
    "                pivot=\"mid\", inset=True, color=\"grey\", alpha=0.6,\n",
    "                width=0.003):\n",
    "    \"\"\"Draw the arrow (1, f(t, y)) 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_per_inch = (t_max - t_min) / (fig.get_figwidth() * box.width)\n",
    "    y_per_inch = (y_max - y_min) / (fig.get_figheight() * box.height)\n",
    "    if inset:\n",
    "        t_vals = np.linspace(t_min, t_max, n_t + 2)[1:-1]\n",
    "        y_vals = np.linspace(y_min, y_max, n_y + 2)[1:-1]\n",
    "    else:\n",
    "        t_vals = np.linspace(t_min, t_max, n_t)\n",
    "        y_vals = np.linspace(y_min, y_max, n_y)\n",
    "    T, Y = np.meshgrid(t_vals, y_vals)\n",
    "    # arrows fill 70% of the gap between neighbouring grid points\n",
    "    gap_t_in = (t_vals[1] - t_vals[0]) / t_per_inch\n",
    "    gap_y_in = (y_vals[1] - y_vals[0]) / y_per_inch\n",
    "    arrow_inches = 0.7 * min(gap_t_in, gap_y_in)\n",
    "    run = np.ones_like(T)\n",
    "    rise = f(T, Y) * np.ones_like(T)\n",
    "    # measure each arrow in inches on screen, then scale to a fixed length\n",
    "    run_in = run / t_per_inch\n",
    "    rise_in = rise / y_per_inch\n",
    "    length_in = np.hypot(run_in, rise_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, Y, U, V, angles=\"xy\", scale_units=\"xy\", scale=1,\n",
    "              pivot=pivot, color=color, alpha=alpha,\n",
    "              width=width, headwidth=3.5, headlength=4.5)\n",
    "    return T, Y, rise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "Hstk",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:45.771708Z",
     "iopub.status.busy": "2026-11-13T23:25:45.771549Z",
     "iopub.status.idle": "2026-11-13T23:25:45.774304Z",
     "shell.execute_reply": "2026-11-13T23:25:45.773589Z"
    }
   },
   "outputs": [],
   "source": [
    "n_grid_slider = type('_W', (), {'value': 4})()  # static default"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "nWHF",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:45.775796Z",
     "iopub.status.busy": "2026-11-13T23:25:45.775658Z",
     "iopub.status.idle": "2026-11-13T23:25:45.959668Z",
     "shell.execute_reply": "2026-11-13T23:25:45.958759Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "marimo": {
     "config": {
      "hide_code": true
     }
    },
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x550 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_n = n_grid_slider.value\n",
    "\n",
    "_fig2, _ax2 = plt.subplots(figsize=(8, 5.5))\n",
    "_ax2.set_xlim(-0.4, 3.8)\n",
    "_ax2.set_ylim(-0.4, 3.4)\n",
    "_ax2.set_aspect(\"equal\")\n",
    "_ax2.set_xlabel(r\"$t$\", fontsize=13)\n",
    "_ax2.set_ylabel(r\"$y$\", fontsize=13)\n",
    "_ax2.set_title(\n",
    "    rf\"Direction field for $y' = t - y$:   {_n} × {_n} = {_n * _n} arrows\",\n",
    "    fontsize=13,\n",
    ")\n",
    "_ax2.grid(True, alpha=0.3)\n",
    "_fig2.tight_layout()\n",
    "\n",
    "_T2, _Y2, _F2 = draw_arrows(\n",
    "    _ax2, f_relax, 0, 3, 0, 3, _n, _n,\n",
    "    pivot=\"tail\", inset=False, color=\"#922b21\", alpha=0.85,\n",
    "    width=0.006 if _n <= 6 else 0.004,\n",
    ")\n",
    "if _n <= 6:\n",
    "    _ax2.plot(_T2, _Y2, \"o\", color=\"#922b21\", markersize=6)\n",
    "if _n <= 5:\n",
    "    for _tp, _yp, _fp in zip(_T2.ravel(), _Y2.ravel(), _F2.ravel()):\n",
    "        _ax2.text(_tp - 0.06, _yp + 0.06, f\"{_fp:g}\", ha=\"right\",\n",
    "                  va=\"bottom\", fontsize=11, color=\"#1a5276\")\n",
    "_fig2;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "iLit",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "With enough arrows a pattern jumps out: the arrows are flat along the line $y = t$ (where $f = 0$), point down above it and up below it. You can almost *see* the solution curves already. A solution curve is simply a curve that is **tangent to the arrows everywhere**.\n",
