2nd_Mécanique_1_02_ELEVE_2.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "2nd_Mécanique_1_02_ELEVE 2.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UYtYa-G2f0Tp",
        "colab_type": "text"
      },
      "source": [
        "# **Mécanique**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-qBvlZHPJkS1",
        "colab_type": "text"
      },
      "source": [
        "*Avant donc que d'écrire, apprenez à penser.\n",
        "Selon que notre idée est plus ou moins obscure, l'expression la suit, ou moins nette, ou plus pure.\n",
        "Ce que l'on conçoit bien s'énonce clairement, et les mots pour le dire arrivent aisément.                                                    - Nicolas Boileau, L'Art poétique*"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9cLGwywatkE0",
        "colab_type": "text"
      },
      "source": [
        "**Capacités numériques travaillées**: \n",
        "1.   représenter un nuage de points \n",
        "associé à la caractéristique d’un dipôle et modéliser la \n",
        "caractéristique de ce dipôle à l’aide d’un langage de \n",
        "programmation.\n",
        "2.  représenter des vecteurs vitesse d’un \n",
        "système modélisé par un point lors d’un mouvement à l’aide \n",
        "d’un langage de programmation. \n",
        "1.    représenter des vecteurs variation de \n",
        "vitesse d’un système modélisé par un point lors d’une évolution \n",
        "unidimensionnelle ou bidimensionnelle à l’aide d’un langage de \n",
        "programmation.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VCyJ5c6dJylu",
        "colab_type": "text"
      },
      "source": [
        ""
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VnKbxReNW25X",
        "colab_type": "text"
      },
      "source": [
        "https://ledatascientist.com/python-pour-la-data-science-les-bases/"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5O9ecjpgdMNT",
        "colab_type": "text"
      },
      "source": [
        "[Pour en savoir plus](http://www.python-simple.com/python-matplotlib/pyplot.php)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GeB7NugqKvua",
        "colab_type": "text"
      },
      "source": [
        "# **M1 Tracé des positions successives d'un mobile lors d'un lancer de balle**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6XUOyVi8MV7c",
        "colab_type": "text"
      },
      "source": [
        " \n",
        "On étudie le mouvement d'un ballon de basket à partir d'une chronophotographie dans le but de tracer les vecteurs vitesses au cours du temps.\n",
        "Les positions relevées toutes les 66 ms  sont rassemblées dans un tableau. \n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gBTsp_Bo66M8",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "\n",
        "*   t\t0\t0.066\t0.132\t0.198\t0.264\t0.330\t0.396\t0.462\t0.528\t0.594\t0.66\n",
        "*   x\t0.01\t0.25\t0.57\t0.91\t1.22\t1.54\t1.87\t2.16\t2.49\t2.81\t3.15\n",
        "*   y\t0.015\t0.34\t0.681\t1.01\t1.297\t1.559\t1.768\t1.95\t2.08\t2.158\t2.193\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FmeAamCjacaf",
        "colab_type": "text"
      },
      "source": [
        "## Créer un tableau de données"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Tbjqe4r-X002",
        "colab_type": "text"
      },
      "source": [
        "Pour créer un tableau de données\n",
        "https://ledatascientist.com/decouvrir-numpy/"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wFm-DoK9X5rf",
        "colab_type": "code",
        "outputId": "f92dc5c2-19ef-427c-ce47-42ab61c5737a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 53
        }
      },
      "source": [
        "b = np.array([(0,0.01,0.015), (0.066,0.25,0.34)])\n",
        "print(b)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[0.    0.01  0.015]\n",
            " [0.066 0.25  0.34 ]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "53pZ_inUFlHb",
        "colab_type": "text"
      },
      "source": [
