.PhV Tutorium Gruppe 3.md

Jupyter-Notebooks zu den Tutorien in Physik V.

(PS: manchmal ist GitHub etwas überfordert mit der Vorschau der ganzen Notebooks — am Besten runterladen, oder im Binder anschauen!)

Tutorium 1.ipynb

Tutorium 10.ipynb

Tutorium 11.ipynb

Tutorium 12.ipynb

Tutorium 13.ipynb

Tutorium 3.ipynb

Tutorium 4.ipynb

{
 "cells": [
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   "cell_type": "markdown",
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   "source": [
    "# Physik V Gruppe 3 — Tutorium #4\n",
    "\n",
    "> 26.11.2020         ralf@uni-bonn.de"
   ]
  },
  {
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     "source_hidden": true
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   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import astropy.units as u\n",
    "import astropy.constants as const\n",
    "\n",
    "# import sympy as sy\n",
    "# from uncertainties import ufloat, unumpy as unp\n",
    "\n",
    "u.c = u.def_unit('c', const.c)  # verwende 'c' als Einheit, statt als Konstante"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
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   "source": [
    "from IPython.display import display, Math, Latex, Markdown\n",
    "from IPython.core.magic import register_line_magic, needs_local_scope\n",
    "import re\n",
    "\n",
    "def _pretty(s):\n",
    "    \n",
    "    try:\n",
    "        # `import pint`\n",
    "        if isinstance(s, pint.quantity.Quantity):\n",
    "            return re.sub(r\"\\\\$\", \"\", f\"{s:.5~L}\")\n",
    "    except:\n",
    "        pass\n",
    "    try:\n",
    "        # `import sympy as sy`\n",
    "        if isinstance(s, sy.core.expr.Expr):\n",
    "            return sy.latex(s)\n",
    "    except:\n",
    "        pass\n",
    "    try:\n",
    "        # `import astropy.units as u`\n",
    "        if isinstance(s, (int, float)):\n",
    "            s = u.Quantity(s)\n",
    "        if isinstance(s, u.quantity.Quantity):\n",
    "            return s.to_string(format=\"latex\").lstrip(\"$\").rstrip(\"$\")\n",
    "    except Exception as e:\n",
    "        raise e\n",
    "        pass\n",
    "    \n",
    "    return str(s)\n",
    "\n",
    "def tex(*s, tag=\"align\"):\n",
    "    display(Latex(r\"\\begin{\"+tag+\"}\" + \"\\n\"+ ' '.join(_pretty(e) for e in s) + \"\\n\" + r\"\\end{\"+tag+\"}\"))\n",
    "\n",
    "@register_line_magic(\"tex\")\n",
    "@needs_local_scope\n",
    "def _tex(line, local_ns):\n",
    "    # TODO: handle single `<` and `>`\n",
    "    tex(re.sub(\"<(.*?)>\", lambda m: _pretty(eval(m.group(1))), line))\n",
    "\n",
    "del _tex  # prevent conflicts in interactive session"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "jupyter": {
     "source_hidden": true
    }
   },
   "source": [
    "(TeX Commands)\n",
    "\n",
    "$$\n",
    "\\newcommand\\dv[2]{\\frac{\\mathrm d #1}{\\mathrm d #2}}\n",
    "\\newcommand\\sub[1]{_{\\text{#1}}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Blatt 2: A2. Yukawa-Potential"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-26T12:35:23.514009Z",
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     "shell.execute_reply.started": "2020-11-26T12:35:23.513973Z"
    }
   },
   "outputs": [],
   "source": [
    "m_pi = 140*u.MeV"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "R = \\frac\\hbar{M_X c} \\overset{\\text{nat}}=  \\frac1m \n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-26T12:35:23.520096Z",
     "iopub.status.busy": "2020-11-26T12:35:23.519779Z",
     "iopub.status.idle": "2020-11-26T12:35:23.532900Z",
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     "shell.execute_reply.started": "2020-11-26T12:35:23.520070Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$0.0071428571 \\; \\mathrm{\\frac{1}{MeV}}$"
      ],
      "text/plain": [
       "<Quantity 0.00714286 1 / MeV>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R_nat = 1/m_pi\n",
    "R_nat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Frage Blatt:** Welche Reichweite ergibt sich für den Austausch von Pionen (`m = m_pi`)?\n",
    "\n",
    "**Hausaufgabe:** Mit was muss ich `R_nat` multiplizieren, um auf *Meter* zu kommen?\n",