    "\n",
    "How do we draw one? Start at a point, take a tiny step along the arrow there, look up the new arrow, take another tiny step, and repeat. Here is that recipe in code; we will use it to draw every curve below. (Keep it in mind for Section 2.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "ZHCJ",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:45.961536Z",
     "iopub.status.busy": "2026-11-13T23:25:45.961339Z",
     "iopub.status.idle": "2026-11-13T23:25:45.965370Z",
     "shell.execute_reply": "2026-11-13T23:25:45.964609Z"
    }
   },
   "outputs": [],
   "source": [
    "def follow_arrows(f, t_start, y_start, t_stop, n_steps=2000):\n",
    "    \"\"\"Trace a solution curve: take a tiny step along the arrow, then look again.\"\"\"\n",
    "    h = (t_stop - t_start) / n_steps\n",
    "    t_values = [t_start]\n",
    "    y_values = [y_start]\n",
    "    for step in range(n_steps):\n",
    "        t_now = t_values[-1]\n",
    "        y_now = y_values[-1]\n",
    "        if abs(y_now) > 100:      # the curve has shot off the picture\n",
    "            break\n",
    "        t_values.append(t_now + h)\n",
    "        y_values.append(y_now + h * f(t_now, y_now))\n",
    "    return np.array(t_values), np.array(y_values)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ROlb",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "### 1.3 A gallery of direction fields\n",
    "\n",
    "Here are six more ODEs, several straight from this week's lectures. The arrows are drawn exactly as above, and the curves come from `follow_arrows`, never from a formula.\n",
    "\n",
    "**Predict first**, before you switch to each one:\n",
    "\n",
    "1. $y' = t$: will the arrows change as you move *up and down*? As you move *left and right*?\n",
    "2. $y' = t - y$: you already know where the arrows are flat. What do you expect the curves to do in the long run?\n",
    "3. $y' = y(1 - y)$: which starting values $y_0$ give a solution that never changes at all?\n",
    "4. $y' = 4t^3y^2$: the lectures found $y = -1/(t^4 - 1)$ for $y(0) = 1$. What happens at $t = 1$? Will the arrows \"know\"?\n",
    "5. $y' = y^2 - t$: there is *no* formula for this one from any of the methods this week. Can you still say what happens if $y_0$ is large? If $y_0$ is very negative?\n",
    "\n",
    "Tick **Show where the slope is zero** to mark the points where $f(t, y) = 0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "qnkX",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:45.966861Z",
     "iopub.status.busy": "2026-11-13T23:25:45.966722Z",
     "iopub.status.idle": "2026-11-13T23:25:45.969972Z",
     "shell.execute_reply": "2026-11-13T23:25:45.969205Z"
    }
   },
   "outputs": [],
   "source": [
    "def f_growth(t, y):\n",
    "    return 0.5 * y\n",
    "\n",
    "def f_decay(t, y):\n",
    "    return -0.5 * y\n",
    "\n",
    "def f_ramp(t, y):\n",
    "    return t\n",
    "\n",
    "def f_logistic(t, y):\n",
    "    return y * (1 - y)\n",
    "\n",
    "def f_blowup(t, y):\n",
    "    return 4 * t**3 * y**2\n",
    "\n",
    "def f_riccati(t, y):\n",
    "    return y**2 - t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "TqIu",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:45.971633Z",
     "iopub.status.busy": "2026-11-13T23:25:45.971484Z",
     "iopub.status.idle": "2026-11-13T23:25:45.978770Z",
     "shell.execute_reply": "2026-11-13T23:25:45.978156Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "marimo": {
     "config": {
      "hide_code": true
     }
    },
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [],
   "source": [
    "_s = np.linspace(-10, 10, 400)\n",
    "_sqrt_t = np.sqrt(np.linspace(0, 6, 400))\n",
    "gallery = {\n",
    "    \"growth\": dict(\n",
    "        f=f_growth, latex=r\"y' = 0.5\\,y\",\n",
    "        t_range=(0, 6), y_range=(-1, 5),\n",
    "        y0_range=(-1.0, 3.0, 0.1), y0=0.5,\n",