        "##ANALYSE"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "c9gHJfauFoQF",
        "colab_type": "text"
      },
      "source": [
        "*   Quelle commande pour créer un tableau de valeur ?\n",
        "*   Quels sont les séparateurs de données ? "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LQ9ohvYFgGCJ",
        "colab_type": "text"
      },
      "source": [
        "## Analysez les lignes de programmes puis exécutez-le !"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jvBNLe5pKLQl",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from matplotlib.pyplot import*\n",
        "\n",
        "x=[0.01,0.25,0.57,0.91,1.22,1.54,1.87,2.16,2.49,2.81,3.15]\n",
        "y=[0.01549,0.3404,0.6812,1.010,1.297,1.559,1.768,1.95,2.08,2.158,2.193]\n",
        "\n",
        "# Création et Affichage des données sous forme de tableau\n",
        "print(np.array([\"abscisse\",(x), \"ordonnée\",(y)]))\n",
        "plot(x,y,'D',label=\"y=f(x)\")\n",
        "axis([0,5,0,3])\n",
        "xlabel(\"X\")\n",
        "ylabel(\"y\")\n",
        "grid()\n",
        "legend()\n",
        "title(\"Trajectoire de la balle\")\n",
        "show()\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PC-RRpW3F6qj",
        "colab_type": "text"
      },
      "source": [
        "## Analyse des lignes du programme"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PHET2el0GAfO",
        "colab_type": "text"
      },
      "source": [
        "*   Commentez la ligne 13"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "940miHtOGcOa"
      },
      "source": [
        "##Modifiez les lignes du programme"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8V4c4se0Gdeh",
        "colab_type": "text"
      },
      "source": [
        "*   Changer les marqueurs des points\n",
        "*   Changer le titre du graphique"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "D6RH6IJYipeE",
        "colab_type": "text"
      },
      "source": [
        "## Une Version améliorée avec correlation de Pearson"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vr27AMCZVXPY",
        "colab_type": "text"
      },
      "source": [
        "https://www.datacorner.fr/correlation/\n",
        "\n",
        "https://openclassrooms.com/fr/courses/4525266-decrivez-et-nettoyez-votre-jeu-de-donnees/4725622-analysez-la-correlation-entre-deux-variables-quantitatives \n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XAexXVEMiaSh",
        "colab_type": "code",
        "outputId": "8caae33c-ad09-47f4-b8d5-ea95d94f4276",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 315
        }
      },
      "source": [
        "from matplotlib.pyplot import*\n",
        "from scipy.stats import pearsonr\n",
        "#Création du tableau des valeurs du temps\n",
        "t=[]\n",
        "for i in range(11):\n",
        "  # Génère la 1ere ligne du tableau ( t)\n",
        "    t.append(i*0.066)\n",
        "# Liste des valeurs des corrdonnées x,y\n",
        "x=[0.01,0.25,0.57,0.91,1.22,1.54,1.87,2.16,2.49,2.81,3.15]\n",
        "y=[0.01549,0.3404,0.6812,1.010,1.297,1.559,1.768,1.95,2.08,2.158,2.193]\n",
        "plot(x,y,'D',color = 'red', linestyle = 'dashed', linewidth = 2,\n",
        "  markerfacecolor = 'blue', markersize = 5,label=\"y=f(x)\")\n",
        "xlabel(\"X\")\n",
        "ylabel(\"y\")\n",
        "axis([0,4,0,3])\n",
        "grid()\n",
        "legend()\n",
        "title(\"Trajectoire de la balle\",color = 'blue', fontsize = 16)\n",
        "show()\n",
        "#Coefficient de Pearson\n",
        "#Le coefficient de Pearson ou Pearson r est une mesure qui exprime à quel point\n",
        "#deux variables sont linéairement corrélées. Il est égale au quotient de la \n",
        "#covariance des deux variables et du produit des deux écarts-types\n",
        "coeff_pearson,_ = pearsonr(x,y)\n",
