{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "interactive-link",
   "metadata": {},
   "source": [
    "> **This is a saved, working copy.** Every cell below runs exactly as\n",
    "> shown, just like it did in the browser.\n",
    "> For the live browser version of this homework (handy if you want to\n",
    "> tinker), see [Homework 2 — interactive](https://math4120.pages.dev/wasm/hw2_homework.html).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ipython-import",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:26:30.961562Z",
     "iopub.status.busy": "2026-11-13T23:26:30.961290Z",
     "iopub.status.idle": "2026-11-13T23:26:30.965733Z",
     "shell.execute_reply": "2026-11-13T23:26:30.964912Z"
    }
   },
   "outputs": [],
   "source": [
    "from IPython.display import Markdown, HTML\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "Hbol",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "# Computational Assignment — Numerical Differentiation\n",
    "\n",
    "**MATH4120 — Mathematical Modelling and Programming** Lancaster University, 2026–27\n",
    "\n",
    "---\n",
    "\n",
    "**Submission.** Fill in the blanks below, run every cell, then save this notebook as a `.ipynb` file (File → Download → Notebook) and submit it on Moodle. Your submission is graded on the completed code *and* the short written answers in the Markdown cells — write your answers directly into this notebook, don't attach a separate document."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "MJUe",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:26:30.967548Z",
     "iopub.status.busy": "2026-11-13T23:26:30.967362Z",
     "iopub.status.idle": "2026-11-13T23:26:31.363093Z",
     "shell.execute_reply": "2026-11-13T23:26:31.361241Z"
    }
   },
   "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": [
    "## The idea\n",
    "\n",
    "The derivative of $f$ at a point $x_0$ is defined as a limit: $$f'(x_0) = \\lim_{h \\to 0} \\frac{f(x_0 + h) - f(x_0)}{h}.$$\n",
    "\n",
    "We can't actually take $h \\to 0$ on a computer, but we can pick a small $h$ and use the ratio directly — that's a **finite difference approximation**. There are two natural choices:\n",
    "\n",
    "- **Forward difference**: $\\dfrac{f(x_0 + h) - f(x_0)}{h}$ — exactly the limit definition above, with $h$ small but not zero.\n",
    "- **Centred difference**: $\\dfrac{f(x_0 + h) - f(x_0 - h)}{2h}$ — uses one point on each side of $x_0$ instead of just one side.\n",
    "\n",
    "Both should approach the true derivative as $h \\to 0$. The question this assignment investigates: **how fast**, and does it matter which one you pick?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bkHC",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## Parameters\n",
    "\n",
    "We'll differentiate $f(x) = \\sin(x)$ at $x_0 = 1.0$, where the exact derivative $f'(x_0) = \\cos(x_0)$ is known — so we can measure the error of each approximation directly, the same way Chapter 6 measured Euler's method against a known exact solution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "lEQa",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:26:31.366808Z",
     "iopub.status.busy": "2026-11-13T23:26:31.366406Z",
     "iopub.status.idle": "2026-11-13T23:26:31.371488Z",
     "shell.execute_reply": "2026-11-13T23:26:31.370179Z"
    }
   },
   "outputs": [],
   "source": [
    "def f_hw2(x):\n",
    "    return np.sin(x)\n",
    "\n",
    "def df_exact_hw2(x):\n",
    "    return np.cos(x)\n",
    "\n",
    "x0_hw2 = 1.0"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "PKri",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## Exercise 1 — forward difference\n",
    "\n",
    "**Task.** In the cell below, replace the `0.0` placeholder with the forward difference formula, using `f_hw2`, `x0_hw2`, and `h_ex1`. You should get a value close to (but not exactly equal to) $\\cos(1.0) \\approx 0.5403$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "Xref",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:26:31.373656Z",
     "iopub.status.busy": "2026-11-13T23:26:31.373457Z",
     "iopub.status.idle": "2026-11-13T23:26:31.379980Z",
     "shell.execute_reply": "2026-11-13T23:26:31.378800Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h_ex1 = 0.1\n",
    "df_forward_ex1 = 0.0    # ← fill this in\n",
    "df_forward_ex1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "SFPL",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## Exercise 2 — centred difference\n",
    "\n",
    "**Task.** Same idea, but now use the centred difference formula. Replace the `0.0` placeholder using `f_hw2`, `x0_hw2`, and `h_ex2`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "BYtC",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:26:31.382321Z",
     "iopub.status.busy": "2026-11-13T23:26:31.382151Z",
     "iopub.status.idle": "2026-11-13T23:26:31.386591Z",
     "shell.execute_reply": "2026-11-13T23:26:31.385639Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h_ex2 = 0.1\n",
    "df_centred_ex2 = 0.0    # ← fill this in\n",
    "df_centred_ex2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "RGSE",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## Exercise 3 — convergence study\n",
    "\n",
    "Now repeat both approximations for a whole range of $h$ values, from $h = 10^{-1}$ down to $h = 10^{-6}$, and measure the error against the exact derivative at each one.\n",
    "\n",
    "**Task.** Complete the two array formulas below — they're the same formulas as Exercises 1 and 2, just applied to the array `h_arr` instead of a single number."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "Kclp",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:26:31.388246Z",