    "        family=[-0.5, 0.2, 1.0, 2.0, 3.0],\n",
    "        zero_curves=[(_s, 0 * _s)],\n",
    "        notice=r\"The arrows depend only on $y$: every **row** of arrows is identical, and they get steeper the higher you go, so growth speeds up. Along $y = 0$ the arrows are flat: a solution that starts at $0$ stays there forever. Switch to *decay* and every arrow flips: growth becomes decay.\",\n",
    "    ),\n",
    "    \"decay\": dict(\n",
    "        f=f_decay, latex=r\"y' = -0.5\\,y\",\n",
    "        t_range=(0, 6), y_range=(-1, 5),\n",
    "        y0_range=(-1.0, 5.0, 0.1), y0=4.0,\n",
    "        family=[-0.8, 1.0, 2.0, 3.0, 4.8],\n",
    "        zero_curves=[(_s, 0 * _s)],\n",
    "        notice=r\"The same picture as growth with every arrow flipped. Now all the arrows point *towards* $y = 0$, so every solution decays to $0$, from above or from below.\",\n",
    "    ),\n",
    "    \"ramp\": dict(\n",
    "        f=f_ramp, latex=r\"y' = t\",\n",
    "        t_range=(-3, 3), y_range=(-5, 5),\n",
    "        y0_range=(-1.0, 5.0, 0.1), y0=2.0,\n",
    "        family=[-1.0, 0.0, 1.0, 3.0, 4.0],\n",
    "        zero_curves=[(0 * _s, _s)],\n",
    "        notice=r\"Now the arrows depend only on $t$: every **column** is identical. So if you slide a solution curve straight up or down it still fits the arrows, and every curve is a shifted copy of one parabola: $y = \\tfrac12 t^2 + C$. The arrows are flat along $t = 0$, which is where every curve has its minimum.\",\n",
    "    ),\n",
    "    \"relax\": dict(\n",
    "        f=f_relax, latex=r\"y' = t - y\",\n",
    "        t_range=(0, 6), y_range=(-2, 6),\n",
    "        y0_range=(-2.0, 6.0, 0.1), y0=5.0,\n",
    "        family=[-2.0, 0.0, 1.0, 3.0, 6.0],\n",
    "        zero_curves=[(_s, _s)],\n",
    "        notice=r\"Curves above $y = t$ head down, curves below head up, and they cross the line $y = t$ exactly where they are flat: that's where they turn around. In the long run they all **funnel onto the line $y = t - 1$**. That line is itself a solution: along it the slope is $t - (t - 1) = 1$, the slope of the line. The integrating factor gives the same story as a formula: $y = t - 1 + Ce^{-t}$, and $Ce^{-t} \\to 0$.\",\n",
    "    ),\n",
    "    \"logistic\": dict(\n",
    "        f=f_logistic, latex=r\"y' = y\\,(1 - y)\",\n",
    "        t_range=(0, 8), y_range=(-0.5, 1.5),\n",
    "        y0_range=(-0.2, 1.5, 0.02), y0=0.04,\n",
    "        family=[-0.02, 0.02, 0.2, 0.5, 1.3, 1.5],\n",
    "        zero_curves=[(_s, 0 * _s), (_s, 0 * _s + 1)],\n",
    "        notice=r\"Again only $y$ matters, so every row is identical. The arrows are flat at $y = 0$ and $y = 1$: start exactly there and nothing ever changes. These are **equilibria**. Start between them and you climb to $1$; start above $1$ and you fall back to $1$; start below $0$ and you fall away. Chapter 5 is all about pictures like this one.\",\n",
    "    ),\n",
    "    \"blowup\": dict(\n",
    "        f=f_blowup, latex=r\"y' = 4t^3y^2\",\n",
    "        t_range=(0, 1.5), y_range=(-2, 5),\n",
    "        y0_range=(-2.0, 2.0, 0.1), y0=1.0,\n",
    "        family=[-1.5, -0.5, 0.3, 0.5, 1.5],\n",
    "        zero_curves=[(_s, 0 * _s)],\n",
    "        notice=r\"Near $t = 0$ the arrows are almost flat, then they steepen ferociously. With $y(0) = 1$ the formula $y = -1/(t^4 - 1)$ shoots to infinity at $t = 1$, and the traced curve does the same: the solution **blows up in finite time**. Try $y_0 = 0.5$: it blows up later, at $t = 2^{1/4} \\approx 1.19$. Negative $y_0$ never blows up. The formula and the picture agree; the picture just shows all starting values at once.\",\n",
    "    ),\n",
    "    \"riccati\": dict(\n",
    "        f=f_riccati, latex=r\"y' = y^2 - t\",\n",
    "        t_range=(0, 6), y_range=(-3, 3),\n",
    "        y0_range=(-3.0, 3.0, 0.05), y0=0.5,\n",