        "print(\"coefficient de Pearson = {}\".format(coeff_pearson))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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MiULquMPdd8Npp8HHH8OnnwbdYUWkTVOikMCGDXDJJfDDH8KWLTB6NDz/fNDs\nJCJtmq5RSHA94rzz4OWXgyamBx+E88+POioRyRFKFAK33x4kif32g7/8JXgKnYhISIlC4Oabg+sT\nN94IPXpEHY2I5Bhdo2iLNm6E0lJYty6Y79QJ7rpLSUJE6qUzirbmo4+C6xFz5sDixXDZZVFHJCI5\nTmcUbcm//hXcHzFnTvD0ueuvjzoiEckDShStWTxOVZ/+EI/D/fdDYSGsXBkM3DdvHhxzTNQRikge\nyFqiMLOHzexjM3ujgfVmZr8zsyVm9pqZ6Vsrk8JHlZa+P5KqM74NV1wBmzfDddfB3/4GPXtGHaGI\n5IlsnlFMBM5Msf6bwEHhdDnwxyzG0rYkPM/6dsZQvOX/qKIAxo2D3/wG2uvSlIikL2uJwt1nAZ+l\nKDIEeMQDc4CuZrZ3tuJpMxKSRM3zrGdSSDEVVP3uwaAZSkSkCcxrBn3LRuVmfYBydz+8nnXlwC3u\n/mI4/wLwE3efV0/ZywnOOujZs+eAsrKyrMWcKZWVlXTu3LnF93vEiIu5ZdVV3M6YL60bzW2M2/OP\nvD7p4dplUcXZVIozc/IhRlCcmVZUVDTf3Y9t1sbunrUJ6AO80cC6cuDrCfMvAMc2Vme/fv08H8Tj\n8Zbf6bZt7pdc4pUU+CDiHtxFF0yDiHtlQQ/36dOjj7MZFGfm5EOM7ooz04B53szv8ih7Pf0H6J0w\n3ytcJs2xYQNceCE89BAxqqnocA6DmAHAIGboedYi0mxRJoqpwIVh76cTgDXuviLCePLXqlVw6qnw\n6KPBg4b+8hdi056homAYo7lNSUJEdkjWur+Y2RNAIdDDzJYDNwEdANz9XuA54CxgCVANjMxWLK3a\nZ5/B8cfD++9D794wdWrtoH6x8jJKR44iNkFJQkSaL2uJwt2/28h6B0Zla/9txu67w9lnB6O//uUv\nsNdedeuKiogtWxhdbCLSKqhDfT5yD84kuncP5u+8M7iZTo8rFZEs0BAe+WbTpuBZ1scfD6tXB8va\nt1eSEJGsUaLIJ59+CqefDg8/HIwCu2BB1BGJSBugpqd8sXAhfOtbsHQpfOUr8H//B8c2794ZEZGm\n0BlFPvjrX+HEE4MkMWBAcOFaSUJEWogSRa57+20oKYG1a2HoUJg1C/bZJ+qoRKQNUdNTrjv4YBg9\nGnbeOXh86U7K7SLSspQoctHnnwd3Wx9ySDB/881gFm1MItJm6edprnnnHTjhBDjjjCBZgJKEiERK\niSKXTJ8eJIl33oFu3YJ7JkREIqZEkSvuuw8GDw6anc4+G/75z2DsJhGRiClRRG3LluA51ldeGbwe\nOxaeeQby4EEoItI26GJ21EvHLoUAAAv6SURBVGbPhrvugg4d4P774aKLoo5IRGQ7OqNoSfE4VX36\nb//c6qIiuP12eOEFJQkRyUlKFC0lHqeqZDil74+k6ptD4Y9/rFt3/fVw8snRxSYikoKanlpCmCSK\nqyczk0LmbhxIxQ9KiO2xB5x3XtTRiYikpDOKbEtKEgAzKaSYcqouvHL7ZigRkRykRJFlVSNHUVo9\ntjZJ1JhJIaXVY6kaqYf8iUhuU6LIsti9d1La7hcMYsZ2ywcxg9KCW4lNuCeawERE0qREkW1mxLau\no4KS2mQxiBlUFAwjVl4W9HoSEclhShTZNngwTJhA7OHfU1EwjNHcpiQhInlFvZ6y4b336Pz221BY\nGMyH90fE+vShdOQoYhOUJEQkfyhRZNrrr8PgwXy1qipIFAcfXLeuqIjYsoWRhSYi0hxqesqkf/0L\nTjkFVqyg8oADYO+9o45IRGSHKVFkyvPPwze+AV98Ad/+Nq/fcgvstlvUUYmI7DAlikx44olgaPD1\n6+Hii2HyZLbtvHPUUYmIZIQSxY5atgwuvDAYInzMGHjwQWivSz8i0npkNVGY2Zlm9raZLTGzcfWs\nv8jMPjGzBeF0aTbjyYo+fYKHDt1yC9x6qx5bKiKtTtZ++ppZO+Ae4HRgOTDXzKa6e3K3nyfd/eps\nxZEV27bBu+/CQQcF8xdfHG08IiJZlM0ziuOAJe6+1N03AZOAIVncX8vYvBkuuAAGDoTXXos6GhGR\nrMtmotgH+DBhfnm4LNl5ZvaamT1lZrn9kOjqavj2t+Hxx2HrVli9OuqIRESyztw9OxWbDQXOdPdL\nw/kLgOMTm5nMrDtQ6e4bzewK4Dvufmo9dV0OXA7Qs2fPAWVlZVmJOZX2lZUcccMNdHnjDTZ16cLr\nv/416xJvpktSWVlJ5zx47rXizKx8iDMfYgTFmWlFRUXz3f3YZm3s7lmZgBOBaQnzNwA3pCjfDljT\nWL39+vXzFvfRR+5HHukO7r17uy9a1Ogm8Xg8+3FlgOLMrHyIMx9idFecmQbM82Z+n2ez6WkucJCZ\n7W9mOwMjgKmJBcws8dbls4FFWYyneTZvDsZleu01OOQQ+Oc/g39FRNqIrCUKd98CXA1MI0gAZe7+\nppn93MzODotdY2Zvmtm/gWuAi7IVT7N16AA33QTHHQezZ0Pv3L6MIiKSaVm9M8zdnwOeS1o2PuH1\nDQRNUrmnqgpiseD1d78Lw4dDu3bRxiQiEgHdmV2figro2xfmzatbpiQhIm2UEkWyxx6DIUPg44/h\nySejjkZEJHJKFPE4VX36QzwOv/sdfO97wT0S48YFQ3KIiLRxbXv0unicqpLhlFaPpXTwOcQ2rwmW\n33YbjB4dbWwiIjmi7SaKMEkUV09mJoXM3TyQCoqJjRmlJCEikqBtNj0lJQmAmRRSTAVV90wImqFE\nRARoo4miauQoSqvH1iaJGjMppLR6LFUjR0UTmIhIDmqTiSI24R5Kd76ZQczYbvkgZlBacCuxCfdE\nE5iISA5qk4mCdu2IbV1LBcW1yWIQM6goGEasvCwYskNERIC2mCgWL4ZzzoGtW4mdeyYVBcMYzW1K\nEiIiDWhbiWL1aiguhs8+g5ISKCsjVl5G6X4TlCRERBrQdrrHbtoE554bnFEcdRQ88UQwLEdREbFl\nyU9nFRGRGm3njOLKK2HWLPjKV+DZZyEPHjQiIpIL2k6iGDIE9tgjSBK9ekUdjYhI3mg7TU9DhsDp\np0NBQdSRiIjkldZ9RjFnDrz4Yt28koSISJO13kTx3ntw9tlw2mlBwhARkWZpnYniiy+CbrCffAKF\nhTBgQNQRiYjkrdaXKDZvhmHDYNEiOOwwKCsLnnstIiLN0roShTuMGgX/+EfQw6m8HLp0iToqEZG8\n1roSxZ13wgMPQMeOMHUq9OkTdUQiInmvdSWKww8PziAeeQSOPz7qaEREWoXWdR/F4MGwdCnsvnvU\nkYiItBr5f0bx4YcwfXrdvJKEiEhG5XeiWLcuGAV28OBgaA4REcm4/E0UW7bAiBHw2mvQty+cdFLU\nEYmItEp5d42iXXU1VX36EzvmEHjuOejeHSoq1OQkIpIleXdGsct/VlD6/kiqpkyD9u1hyhQ48MCo\nwxIRabWymijM7Ewze9vMlpjZuHrW72JmT4brXzKzPo3VucQP4HbGUEwFVTvtGjRBiYhI1mQtUZhZ\nO+Ae4JtAf+C7ZtY/qdglwOfufiDwG+DXjdVbya4AzKSQ4k3PUFUyHOLxjMYuIiJ1snlGcRywxN2X\nuvsmYBIwJKnMEOBP4eungNPMzNLdwUwKKa0eS9XIURkJWEREviybF7P3AT5MmF8OJN8uXVvG3beY\n2RqgO/BpYiEzuxy4PJjrDhwLQGfW8XcWb3vgfV+yxmxd5t/CDulB0vvIUYozs/IhznyIERRnph3c\n3A3zoteTu98P3A9gZvPcPz024pAaFcTpijNDFGfm5EOMoDgzzczmNXfbbDY9/QfonTDfK1xWbxkz\naw90AVZnMSYREWmibCaKucBBZra/me0MjACmJpWZCnw/fD0UmO7unsWYRESkibLW9BRec7gamAa0\nAx529zfN7OfAPHefCjwE/NnMlgCfESSTxtyfrZgzTHFmluLMnHyIERRnpjU7TtMPeBERSSXv7swW\nEZGWpUQhIiIp5WyiyMbwH9mQRpwXmdknZrYgnC6NIMaHzexjM3ujgfVmZr8L38NrZnZMS8cYxtFY\nnIVmtibhWI6PIMbeZhY3s4Vm9qaZXVtPmciPZ5px5sLx7GhmL5vZv8M4f1ZPmcj/1tOMM/K/9YRY\n2pnZq2ZWXs+6ph9Pd8+5ieDi97tAX2Bn4N9A/6QyPwDuDV+PAJ7M0TgvAu6O+HieAhwDvNHA+rOA\n5wEDTgBeytE4C4HyiI/l3sAx4etdgXfq+cwjP55pxpkLx9OAzuHrDsBLwAlJZXLhbz2dOCP/W0+I\n5cfA4/V9vs05nrl6RpH14T8yJJ04I+fuswh6lTVkCPCIB+YAXc1s75aJrk4acUbO3Ve4+yvh63XA\nIoIRBhJFfjzTjDNy4TGqDGc7hFNyD5vI/9bTjDMnmFkvoBh4sIEiTT6euZoo6hv+I/l/8u2G/wBq\nhv9oSenECXBe2ATxlJn1rmd91NJ9H7ngxPD0/3kzOyzKQMJT9qMJfl0myqnjmSJOyIHjGTaTLAA+\nBv7u7g0ezwj/1tOJE3Ljb/23wFhgWwPrm3w8czVRtCbPAn3c/Ujg79Rlcmm6V4D93P2rwO+Bv0QV\niJl1Bp4GrnP3tVHF0ZhG4syJ4+nuW939KILRG44zs8OjiKMxacQZ+d+6mZUAH7v7/EzWm6uJIl+G\n/2g0Tndf7e4bw9kHgQEtFFtTpHO8I+fua2tO/939OaCDmfVo6TjMrAPBl+9j7v5MPUVy4ng2Fmeu\nHM+EeL4A4sCZSaty4W+9VkNx5sjf+knA2Wa2jKAp/FQzezSpTJOPZ64minwZ/qPROJPaps8maCvO\nNVOBC8PeOicAa9x9RdRBJTOzvWraUs3sOIL/f1v0CyPc/0PAIne/s4FikR/PdOLMkePZ08y6hq87\nAacDbyUVi/xvPZ04c+Fv3d1vcPde7t6H4Ptourt/L6lYk49nTo4e69kb/iOKOK8xs7OBLWGcF7V0\nnGb2BEEPlx5mthy4ieBiHO5+L/AcQU+dJUA1MLKlY0wzzqHAVWa2BVgPjIjgx8FJwAXA62F7NcBP\ngX0T4syF45lOnLlwPPcG/mTBg852AsrcvTzX/tbTjDPyv/WG7Ojx1BAeIiKSUq42PYmISI5QohAR\nkZSUKEREJCUlChERSUmJQkREUlKiENkBFozS+p6Z7R7Odwvn+0QbmUjmKFGI7AB3/xD4I3BLuOgW\n4H53XxZZUCIZpvsoRHZQOFTGfOBh4DLgKHffHG1UIpmTk3dmi+QTd99sZmOAvwJnKElIa6OmJ5HM\n+CawAsjJkU9FdoQShcgOMrOjCAaJOwH4URQPfRLJJiUKkR0Qjr76R4LnPXwA3AbcHm1UIpmlRCGy\nYy4DPnD3v4fzfwAONbNBEcYkklHq9SQiIinpjEJERFJSohARkZSUKEREJCUlChERSUmJQkREUlKi\nEBGRlJQoREQkpf8PwKTefk2zWfsAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "coefficient de Pearson = 0.9726703063434554\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "XeBgJEwVHJ2m"
      },
      "source": [
        "##Modifiez les lignes du programme"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "55jy3BNSHKj9",
        "colab_type": "text"
      },
      "source": [
        "*   Changer la couleur du titre\n",
        "*   Changer le type de ligne\n",
        "*   Chnager la couleur de la ligne reliant les points\n",
        "*   Les valeurs ( x,y) sont elles corrélées ou non ? "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "V1aZ921yV0J4",
        "colab_type": "text"
      },
      "source": [
        "# Corrélation avec Panda  A VOIR"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Rgt8gh1SVwYV",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from matplotlib.pyplot import*\n",
        "import pandas as pd\n",
        "#Création du tableau des valeurs du temps\n",
        "t=[]\n",
        "for i in range(11):\n",
        "  # Génère la 1ere ligne du tableau ( t)\n",
        "    t.append(i*0.066)\n",
        "# Liste des valeurs des corrdonnées x,y\n",
        "x=[0.01,0.25,0.57,0.91,1.22,1.54,1.87,2.16,2.49,2.81,3.15]\n",
        "y=[0.01549,0.3404,0.6812,1.010,1.297,1.559,1.768,1.95,2.08,2.158,2.193]\n",
        "plot(x,y,'D',color = 'red', linestyle = 'dashed', linewidth = 2,\n",
        "  markerfacecolor = 'blue', markersize = 5,label=\"y=f(x)\")\n",
        "xlabel(\"X\")\n",
        "ylabel(\"y\")\n",
        "axis([0,4,0,3])\n",
        "grid()\n",
        "legend()\n",
        "title(\"Trajectoire de la balle\",color = 'blue', fontsize = 16)\n",
        "show()\n",
        "#Coefficient de Pearson\n",
        "#Le coefficient de Pearson ou Pearson r est une mesure qui exprime à quel point\n",
        "#deux variables sont linéairement corrélées. Il est égale au quotient de la \n",
        "#covariance des deux variables et du produit des deux écarts-types\n",
        "coef=k.corr(method='pearson')\n",
        "print(\"coefficient de Pearson={}\".format(coef))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "O1fLl0IiG5J4"
      },
      "source": [
        "##Modifiez les lignes du programme"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7KX-OeNUG5u_",
        "colab_type": "text"
      },