    "\n",
    "\n",
    "&rarr; zB im Papier von [L. Myers: Natural System of Units in General Relativity](https://www.seas.upenn.edu/~amyers/NaturalUnits.pdf) gibt es eine hübsche Tabelle mit Vorfaktoren für die Umrechnung in/von natürliche Einheiten. Bei `mass` steht zB $c^{-2}$, was allerdings die Umrechnung **von** natürlichen **in** SI-Einheiten ist. Aufpassen!\n",
    "\n",
    "Beispiel:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-26T12:35:23.534432Z",
     "iopub.status.busy": "2020-11-26T12:35:23.534144Z",
     "iopub.status.idle": "2020-11-26T12:35:23.540470Z",
     "shell.execute_reply": "2020-11-26T12:35:23.539909Z",
     "shell.execute_reply.started": "2020-11-26T12:35:23.534397Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$5.6095886 \\times 10^{35} \\; \\mathrm{eV}$"
      ],
      "text/plain": [
       "<Quantity 5.6095886e+35 eV>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "( (1*u.kg) * const.c**2 ).to(\"eV\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Für die Umrechnung von `1/eV` in Meter:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-26T12:35:23.541351Z",
     "iopub.status.busy": "2020-11-26T12:35:23.541198Z",
     "iopub.status.idle": "2020-11-26T12:35:23.547583Z",
     "shell.execute_reply": "2020-11-26T12:35:23.546528Z",
     "shell.execute_reply.started": "2020-11-26T12:35:23.541332Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$1.4094784 \\; \\mathrm{fm}$"
      ],
      "text/plain": [
       "<Quantity 1.40947843 fm>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(R_nat * const.hbar * const.c).to(\"fm\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## H1. Radionuklidbatterien"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Aktivität:\n",
    "\n",
    "$$\n",
    "A(t) = -\\dv{N(t)}t = \\lambda N_0 e^{-\\lambda t}\n",
    "\\qquad \\lambda = \\frac{\\ln 2}{T_{1/2}}\n",
    "$$\n",
    "\n",
    "\n",
    "für $t=0$:\n",
    "\n",
    "$$\n",
    "A(0) = \\frac{\\ln 2\\ N_0}{T_{1/2}} \\qquad \\Rightarrow  N\\sub{Pu} \\equiv N_0 = \\dots\n",
    "$$\n",
    "\n",
    "Leistung der Batterie:\n",
    "\n",
    "$$\n",
    "A_0 = \\frac P{E_\\alpha\\, \\kappa} \\equiv A(0)\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-26T12:35:23.548951Z",
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     "shell.execute_reply.started": "2020-11-26T12:35:23.548916Z"
    }
   },
   "outputs": [],
   "source": [
    "P0 = 480*u.W\n",
    "T12 = 87.7*u.a\n",
    "E_alpha = 5.593*u.MeV\n",
    "\n",
    "kappa = 5*u.percent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-26T12:35:23.553755Z",
     "iopub.status.busy": "2020-11-26T12:35:23.553592Z",
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     "shell.execute_reply.started": "2020-11-26T12:35:23.553735Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "A_0 = 1.0713121 \\times 10^{16} \\; \\mathrm{Bq}\n",
       "\\end{align}"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A0 = P0 / (E_alpha*kappa)\n",
    "%tex A_0 = <A0.to(\"Bq\")>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "mit\n",
    "\n",
    "$$\n",
    "N\\sub{Pu} = N_A \\, \\frac{M}{m\\sub{mol}}\n",
    "$$\n",
    "\n",
    "kommen wir auf die Masse:\n",
    "\n",
    "\n",
    "$$\n",
    "M = \\frac{N\\sub{Pu} \\, m\\sub{mol}}{N_A} = \\frac{A_0\\,T_{1/2}\\, m\\sub{mol}}{N_A\\,\\ln 2}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-26T12:35:23.563897Z",
     "iopub.status.busy": "2020-11-26T12:35:23.563626Z",
     "iopub.status.idle": "2020-11-26T12:35:23.570233Z",
     "shell.execute_reply": "2020-11-26T12:35:23.569560Z",
     "shell.execute_reply.started": "2020-11-26T12:35:23.563864Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "M = 16.905195 \\; \\mathrm{kg}\n",
       "\\end{align}"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m_mol = 238 * u.g/u.mol\n",
    "\n",
    "M = A0 * T12 * m_mol / (const.N_A * np.log(2))\n",
    "%tex M = <M.decompose()>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## b)\n",
    "\n",
    "$$\n",
    "P(t) = P_0 \\, e^{-\\lambda t}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-26T12:35:23.571773Z",
     "iopub.status.busy": "2020-11-26T12:35:23.571501Z",