    "        family=[-2.5, -1.0, 0.0, 0.7, 1.0],\n",
    "        zero_curves=[(np.linspace(0, 6, 400), _sqrt_t),\n",
    "                     (np.linspace(0, 6, 400), -_sqrt_t)],\n",
    "        notice=r\"None of this week's methods give a formula for this ODE, yet the picture tells the whole story. The arrows are flat on the parabola $y^2 = t$. Curves that start low get trapped in a **funnel** and follow $y \\approx -\\sqrt{t}$ for ever. Curves that start high escape and blow up. A knife-edge near $y_0 \\approx 0.73$ separates the two fates: try $y_0 = 0.70$ and then $0.75$. Drawing this picture needed nothing but $f$ and `follow_arrows`, which is the idea behind every numerical solver (Chapter 6).\",\n",
    "    ),\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "Vxnm",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:45.980160Z",
     "iopub.status.busy": "2026-11-13T23:25:45.980030Z",
     "iopub.status.idle": "2026-11-13T23:25:45.982511Z",
     "shell.execute_reply": "2026-11-13T23:25:45.981821Z"
    }
   },
   "outputs": [],
   "source": [
    "ode_dropdown = type('_W', (), {'value': 'relax'})()  # static default"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "DnEU",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:45.984159Z",
     "iopub.status.busy": "2026-11-13T23:25:45.984023Z",
     "iopub.status.idle": "2026-11-13T23:25:45.986607Z",
     "shell.execute_reply": "2026-11-13T23:25:45.985806Z"
    }
   },
   "outputs": [],
   "source": [
    "zero_checkbox = type('_W', (), {'value': False})()  # static default"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "ulZA",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:45.988067Z",
     "iopub.status.busy": "2026-11-13T23:25:45.987929Z",
     "iopub.status.idle": "2026-11-13T23:25:45.990905Z",
     "shell.execute_reply": "2026-11-13T23:25:45.990010Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "marimo": {
     "config": {
      "hide_code": true
     }
    },
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [],
   "source": [
    "# the chosen example, plus slider settings for it\n",
    "ode_now = dict(gallery[ode_dropdown.value])\n",
    "ode_now[\"t_step\"] = (ode_now[\"t_range\"][1] - ode_now[\"t_range\"][0]) / 60\n",
    "ode_now[\"t_trace0\"] = ode_now[\"t_range\"][0] + 40 * ode_now[\"t_step\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "ecfG",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:45.992631Z",
     "iopub.status.busy": "2026-11-13T23:25:45.992428Z",
     "iopub.status.idle": "2026-11-13T23:25:45.995338Z",
     "shell.execute_reply": "2026-11-13T23:25:45.994716Z"
    }
   },
   "outputs": [],
   "source": [
    "y0_gallery_slider = type('_W', (), {'value': ode_now[\"y0\"]})()  # static default\n",
    "t_trace_slider = type('_W', (), {'value': ode_now[\"t_trace0\"]})()  # static default"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "Pvdt",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:45.997110Z",
     "iopub.status.busy": "2026-11-13T23:25:45.996964Z",
     "iopub.status.idle": "2026-11-13T23:25:46.002543Z",
     "shell.execute_reply": "2026-11-13T23:25:46.001735Z"
    }
   },
   "outputs": [],
   "source": [
    "# faded family of solution curves (depends only on which ODE is chosen)\n",
    "family_curves = []\n",
    "for y0_member in ode_now[\"family\"]:\n",
    "    family_curves.append(\n",
    "        follow_arrows(ode_now[\"f\"], ode_now[\"t_range\"][0], y0_member,\n",
    "                      ode_now[\"t_range\"][1])\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "ZBYS",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:46.004104Z",
     "iopub.status.busy": "2026-11-13T23:25:46.003954Z",
     "iopub.status.idle": "2026-11-13T23:25:46.241331Z",
     "shell.execute_reply": "2026-11-13T23:25:46.240535Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "marimo": {
     "config": {
      "hide_code": true
     }
    },