      "source": [
        "*   "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Pq61kdcC0KsQ",
        "colab_type": "text"
      },
      "source": [
        "# Avec BARRES d 'ERREUR"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6-1SNWnSxvIn",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from matplotlib.pyplot import *\n",
        "import matplotlib.pyplot as plt\n",
        "x=[1,2,3,4]\n",
        "y=[2,4,6,9]\n",
        "plot(x,y,'D',label=\"y=f(x)\")\n",
        "xlabel(\"X\")\n",
        "ylabel(\"y\")\n",
        "axis([0,5,0,10])\n",
        "grid()\n",
        "legend()\n",
        "title(\"Trajectoire de la balle\",color = 'blue', fontsize = 16)\n",
        "show()\n",
        "xErrorValues = [0.5, 0.5, 0.5, 0.5]\n",
        "yErrorValues = [0.5, 0.5, 0.5,0.5]\n",
        "plt.scatter(x, y, zorder = 2)\n",
        "plt.errorbar(x, y, xerr = xErrorValues, yerr = yErrorValues,\n",
        "  fmt = 'none', capsize = 10, ecolor = 'red', zorder = 1)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "_Q1GFWx-HoaP"
      },
      "source": [
        "##Modifiez les lignes du programme"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pW1VpNYzHpN-",
        "colab_type": "text"
      },
      "source": [
        "*   Modifier le programme pour que l'incertitude soit demandé à l'utilisateur ( en % ) , la calcul et l'affiche."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mxa17TLki6TM",
        "colab_type": "text"
      },
      "source": [
        "## Plongeons d'un nagueur"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "alF_fg5faQ7X",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from matplotlib.pyplot import*\n",
        "title(\"Nuage de points de la fonction f définie par f(x)=100-1/2.g.x^2\")\n",
        "# Légende des axes des abscises et ordonnées\n",
        "xlabel('axe des X')\n",
        "ylabel('axe des Y')\n",
        "g=9.81\n",
        "# Min et max des axes\n",
        "axis([0,10,0,102])\n",
        "for i in range(11):\n",
        "    plot(i,100-0.5*g*i**2,'r.',ms=10)\n",
        "savefig('NuagePoint_V1.jpg')\n",
        "grid()    # Affiche une grille\n",
        "show()    # Affiche la figure\t"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BrRkx_-_cEYT",
        "colab_type": "text"
      },
      "source": [
        "## Analysez les lignes du programme et éxécutez-le !"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wBb5usoNcKAR",
        "colab_type": "text"
      },
      "source": [
        "##Modifiez les lignes du programme"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "N5jyrR4HcRAx",
        "colab_type": "text"
      },
      "source": [
        "Modifier les lignes du programmes pour\n",
        "\n",
        "1.   Adapter l'échelle des abscisses\n",
        "2.   Permettre à l'utilisateur de changer la valeur de g ( pour étudier la trajectoire sur Mars par ex )\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "67ferha2lIro",
        "colab_type": "code",
        "outputId": "f779b6ce-d4f3-4f2e-b6cc-cee9be32a432",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 278
        }
      },
      "source": [
        "from matplotlib.pyplot import*\n",
        "from numpy import*\n",
        "X=2;Y=4\n",
        "U=4;V=5\n",
        "#...................\n",
        "ax=axes()\n",
        "# Dessine un vecteur U d'origine ( x,y) et de norme Ux=U et Ux=V, ..)\n",
        "ax.quiver(X, Y, U, V,units='x',color = 'blue',scale=1)\n",
        "grid()\n",
        "#................\n",
        "ax.set_aspect('equal')\n",
        "xlim(0,12)\n",
        "ylim(0,10)\n",
        "title('Dessiner un vecteur avec Quiver',fontsize=8)\n",
        "savefig('Vecteur2.jpg', bbox_inches='tight')\n",
        "show()\n",
        "close()\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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LS9JcScOS1kl6SNJ5rQxmZjaWvib23QF8KiLuk7QnsFbSbRGxrkXZzMxeoOFnWhGxOSLu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\nQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mSPjbwMqf5v_",