     "iopub.status.busy": "2026-11-13T23:26:31.388090Z",
     "iopub.status.idle": "2026-11-13T23:26:31.392010Z",
     "shell.execute_reply": "2026-11-13T23:26:31.390955Z"
    }
   },
   "outputs": [],
   "source": [
    "h_arr = 10.0 ** (-np.arange(1, 7, dtype=float))\n",
    "df_forward_arr = np.zeros_like(h_arr)   # ← same formula as Exercise 1, but with h_arr\n",
    "df_centred_arr = np.zeros_like(h_arr)   # ← same formula as Exercise 2, but with h_arr\n",
    "forward_error = np.abs(df_forward_arr - df_exact_hw2(x0_hw2))\n",
    "centred_error = np.abs(df_centred_arr - df_exact_hw2(x0_hw2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "emfo",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:26:31.393916Z",
     "iopub.status.busy": "2026-11-13T23:26:31.393722Z",
     "iopub.status.idle": "2026-11-13T23:26:31.921097Z",
     "shell.execute_reply": "2026-11-13T23:26:31.920007Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "marimo": {
     "config": {
      "hide_code": true
     }
    },
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 700x450 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_fig, _ax = plt.subplots(figsize=(7, 4.5))\n",
    "_ax.loglog(h_arr, forward_error, \"o-\", color=\"#1a5276\", linewidth=2,\n",
    "           markersize=7, label=\"forward difference\")\n",
    "_ax.loglog(h_arr, centred_error, \"s-\", color=\"tomato\", linewidth=2,\n",
    "           markersize=7, label=\"centred difference\")\n",
    "_h_ref = [h_arr.min(), h_arr.max()]\n",
    "_ax.loglog(_h_ref, [forward_error[-1] / h_arr[-1] * _h for _h in _h_ref],\n",
    "           \"k--\", linewidth=1.2, label=\"slope 1\")\n",
    "_ax.loglog(_h_ref, [centred_error[-1] / h_arr[-1] ** 2 * _h ** 2 for _h in _h_ref],\n",
    "           \"k:\", linewidth=1.2, label=\"slope 2\")\n",
    "_ax.set_xlabel(r\"Step size $h$\", fontsize=13)\n",
    "_ax.set_ylabel(\"Error\", fontsize=13)\n",
    "_ax.set_title(\"Forward vs centred difference: convergence as $h \\\\to 0$\", fontsize=13)\n",
    "_ax.legend(fontsize=10)\n",
    "_ax.grid(True, which=\"both\", alpha=0.3)\n",
    "_fig.tight_layout()\n",
    "_fig;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "Hstk",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## Written answer — required\n",
    "\n",
    "**Task.** Looking at the log-log plot above: which line is steeper, and what does that tell you about how each method's error shrinks as $h$ gets smaller? Relate the slopes you see (1 and 2) to how many times you'd need to halve $h$ to gain one extra decimal digit of accuracy with each method.\n",
    "\n",
    "*Double-click this cell and write 3–5 sentences.*"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "nWHF",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## Extension — when smaller isn't better\n",
    "\n",
    "So far, smaller $h$ has always meant a smaller error. That can't continue forever — a computer only stores about 16 significant digits, and `f_hw2(x0_hw2 + h) - f_hw2(x0_hw2)` subtracts two nearly-equal numbers, which destroys precision when $h$ gets *very* small (a phenomenon called **catastrophic cancellation**).\n",
    "\n",
    "**Task.** Run the cell below, which extends the study down to $h = 10^{-14}$. Describe in a sentence or two what happens to the two error curves once $h$ gets small enough, and why shrinking $h$ further stops helping (or starts hurting).\n",
    "\n",
    "*Double-click this cell and write 2–3 sentences.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "iLit",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:26:31.923430Z",
     "iopub.status.busy": "2026-11-13T23:26:31.923252Z",
     "iopub.status.idle": "2026-11-13T23:26:31.927895Z",
     "shell.execute_reply": "2026-11-13T23:26:31.926810Z"
    }
   },
   "outputs": [],
   "source": [
    "h_arr_ext = 10.0 ** (-np.arange(1, 15, dtype=float))\n",
    "df_forward_ext = (f_hw2(x0_hw2 + h_arr_ext) - f_hw2(x0_hw2)) / h_arr_ext\n",
    "df_centred_ext = (f_hw2(x0_hw2 + h_arr_ext) - f_hw2(x0_hw2 - h_arr_ext)) / (2 * h_arr_ext)\n",
    "forward_error_ext = np.abs(df_forward_ext - df_exact_hw2(x0_hw2))\n",
    "centred_error_ext = np.abs(df_centred_ext - df_exact_hw2(x0_hw2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ZHCJ",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:26:31.930135Z",
     "iopub.status.busy": "2026-11-13T23:26:31.929932Z",
     "iopub.status.idle": "2026-11-13T23:26:32.246733Z",
     "shell.execute_reply": "2026-11-13T23:26:32.245696Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "marimo": {
     "config": {
      "hide_code": true
     }
    },
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x450 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_fig, _ax = plt.subplots(figsize=(7, 4.5))\n",
    "_ax.loglog(h_arr_ext, forward_error_ext, \"o-\", color=\"#1a5276\", linewidth=2,\n",
    "           markersize=5, label=\"forward difference\")\n",
    "_ax.loglog(h_arr_ext, centred_error_ext, \"s-\", color=\"tomato\", linewidth=2,\n",
    "           markersize=5, label=\"centred difference\")\n",
    "_ax.set_xlabel(r\"Step size $h$\", fontsize=13)\n",
    "_ax.set_ylabel(\"Error\", fontsize=13)\n",
    "_ax.set_title(\"Extending to very small $h$: round-off takes over\", fontsize=13)\n",
    "_ax.legend(fontsize=10)\n",
    "_ax.grid(True, which=\"both\", alpha=0.3)\n",
    "_ax.invert_xaxis()\n",
    "_fig.tight_layout()\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": "Computational Assignment — Numerical Differentiation",
    "width": "medium"
   },
   "marimo_version": "0.25.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