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "/// details | What to notice\n",
       "\n",
       "Curves above $y = t$ head down, curves below head up, and they cross the line $y = t$ exactly where they are flat: that's where they turn around. In the long run they all **funnel onto the line $y = t - 1$**. That line is itself a solution: along it the slope is $t - (t - 1) = 1$, the slope of the line. The integrating factor gives the same story as a formula: $y = t - 1 + Ce^{-t}$, and $Ce^{-t} \\to 0$.\n",
       "\n",
       "///"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ex_g = ode_now\n",
    "_f_g = _ex_g[\"f\"]\n",
    "_t_lo_g, _t_hi_g = _ex_g[\"t_range\"]\n",
    "_y_lo_g, _y_hi_g = _ex_g[\"y_range\"]\n",
    "_y0_g = y0_gallery_slider.value\n",
    "_t_end_g = t_trace_slider.value\n",
    "\n",
    "_fig3, _ax3 = plt.subplots(figsize=(9, 5))\n",
    "_ax3.set_xlim(_t_lo_g, _t_hi_g)\n",
    "_ax3.set_ylim(_y_lo_g, _y_hi_g)\n",
    "_ax3.set_xlabel(r\"$t$\", fontsize=13)\n",
    "_ax3.set_ylabel(r\"$y$\", fontsize=13)\n",
    "_ax3.set_title(rf\"Direction field for ${_ex_g['latex']}$\", fontsize=13)\n",
    "_ax3.grid(True, alpha=0.2)\n",
    "_fig3.tight_layout()\n",
    "\n",
    "draw_arrows(_ax3, _f_g, _t_lo_g, _t_hi_g, _y_lo_g, _y_hi_g, 25, 15)\n",
    "\n",
    "_col_fam_g = [\"#1a5276\", \"#1e8449\", \"#922b21\", \"#7d3c98\", \"#b7950b\", \"#117a65\"]\n",
    "for _i_fam, (_t_fam, _y_fam) in enumerate(family_curves):\n",
    "    _ax3.plot(_t_fam, _y_fam, color=_col_fam_g[_i_fam % 6],\n",
    "              linewidth=1.3, alpha=0.5)\n",
    "\n",
    "if zero_checkbox.value:\n",
    "    for _i_z, (_t_z, _y_z) in enumerate(_ex_g[\"zero_curves\"]):\n",
    "        _ax3.plot(_t_z, _y_z, \"--\", color=\"#e67e22\", linewidth=2.2,\n",
    "                  label=\"slope = 0\" if _i_z == 0 else None)\n",
    "\n",
    "# the highlighted solution, traced up to t_end\n",
    "_t_tr, _y_tr = follow_arrows(_f_g, _t_lo_g, _y0_g, _t_hi_g)\n",
    "_keep = _t_tr <= _t_end_g + 1e-9\n",
    "_ax3.plot(_t_tr[_keep], _y_tr[_keep], color=\"#1a5276\", linewidth=2.8,\n",
    "          label=rf\"$y({_t_lo_g:g}) = {_y0_g:g}$\")\n",
    "_t_now, _y_now = _t_tr[_keep][-1], _y_tr[_keep][-1]\n",
    "if _y_lo_g <= _y_now <= _y_hi_g:\n",
    "    _ax3.plot(_t_now, _y_now, \"o\", color=\"#922b21\", markersize=9, zorder=5)\n",
    "_ax3.legend(fontsize=11, loc=\"best\", framealpha=0.9)\n",
    "\n",
    "Markdown(\"/// details | What to notice\\n\\n\" + _ex_g[\"notice\"] + \"\\n\\n///\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aLJB",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "Notice in every picture: **two solution curves never cross**. The field gives exactly one slope at each point, so if two curves met they would have to leave that point in the same direction, and from then on they would be the same curve."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "nHfw",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## 2. The discrete origin of the ODE\n",
    "\n",
    "In Week 1 we wrote the discrete model $N_{n+1} = r\\,N_n$ for geometric growth. Let $h$ be the time step between generations and $r = 1 + kh$.  Then $$N_{n+1} = N_n + h\\,k\\,N_n \\qquad\\Longrightarrow\\qquad \\frac{N_{n+1} - N_n}{h} = k\\,N_n.$$ As $h \\to 0$ the left side is the definition of $\\mathrm{d}N/\\mathrm{d}t$, and we recover $N' = kN$.  **The ODE is the continuous limit of the difference equation.**\n",
    "\n",
    "The update rule $y_{n+1} = y_n + h\\,f(t_n, y_n)$ is **Euler's method** — the simplest numerical solver.  Look back at `follow_arrows` in Section 1: `y_now + h * f(t_now, y_now)` is exactly this rule, with a tiny $h$.  Every curve in the gallery was drawn by Euler's method.  Here we make $h$ big and watch what happens as it shrinks.  Chapter 6 asks how to make it accurate and efficient."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "xXTn",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:46.243715Z",