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     "shell.execute_reply.started": "2020-11-26T12:35:23.571738Z"
    }
   },
   "outputs": [],
   "source": [
    "lam = np.log(2)/T12\n",
    "\n",
    "def P(t):\n",
    "    t = u.Quantity(t, u.a)  # nehme 'a' als Standard-Einheit\n",
    "    return P0 * np.exp(-lam * t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-26T12:35:23.577070Z",
     "iopub.status.busy": "2020-11-26T12:35:23.576894Z",
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     "shell.execute_reply.started": "2020-11-26T12:35:23.577049Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$468.75266 \\; \\mathrm{W}$"
      ],
      "text/plain": [
       "<Quantity 468.75266094 W>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P(3*u.a)  # äquivalent zu P(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-26T12:35:23.583705Z",
     "iopub.status.busy": "2020-11-26T12:35:23.583519Z",
     "iopub.status.idle": "2020-11-26T12:35:23.587409Z",
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     "shell.execute_reply.started": "2020-11-26T12:35:23.583684Z"
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   },
   "outputs": [],
   "source": [
    "from datetime import datetime\n",
    "# oder: pendulum, delorean\n",
    "\n",
    "dt_start = datetime(1977, 9, 5)\n",
    "dt_saturn = datetime(1980, 8, 22)\n",
    "dt_today = datetime.now()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-26T12:35:23.588853Z",
     "iopub.status.busy": "2020-11-26T12:35:23.588583Z",
     "iopub.status.idle": "2020-11-26T12:35:23.593385Z",
     "shell.execute_reply": "2020-11-26T12:35:23.592616Z",
     "shell.execute_reply.started": "2020-11-26T12:35:23.588817Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "datetime.timedelta(days=1082)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "delta_saturn = dt_saturn - dt_start\n",
    "delta_saturn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Gesamtzahl der Sekunden:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-26T12:35:23.594804Z",
     "iopub.status.busy": "2020-11-26T12:35:23.594518Z",
     "iopub.status.idle": "2020-11-26T12:35:23.599375Z",
     "shell.execute_reply": "2020-11-26T12:35:23.598653Z",
     "shell.execute_reply.started": "2020-11-26T12:35:23.594768Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "93484800.0"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "delta_saturn.total_seconds()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(Achtung, `delta_saturn.seconds` gibt `0` zurück!)\n",
    "\n",
    "Damit lässt sich die verbleibende Leistung beim Vorbeiflug an Saturn berechnen:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-26T12:35:23.600644Z",
     "iopub.status.busy": "2020-11-26T12:35:23.600397Z",
     "iopub.status.idle": "2020-11-26T12:35:23.605740Z",
     "shell.execute_reply": "2020-11-26T12:35:23.605129Z",
     "shell.execute_reply.started": "2020-11-26T12:35:23.600613Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$468.89215 \\; \\mathrm{W}$"
      ],
      "text/plain": [
       "<Quantity 468.8921521 W>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P(delta_saturn.total_seconds() * u.s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-26T12:35:23.606693Z",
     "iopub.status.busy": "2020-11-26T12:35:23.606523Z",
     "iopub.status.idle": "2020-11-26T12:35:23.613658Z",
     "shell.execute_reply": "2020-11-26T12:35:23.613081Z",
     "shell.execute_reply.started": "2020-11-26T12:35:23.606672Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "P\\sub{Saturn} = 468.89215 \\; \\mathrm{W}\n",
       "\\end{align}"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "P\\sub{heute} = 341.08733 \\; \\mathrm{W}\n",
       "\\end{align}"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%tex P\\sub{Saturn} = <P(delta_saturn.total_seconds() * u.s)>\n",
    "%tex P\\sub{heute} = <P((dt_today - dt_start).total_seconds()*u.s)>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-26T12:35:23.614800Z",
     "iopub.status.busy": "2020-11-26T12:35:23.614627Z",
     "iopub.status.idle": "2020-11-26T12:35:23.619919Z",
     "shell.execute_reply": "2020-11-26T12:35:23.619195Z",