        "colab_type": "text"
      },
      "source": [
        "# **M2 Tracé de vecteurs Vitesse lors d'un mouvement rectiligne ( Ex: La chute libre d'une balle)** "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LL2zpWSmkrIv",
        "colab_type": "text"
      },
      "source": [
        "Pour Quiver, cf [https://matplotlib.org/api/_as_gen/matplotlib.pyplot.quiver.html](https://matplotlib.org/api/_as_gen/matplotlib.pyplot.quiver.html)\n",
        "\n",
        "https://pythonforundergradengineers.com/quiver-plot-with-matplotlib-and-jupyter-notebooks.html "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "s0MS45aIgUZn",
        "colab_type": "code",
        "outputId": "c5954658-3d60-496f-d2a4-8b2c0a705aa9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        }
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "x=np.array([0,0,0,0])\n",
        "y=np.array([1.698,1.691,1.674,1.643])\n",
        "plt.plot(x,y,'o',markersize= 3)\n",
        "N=4\n",
        "Dt=0.035\n",
        "for k in range (0,N-1) :\n",
        "    vy=(y[k+1]-y[k])\n",
        "    echelle=0.4\n",
        "    vy=vy*echelle\n",
        "    plt.quiver(x[k],y[k],0,vy,color='red', scale=1,scale_units='xy')\n",
        "plt.xlabel(\"x (en m)\")\n",
        "plt.ylabel(\"y (en m)\")\n",
        "plt.title(\"Vecteurs vitesse\")\n",
        "plt.text(-0.046,1.65,\"Echelle 1cm <-> 0.4 m/s\", color=\"blue\")\n",
        "plt.grid()\n",
        "plt.show() "
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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tbA/iFuAG4IMR8U7hAkmVwKclDYuIa/Is0MzMSqPRgIiIE3eyrAaoyaUiMzNrF4o9BvF+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\nmRwQZmaWyQFhZmaZ/hdnprT3nMcnRQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1AN2I6Oz0PED",
        "colab_type": "text"
      },
      "source": [
        "## Analysez les lignes du programme"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IHGtAIw9gWXv",
        "colab_type": "text"
      },
      "source": [
        "1.   Quelle commande indique que les valeurs sont dans un tableau  ?\n",
        "2.   Quelle commande pour afficher un point ?\n",
        "1.   Quelle bibliothèque appelons-nous pour cela en début de programme ? \n",
        "2.   Quelle est la commande pour afficher un vecteur ?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sWQLUu1oggZh",
        "colab_type": "text"
      },
      "source": [
        "##Modifiez les lignes du programme"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EVuWlyB8gkZH",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "2.   Changer les titre les grandeurs en abcisses et en ordonnées\n",
        "1.   Ajouter d'autres points ( x,y)\n",
        "2.   pour agrandir les vecteurs\n",
        "2.   pour demander à l'utilisateur la durée entre 2 images lors de l'enregistrement\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wREWyJNdz7gc",
        "colab_type": "text"
      },
      "source": [
        "# **M3 Tracé de vecteurs Déplacement lors d'un mouvement plan ( Ex: Lancer d'une balle )** "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6YIUyecyKL1Q",
        "colab_type": "text"
      },
      "source": [
        "Tracé du vecteur position au cours du temps"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iM171-fu1eFJ",
        "colab_type": "code",
        "outputId": "f7522100-2c52-4710-f720-1acdc71de73d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        }
      },
      "source": [
        "from matplotlib.pyplot import*\n",
        "\n",
        "#Création du tableau des valeurs du temps\n",
        "t=[]\n",
        "for i in range(11):\n",
        "    t.append(i*0.066)\n",
        "x=[0.01,0.25,0.57,0.91,1.22,1.54,1.87,2.16,2.49,2.81,3.15]\n",
        "y=[0.01549,0.3404,0.6812,1.010,1.297,1.559,1.768,1.95,2.08,2.158,2.193]\n",
        "plot(x,y,'r+',label=\"y=f(x)\")\n",
        "\n",
        "#On enlève la dernière valeur\n",
