555 lines
24 KiB
Plaintext
555 lines
24 KiB
Plaintext
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{
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"cells": [
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Coûts d'une entreprises\n",
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"\n",
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"Dans ce TP, on propose d'étudier les coûts d'une entreprises. Nous commencerons pas étudier les coûts \"classiques\" puis le coût moyen et enfin les coûts marginal.\n",
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"\n",
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"Des aides sont disponibles à la fin de ce TP."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Coût total\n",
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"\n",
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"L'étude des coûts totaux d'une entreprise a mené à la formule suivante où $q$ décrit la quantité produite (entre 0 et 500):\n",
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"$$ Coût(q) = 0.3q^3 + 1.25q^2 + 7,5q + 900$$"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"1. En vous inspirant de l'annexe sur les fonctions, programmer la fonction coût."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": []
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"2. Calculer les coûts pour 0, 5 et 10 objets"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": []
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"3. On souhaite calculer tous les coûts possibles. Pour cela, inspirer vous de l'annexe sur les boucles et les listes pour calculer les coûts pour les quantités allant de 0 à 500."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"quantites = list(range(0, 11))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": []
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"4. En vous inspirant de l'annexe sur les graphiques, tracer le graphique qui permet de visualiser l'évolution de ces coûts."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"import matplotlib.pyplot as plt\n",
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"%matplotlib inline"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": []
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"5. Décrire l'évolution des coûts pour cette entreprise."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": []
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Étude du coût moyen\n",
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"\n",
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"Le coût moyen est le coût pour une unité produite. Plus ce coût moyen est faible plus le coût unitaire d'une unité est faible. Ce coût se calcule à partir du coût total avec la formule suivante\n",
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"$$ C_m(q) = \\frac{C(q)}{q}$$\n",
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"Dans la suite, on reprend la formule du coût de la partie précédente."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"1. Programmer la fonction qui permet de calculer le coût moyen."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": []
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"2. Calculer les coûts moyennes quand les quantités varient de 1 à 500."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": []
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"3. Tracer le graphique représentant les coûts moyens"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": []
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"4. Décrire la courbe représentative des coûts marginaux. Quelle quantité doit ont produire pour que le coût d'un objet soit le plus faible?"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": []
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Coût marginal\n",
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"\n",
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"Le coût marginal est le coût supplémentaire si l'on décide de produire une unité de plus. Il se calcule à partir du coût total avec la formule suivante:\n",
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"$$ C_M(q) = C(q+1) - C(q)$$"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"1. Programmer la fonction qui permet de calculer le coût marginal.\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": []
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"2. Calculer le coût marginal pour les quantités allant de 1 à 499."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": []
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"3. Tracer le graphique représentant les coûts marginaux."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": []
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"4. Décrire la courbe des coûts marginaux. Que peut-on dire du coût de production si l'on chercher à augmenter la production."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": []
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Annexe"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Programmer des fonctions\n",
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"\n",
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"Les fonctions mathématiques peuvent aisement se programmer avec des fonctions de programmation. Seul la syntaxe change.\n",
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"\n",
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"Si l'on souhaite programmer la fonction\n",
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"\n",
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"$$ f(x) = \\frac{x + 1}{3x - 1} $$\n",
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"On écrira"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [],
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"source": [
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"def f(x):\n",
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" return (x+1)/(3*x-1)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Quelques éléments sont à noter:\n",
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"\n",
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"- Il y a deux points à la fin de la première ligne\n",
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"- Le mot clé `return` est indenté\n",
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"- Toutes les opérations sont écrites avec les parenthèses appropriées.\n",
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"\n",
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"On pourra ensuite utiliser cette fonction pour calculer des images de nombres. Dans ce cas, la syntaxe est la même qu'en math."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"1.0\n",
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"0.3377926421404682\n"
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]
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}
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],
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"source": [
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"print(f(1))\n",
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"print(f(100))"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Boucles et listes\n",
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"\n",
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"En programmation, il existe plusieurs types de variables. Vous connaissez par exemples les `integer` qui sont des nombres entiers, les `string` qui sont les chaines de caractères. Il existe aussi les listes qui permettent de stocker plusieurs valeurs dans une seule variable."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[1, 5, 'a', 10]\n"
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]
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}
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],
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"source": [
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"liste = [1, 5, 'a', 10]\n",
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"print(liste)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"On peut accéder à des valeurs particulières avec des crochets"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"1\n",
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"a\n"
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]
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}
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],
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"source": [
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"print(liste[0])\n",
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"print(liste[2])"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"On peut ajouter des éléments à une liste"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[1, 5, 'a', 10, 100]\n"
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]
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}
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],
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"source": [
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"liste.append(100)\n",
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"print(liste)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Les listes marchent particulièrement bien avec les boucles. On peut alors faire des actions sur chacune des valeurs de la liste."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"5\n",
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"25\n",
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"aaaaa\n",
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"50\n",
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"500\n"
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]
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}
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],
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"source": [
|
||
|
|
"for valeur in liste:\n",
|
||
|
|
" print(valeur * 5)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"Quand on fait des calculs sur des listes, il est utile garder les résultats dans une deuxième liste"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 9,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"deuxieme_liste = [] # On crée une liste vide\n",
|
||
|
|
"for valeur in liste:\n",
|
||
|
|
" deuxieme_liste.append(valeur*5)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 10,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"name": "stdout",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"[5, 25, 'aaaaa', 50, 500]\n"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"print(deuxieme_liste)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"## Tracer une graphique\n",
|
||
|
|
"\n",
|
||
|
|
"On peut tracer des graphiques à partir de deux listes:\n",
|
||
|
|
"\n",
|
||
|
|
"- la liste des abcisses (les x)\n",
|
||
|
|
"- la liste des ordonnées (les y)\n",
|
||
|
|
"\n",
|
||
|
|
"avant de pouvoir tracer ce graphique, il faut s'assurer d'avoir importer la biliothèque qui permet de les réaliser. Il faut donc valider (une seule fois) les lignes suivantes"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 11,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"import matplotlib.pyplot as plt\n",
|
||
|
|
"%matplotlib inline"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"On calcule ou on entre les abscisses et les ordonnées"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 12,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"abscisses = [0, 1, 2, 3, 4]\n",
|
||
|
|
"ordonnees = [2, 4, 5, 0, 1]"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"Et on peut tracer le graphique"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 13,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": [
|
||
|
|
"[<matplotlib.lines.Line2D at 0x7ff498343640>]"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 13,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 432x288 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {
|
||
|
|
"needs_background": "light"
|
||
|
|
},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"plt.plot(abscisses, ordonnees)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": []
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"metadata": {
|
||
|
|
"kernelspec": {
|
||
|
|
"display_name": "Python 3",
|
||
|
|
"language": "python",
|
||
|
|
"name": "python3"
|
||
|
|
},
|
||
|
|
"language_info": {
|
||
|
|
"codemirror_mode": {
|
||
|
|
"name": "ipython",
|
||
|
|
"version": 3
|
||
|
|
},
|
||
|
|
"file_extension": ".py",
|
||
|
|
"mimetype": "text/x-python",
|
||
|
|
"name": "python",
|
||
|
|
"nbconvert_exporter": "python",
|
||
|
|
"pygments_lexer": "ipython3",
|
||
|
|
"version": "3.9.4"
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"nbformat": 4,
|
||
|
|
"nbformat_minor": 4
|
||
|
|
}
|