fix typos and latex formatting, add original image from FEM.ipynb

NeumannElliptic.ipynb

@@ -1,20 +1,4 @@
 {
- "nbformat": 4,
- "nbformat_minor": 0,
- "metadata": {
-  "colab": {
-   "name": "NeumannElliptic.ipynb",
-   "private_outputs": true,
-   "provenance": []
-  },
-  "kernelspec": {
-   "name": "python3",
-   "display_name": "Python 3"
-  },
-  "language_info": {
-   "name": "python"
-  }
- },
  "cells": [
   {
    "cell_type": "markdown",
@@ -35,8 +19,6 @@
    },
    "source": [
     "# Metoda różnic skończonych\n",
-    "\n",
-    "\n",
     "## Laboratorium V\n",
     "### Warunek brzegowy Neumanna\n",
     "\n",
@@ -55,9 +37,11 @@
   },
   {
    "cell_type": "code",
+   "execution_count": null,
    "metadata": {
     "id": "8gjbWJ3-d2PE"
    },
+   "outputs": [],
    "source": [
     "import numpy as np\n",
     "import scipy as sc\n",
@@ -69,15 +53,15 @@
     "from scipy.sparse import lil_matrix, csr_matrix\n",
     "from typing import Optional\n",
     "import time"
-   ],
-   "execution_count": null,
-   "outputs": []
+   ]
   },
   {
    "cell_type": "code",
+   "execution_count": null,
    "metadata": {
     "id": "NWqt8umcd4bj"
    },
+   "outputs": [],
    "source": [
     "class SetupElliptic:\n",
     "    def __init__(self, dx: float, dy: Optional[float] = None):\n",
@@ -99,15 +83,15 @@
     "    @staticmethod\n",
     "    def f(x, y):\n",
     "        return 0"
-   ],
-   "execution_count": null,
-   "outputs": []
+   ]
   },
   {
    "cell_type": "code",
+   "execution_count": null,
    "metadata": {
     "id": "Xj3GLJcwd8n0"
    },
+   "outputs": [],
    "source": [
     "def scheme_elliptic(setup):\n",
     "    size = (setup.x_num + 1) * (setup.y_num + 1)\n",
@@ -127,15 +111,15 @@
     "    w = w.reshape(setup.x_num + 1, setup.y_num + 1)\n",
     "\n",
     "    return w"
-   ],
-   "execution_count": null,
-   "outputs": []
+   ]
   },
   {
    "cell_type": "code",
+   "execution_count": null,
    "metadata": {
     "id": "Z-iBYkbPeB72"
    },
+   "outputs": [],
    "source": [
     "def plot_surface(values: float, setup):\n",
     "    fig = plt.figure()\n",
@@ -159,53 +143,67 @@
     "    fig.colorbar(surf, shrink=0.5, aspect=5)\n",
     "\n",
     "    plt.show()"
-   ],
-   "execution_count": null,
-   "outputs": []
+   ]
   },
   {
    "cell_type": "code",
+   "execution_count": null,
    "metadata": {
     "id": "Mf98GjETd_oN"
    },
+   "outputs": [],
    "source": [
     "%%time\n",
     "# numerical solution\n",
     "setup_elliptic = SetupElliptic(0.005)\n",
     "numerical_elliptic = scheme_elliptic(setup_elliptic)"
-   ],
-   "execution_count": null,
-   "outputs": []
+   ]
   },
   {
    "cell_type": "code",
+   "execution_count": null,
    "metadata": {
     "id": "w6kfztI9fmYJ"
    },
+   "outputs": [],
    "source": [
     "plot_surface(numerical_elliptic, setup_elliptic)"
-   ],
-   "execution_count": null,
-   "outputs": []
+   ]
   },
   {
    "cell_type": "markdown",
-   "source": [
-    "# Rozważyć warunki brzegowe (Dirichleta i Neumanna) różne od zera\n",
-    "\n"
-   ],
    "metadata": {
     "id": "te9q0l4dnxAF"
-   }
+   },
+   "source": [
+    "#### Rozważyć warunki brzegowe (Dirichleta i Neumanna) różne od zera\n",
+    "\n"
+   ]
   },
   {
    "cell_type": "code",
-   "source": [],
+   "execution_count": null,
    "metadata": {
     "id": "_lVkKxp3n3_Z"
    },
-   "execution_count": null,
-   "outputs": []
+   "outputs": [],
+   "source": []
   }
- ]
+ ],
+ "metadata": {
+  "colab": {
+   "name": "NeumannElliptic.ipynb",
+   "private_outputs": true,
+   "provenance": []
+  },
+  "kernelspec": {
+   "display_name": "Python 3",
+   "name": "python3"
+  },
+  "language_info": {
+   "name": "python"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
 }