        "n=len(t)-1\n",
        "#on fait tracer une série de vecteurs\n",
        "for i in range(n) :\n",
        "    arrow(x[i],y[i],x[i+1]-x[i],y[i+1]-y[i],head_width=0.05)\n",
        "# de position initiale x[i],y[i], de coordonnées x[i+1]-x[i] et y[i+1]-y[i]\n",
        "# head_width est la largeur de la tête\n",
        "xlabel(\"x\")\n",
        "ylabel(\"y\")\n",
        "grid()\n",
        "legend()\n",
        "title(\"Vecteurs déplacement\")\n",
        "savefig('Golf_Vecteur_Deplacement.jpg')\n",
        "show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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za+4LADTo/TjVDmzn/mH3epxMRErKy3sNNQK25BtOC40TH1nXuzcPP/IIjuBv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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DehdDwri1hBu",
        "colab_type": "text"
      },
      "source": [
        "## Analysez les lignes du programme"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mHOW1jB61oRU",
        "colab_type": "text"
      },
      "source": [
        "# M4  Tracé du vecteur Vitesse au cours du temps t[i+1]-t[i]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "N_rdHrGJkUWP",
        "colab_type": "text"
      },
      "source": [
        "[ lien](https://matplotlib.org/api/_as_gen/matplotlib.pyplot.quiver.html)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jIGN0LqXJr0_",
        "colab_type": "code",
        "outputId": "03a54d11-64bd-4126-98a5-7700269017c8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        }
      },
      "source": [
        "from matplotlib.pyplot import*\n",
        "\n",
        "#Création du tableau des valeurs du temps de 0 à 10\n",
        "t=[]\n",
        "for i in range(11):\n",
        "    t.append(i*0.066)\n",
        "x=[0.01,0.25,0.57,0.91,1.22,1.54,1.87,2.16,2.49,2.81,3.15]\n",
        "y=[0.01549,0.3404,0.6812,1.010,1.297,1.559,1.768,1.95,2.08,2.158,2.193]\n",
        "plot(x,y,'r+',label=\"y=f(x)\")\n",
        "# Calcul de la longueur du tableau et expulsion de la dernière valeur car on ne peut calculer pour t+1 \n",
        "m=len(t)-1\n",
        "for i in range(m) :\n",
        "    arrow(x[i],y[i],0.15*(x[i+1]-x[i])/(t[i+1]-t[i]),\n",
        "    0.12*(y[i+1]-y[i])/(t[i+1]-t[i]),head_width=0.05)\n",
        "# on multiplie par 0.1 pour que la figure soit lisible.\n",
        "xlim(0,4)\n",
        "ylim(0,3)\n",
        "grid()\n",
        "title(\"Vecteurs déplacement\")\n",
        "savefig('Vecteur_Vitesse.jpg')\n",
        "show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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DvleAtm7dmuHDh9OmTRtEJM9tzmCt7RLDCr4xYWbfvn1c0bIlu4Hhw4cDkLlmlm99VFQU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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HazkToepjW81",
        "colab_type": "text"
      },
      "source": [
        "## Amélioration possibles avec prise en compte de l'expression de la vitesse de la forme x[i+1]-x[i-1])/(t[i+1]-t[i-1])"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "m4a22dxFjWQ0",
        "colab_type": "code",
        "outputId": "780e96d6-54b7-4dc6-ce9c-de0378972cab",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        }
      },
      "source": [
        "from matplotlib.pyplot import*\n",
        "# Problème avec le 1er point !!!\n",
        "#Création du tableau des valeurs du temps de 0 à 10\n",
        "t=[]\n",
        "for i in range(11):\n",
        "    t.append(i*0.066)\n",
        "x=[0.01,0.25,0.57,0.91,1.22,1.54,1.87,2.16,2.49,2.81,3.15]\n",
        "y=[0.01549,0.3404,0.6812,1.010,1.297,1.559,1.768,1.95,2.08,2.158,2.193]\n",
        "plot(x,y,'r+',label=\"y=f(x)\")\n",
        "# Calcul de la longueur du tableau et expulsion de la dernière valeur car on ne peut calculer pour t+1 \n",
        "m=len(t)-1\n",
        "for i in range(m) :\n",
        "    arrow(x[i],y[i],0.15*(x[i+1]-x[i-1])/(t[i+1]-t[i-1]),\n",
        "    0.14*(y[i+1]-y[i-1])/(t[i+1]-t[i-1]),head_width=0.05)\n",