     "iopub.status.busy": "2026-11-13T23:25:46.243561Z",
     "iopub.status.idle": "2026-11-13T23:25:46.246558Z",
     "shell.execute_reply": "2026-11-13T23:25:46.245712Z"
    }
   },
   "outputs": [],
   "source": [
    "h_euler_slider = type('_W', (), {'value': 1.5})()  # static default"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "AjVT",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:46.248160Z",
     "iopub.status.busy": "2026-11-13T23:25:46.248027Z",
     "iopub.status.idle": "2026-11-13T23:25:46.251578Z",
     "shell.execute_reply": "2026-11-13T23:25:46.250769Z"
    }
   },
   "outputs": [],
   "source": [
    "h_eu = h_euler_slider.value\n",
    "k_eu = 0.5\n",
    "y0_eu = 1.0\n",
    "T_eu = 6.0\n",
    "\n",
    "# Euler's method: y_{n+1} = y_n + h * f(t_n, y_n)\n",
    "t_eu = np.arange(0, T_eu + h_eu / 2, h_eu)\n",
    "y_eu = np.zeros(len(t_eu))\n",
    "y_eu[0] = y0_eu\n",
    "for i_eu in range(1, len(t_eu)):\n",
    "    y_eu[i_eu] = y_eu[i_eu - 1] + h_eu * k_eu * y_eu[i_eu - 1]\n",
    "\n",
    "err_eu = abs(y_eu[-1] - y0_eu * np.exp(k_eu * t_eu[-1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "pHFh",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:46.253312Z",
     "iopub.status.busy": "2026-11-13T23:25:46.253134Z",
     "iopub.status.idle": "2026-11-13T23:25:46.441945Z",
     "shell.execute_reply": "2026-11-13T23:25:46.441299Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "marimo": {
     "config": {
      "hide_code": true
     }
    },
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_h = h_euler_slider.value\n",
    "_t_ex = np.linspace(0, T_eu, 500)\n",
    "_y_ex = y0_eu * np.exp(k_eu * _t_ex)\n",
    "\n",
    "_fig_e, _ax_e = plt.subplots(figsize=(9, 4))\n",
    "_ax_e.step(t_eu, y_eu, where=\"post\", color=\"#1a5276\", linewidth=2.0,\n",
    "           label=rf\"Euler staircase ($h = {_h:.2f}$)\")\n",
    "_ax_e.plot(_t_ex, _y_ex, \"k--\", linewidth=1.5,\n",
    "           label=r\"analytic $y_0\\,e^{kt}$\")\n",
    "_ax_e.set_xlabel(r\"$t$\", fontsize=13)\n",
    "_ax_e.set_ylabel(r\"$y(t)$\", fontsize=13)\n",
    "_ax_e.set_title(\n",
    "    rf\"Euler staircase vs exact   (error at $t = {T_eu:.0f}$: {err_eu:.3f})\",\n",
    "    fontsize=13,\n",
    ")\n",
    "_ax_e.legend(fontsize=11)\n",
    "_ax_e.grid(True, alpha=0.3)\n",
    "_fig_e.tight_layout()\n",
    "_fig_e;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "NCOB",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "Drag $h$ down to zero: the staircase converges to the smooth curve. This is not approximation magic — it is literally the definition of the derivative, reversed.\n",
    "\n",
    "Notice that halving $h$ roughly halves the error.  Euler's method has **first-order convergence**.  Chapter 6 introduces methods where halving $h$ reduces the error by a factor of four (second-order) or sixteen (fourth-order)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aqbW",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## Summary\n",
    "\n",
    "- A first-order ODE $y' = f(t, y)$ is a **direction field**: at each point $(t, y)$ draw the arrow $(1,\\ f(t, y))$, i.e. run 1, rise $f$.  Solution curves are tangent to the arrows everywhere; they cannot cross each other.\n",
    "- The field shows the behaviour (equilibria, funnels, blow-up) for all starting values at once, even when there is no formula.\n",
    "- The ODE is the continuous limit of the difference equation $y_{n+1} = y_n + h\\,f(t_n, y_n)$ as $h \\to 0$.\n",
    "- That difference equation is Euler's method.  Chapter 6 is the story of how to do this better."
   ]
  }
 ],
 "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 4 — ODEs: direction fields and the discrete origin",
    "width": "medium"
   },
   "marimo_version": "0.25.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