     "shell.execute_reply.started": "2020-11-26T12:35:23.614781Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$2.4063414 \\times 10^{-135} \\; \\mathrm{W}$"
      ],
      "text/plain": [
       "<Quantity 2.40634138e-135 W>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P(40_000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-26T12:35:23.621003Z",
     "iopub.status.busy": "2020-11-26T12:35:23.620741Z",
     "iopub.status.idle": "2020-11-26T12:35:23.627214Z",
     "shell.execute_reply": "2020-11-26T12:35:23.626369Z",
     "shell.execute_reply.started": "2020-11-26T12:35:23.620970Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "P\\sub{in 40.000} = 1.7099428 \\times 10^{-135} \\; \\mathrm{W}\n",
       "\\end{align}"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%tex P\\sub{in 40.000} = <P((dt_today - dt_start).total_seconds()*u.s + 40000*u.a)>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-26T12:35:23.628674Z",
     "iopub.status.busy": "2020-11-26T12:35:23.628402Z",
     "iopub.status.idle": "2020-11-26T12:35:23.633249Z",
     "shell.execute_reply": "2020-11-26T12:35:23.632698Z",
     "shell.execute_reply.started": "2020-11-26T12:35:23.628640Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$5.0132112 \\times 10^{-138} \\; \\mathrm{}$"
      ],
      "text/plain": [
       "<Quantity 5.01321122e-138>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P(40_000) / P(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br><br><br><br><br><br><br><br><br><br><br>\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-26T12:37:22.497856Z",
     "iopub.status.busy": "2020-11-26T12:37:22.497656Z",
     "iopub.status.idle": "2020-11-26T12:37:22.507171Z",
     "shell.execute_reply": "2020-11-26T12:37:22.506572Z",
     "shell.execute_reply.started": "2020-11-26T12:37:22.497834Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "**conda `environment.yml`:**"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "name: phyv-py38\n",
      "channels:\n",
      "  - conda-forge\n",
      "  - defaults\n",
      "dependencies:\n",
      "  - python=3.8.5\n",
      "  - pip=20.2.4\n",
      "  - numpy=1.19.2\n",
      "  - pip:\n",
      "    - astropy==4.1\n",
      "    - matplotlib==3.3.2\n",
      "    - sympy==1.6.2\n",
      "    - scipy==1.5.2\n",
      "    - pint==0.16.1\n",
      "    - seaborn==0.11.0\n",
      "    - uncertainties==3.1.4\n"
     ]
    },
    {
     "data": {
      "text/markdown": [
       "&nbsp;\n",
       "\n",
       "**Binder badge:**"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/git/https%3A%2F%2Fgist.github.com%2F4b47022b6e439ddbdadd43fb7f99eb70.git/HEAD?filepath=Tutorium%204.ipynb&urlpath=lab)\n"
     ]
    }
   ],
   "source": [
    "from IPython.display import Markdown\n",
    "import sys, pip, numpy, astropy, matplotlib, sympy, scipy, pint, seaborn, uncertainties\n",
    "\n",
    "display(Markdown(\"**conda `environment.yml`:**\"))\n",
    "print(\"name: phyv-py38\\nchannels:\\n  - conda-forge\\n  - defaults\\ndependencies:\")\n",
    "print(f\"  - python={sys.version.split()[0]}\")\n",
    "print(f\"  - pip={pip.__version__}\")\n",
    "print(f\"  - numpy={numpy.__version__}\")\n",
    "print(f\"  - pip:\")  # use double == for pip\n",
    "print(f\"    - astropy=={astropy.__version__}\")\n",
    "print(f\"    - matplotlib=={matplotlib.__version__}\")\n",
    "print(f\"    - sympy=={sympy.__version__}\")\n",
    "print(f\"    - scipy=={scipy.__version__}\")\n",
    "print(f\"    - pint=={pint.__version__}\")\n",
    "print(f\"    - seaborn=={seaborn.__version__}\")\n",
    "print(f\"    - uncertainties=={uncertainties.__version__}\")\n",
    "\n",
    "\n",
    "display(Markdown(\"&nbsp;\\n\\n**Binder badge:**\"))\n",
    "id = \"4b47022b6e439ddbdadd43fb7f99eb70\"\n",
    "fn = \"Tutorium 4.ipynb\"\n",
    "print(f\"[![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/git/https%3A%2F%2Fgist.github.com%2F{id}.git/HEAD?filepath={fn.replace(' ', '%20')}&urlpath=lab)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "3.8.5 (Framework)",
   "language": "python",
   "name": "3.8.5-framework"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}

Tutorium 5.ipynb

environment.yml

Tutorium 6.ipynb

Tutorium 8.ipynb