        "# On multiplie par 0.14 pour que la figure soit lisible.\n",
        "xlim(0,4)\n",
        "ylim(0,2.5)\n",
        "grid()\n",
        "title(\"Vecteurs vitesses\")\n",
        "savefig('Lancer_Vecteur_Vitesse.jpg')\n",
        "show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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R7mJ/oa0d26cP5ceOzbSwe9WgQXm7/SBlffjGBKBhw4axceNGfv/9dxYuXEhKSgoTJkwg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\nP+bFG9suLedVAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YwVS1q-Ky7Hj",
        "colab_type": "text"
      },
      "source": [
        "# **M3 Tracé d'un signal  sinusoidale**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GkOa0GGkzDff",
        "colab_type": "code",
        "outputId": "923981db-f5ea-461f-e175-efaec44d536a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        }
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "#Création d'une variable temps ,t, prenant 1000 valeurs entre 0 et 0,1 secondes#\n",
        "t = np.linspace(0,0.1,1000)\n",
        "# La fréquence est fixée\n",
        "f=100\n",
        "#définition de la fonction y\n",
        "y=3*np.sin(2*np.pi*f*t)\n",
        "plt.plot(t,y,'*',color='blue')\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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bu0jGV/dmZ8TLbVdqWncS4KhaeZaIDBHdSEQ3Dx7f5ji5LOR5W1IRU16kJtX5eaImGblk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\nBAQEeI7/D6fqCz7gGUDIAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sffgKwhTHxZ-",
        "colab_type": "text"
      },
      "source": [
        ""
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sVKenx7_0auk",
        "colab_type": "text"
      },
      "source": [
        "## Analysez les lignes du programme"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BqbP1oXk0fZo",
        "colab_type": "text"
      },
      "source": [
        "Analysez puis exécutez le programme"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3_vfCMBwzK38",
        "colab_type": "text"
      },
      "source": [
        "##Modifiez les lignes du programme"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nJtdmHflzNWC",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "\n",
        "1.  **Ajouter une ligne demandant à l'utilisateur** \n",
        "*  la fréquence du signal\n",
        "*  l'amplitude du signal\n",
        "\n",
        "1.   **Ajouter une ligne pour afficher** \n",
        "* un titre et une légende en abscisse et ordonnée\n",
        "* une grille afin de lire des valeurs\n",
        " \n",
        "2.  ** Ajouter une ligne pour afficher plus ou moins de point**\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tao0aN64HzFN",
        "colab_type": "text"
      },
      "source": [
        "# Addition d'ondes sinusoidales et variation du déphasage"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "32MvFyXZH4Yi",
        "colab_type": "text"
      },
      "source": [
        "**Aides pour la programmation avec Python**\n",
        "1.  Charger les bibliothèques numpy et matplotlib.pyplot. \n",
        "2.  Initialiser les variables suivantes : T à 1 (période 1 seconde), Y1max et Y2max à 2 unités. \n",
        "3.  Demander à l'utilisateur la valeur du déphasage nommée phi\n",
        "4.  Créer une liste d'abscisses nommé t prenant 400 valeurs entre 0 et 4 (en utilisant la boucle « for i \n",
        "in range »). \n",
        "5.  Créer trois listes d'ordonnées y1, y2, y en calculant pour chacune des valeurs de la liste t, \n",
        "respectivement cos(2t/T), cos(2t/T+) et cos(2t/T)+cos(2t/T+). \n",
        "6.  Tracer les trois fonctions et afficher la figure. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "j3yqfj4EJAnF",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import math\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4OmpZjtq25sm",
        "colab_type": "text"
      },
      "source": [
        "#Import de données sous format CSV"
      ]
    }
  ]
}