{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "e5513981",
   "metadata": {},
   "source": [
    "# Première séance — Découvrir Python pour la physique-chimie\n",
    "\n",
    "**Durée : 2 h.** Objectif de la séance : à la fin, tu sauras utiliser un notebook, faire des calculs avec des variables, afficher proprement un résultat, répéter un calcul avec une boucle, écrire une fonction et tracer ton premier graphique.\n",
    "\n",
    "| Partie | Contenu | Durée indicative |\n",
    "|---|---|---|\n",
    "| 0 | Prendre en main le notebook | 10 min |\n",
    "| 1 | Python comme calculatrice, variables, erreurs | 20 min |\n",
    "| 2 | Afficher un résultat | 15 min |\n",
    "| 3 | Listes et boucles | 25 min |\n",
    "| 4 | Fonctions | 20 min |\n",
    "| 5 | Premier graphique | 20 min |\n",
    "| 6 | Mini-projet de synthèse | 10 min |\n",
    "\n",
    "Les exercices marqués **Bonus** sont pour ceux qui vont plus vite : on peut les sauter sans problème."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a012eeb",
   "metadata": {},
   "source": [
    "**Commentaire (corrigé)** — **Déroulé conseillé.** Projeter le notebook et faire les parties 0 et 1 en direct avec la classe (les étudiants exécutent en même temps), puis laisser travailler en autonomie à partir de la partie 2 en faisant un point collectif de 2 minutes à chaque changement de partie. Les cellules « Prédis puis exécute » se prêtent bien à un vote à main levée avant exécution. Si le temps manque, la partie 6 peut être donnée à terminer à la maison ; le notebook « 0. Bases de Python » sert ensuite d'entraînement complémentaire.\n",
    "\n",
    "**Points de vigilance fréquents** : `^` au lieu de `**` ; virgule décimale au lieu du point ; oubli des parenthèses dans `a / b * c` ; indentation après `for` et `def` ; cellules exécutées dans le désordre (variable non définie) ; `print(x)` oublié dans une cellule qui calcule sans rien afficher."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fbad0bf4",
   "metadata": {},
   "source": [
    "**Niveaux de difficulté**\n",
    "\n",
    "| Niveau | Ce qui est attendu |\n",
    "|---|---|\n",
    "| ★☆☆☆ | Reprendre l'exemple en changeant la fonction ou les données. |\n",
    "| ★★☆☆ | Adapter l'exemple : ajouter un élément, choisir un paramètre, interpréter un résultat. |\n",
    "| ★★★☆ | Mettre en équation une situation physique **puis** la coder ; plusieurs notions combinées. |\n",
    "| ★★★★ | Démarche autonome : aucune structure de code fournie, il faut construire la stratégie. |\n",
    "\n",
    "Dans les applications guidées, remplace chaque `____` par le code manquant."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91d3d7e3",
   "metadata": {},
   "source": [
    "---\n",
    "## Partie 0 — Prendre en main le notebook  *(10 min)*\n",
    "\n",
    "Un notebook est une suite de **cellules** :\n",
    "- les cellules de **texte** (comme celle-ci), écrites en *Markdown* ; on peut y mettre des formules : $E = mc^2$ ;\n",
    "- les cellules de **code**, qui contiennent du Python et que l'on **exécute**.\n",
    "\n",
    "**Les gestes à connaître**\n",
    "\n",
    "| Action | Comment |\n",
    "|---|---|\n",
    "| Exécuter une cellule et passer à la suivante | `Maj` + `Entrée` |\n",
    "| Exécuter sans changer de cellule | `Ctrl` + `Entrée` |\n",
    "| Modifier une cellule de texte | double-clic dessus |\n",
    "| Ajouter une cellule | bouton `+` de la barre d'outils |\n",
    "| Tout recommencer proprement | menu *Kernel* (ou *Noyau*) → *Restart & Run All* |\n",
    "\n",
    "Le nombre entre crochets à gauche d'une cellule de code, par exemple `[3]`, indique l'**ordre** dans lequel les cellules ont été exécutées. L'ordre compte : une cellule ne connaît que ce qui a été exécuté **avant elle**.\n",
    "\n",
    "### À toi — exécute la cellule suivante avec `Maj` + `Entrée`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "9fd6d6db",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:55.827809Z",
     "iopub.status.busy": "2026-09-25T21:00:55.827621Z",
     "iopub.status.idle": "2026-09-25T21:00:55.833325Z",
     "shell.execute_reply": "2026-09-25T21:00:55.832501Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bonjour, je fais du Python en TSI1 !\n"
     ]
    }
   ],
   "source": [
    "print(\"Bonjour, je fais du Python en TSI1 !\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9779ce16",
   "metadata": {},
   "source": [
    "Dans une cellule de code, tout ce qui suit le symbole `#` est un **commentaire** : Python l'ignore. On s'en sert pour expliquer son code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "2b09445d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:55.835127Z",
     "iopub.status.busy": "2026-09-25T21:00:55.834552Z",
     "iopub.status.idle": "2026-09-25T21:00:55.838635Z",
     "shell.execute_reply": "2026-09-25T21:00:55.837895Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Seule cette ligne produit un affichage.\n"
     ]
    }
   ],
   "source": [
    "# Ceci est un commentaire : il ne s'affiche pas.\n",
    "print(\"Seule cette ligne produit un affichage.\")   # un commentaire peut aussi être en fin de ligne"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4f7d05d5",
   "metadata": {},
   "source": [
    "### Exercice 0.1 — ★☆☆☆\n",
    "Ajoute une cellule de code **sous celle-ci** (bouton `+`) et fais afficher ton prénom. Ajoute ensuite une cellule de **texte** (change son type dans la barre d'outils : *Code* → *Markdown*) contenant la formule $F = m\\,a$ écrite entre deux symboles `$`."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1918e6a4",
   "metadata": {},
   "source": [
    "---\n",
    "## Partie 1 — Python comme calculatrice, variables, erreurs  *(20 min)*\n",
    "\n",
    "### 1.1 Opérations\n",
    "| Opération | Écriture Python | Exemple | Résultat |\n",
    "|---|---|---|---|\n",
    "| addition, soustraction | `+`, `-` | `7 - 2` | `5` |\n",
    "| multiplication | `*` | `3 * 4` | `12` |\n",
    "| division | `/` | `7 / 2` | `3.5` |\n",
    "| puissance | `**` (**jamais** `^`) | `2 ** 10` | `1024` |\n",
    "| notation scientifique | `e` | `6.02e23` | $6{,}02\\times10^{23}$ |\n",
    "\n",
    "⚠️ Le séparateur décimal est le **point** : on écrit `9.81` et non `9,81`.\n",
    "\n",
    "Dans une cellule, seul le résultat de la **dernière ligne** s'affiche automatiquement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5ead69fb",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:55.840374Z",
     "iopub.status.busy": "2026-09-25T21:00:55.839855Z",
     "iopub.status.idle": "2026-09-25T21:00:55.845894Z",
     "shell.execute_reply": "2026-09-25T21:00:55.844958Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1024"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2 ** 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "39ea34cb",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:55.847658Z",
     "iopub.status.busy": "2026-09-25T21:00:55.847036Z",
     "iopub.status.idle": "2026-09-25T21:00:55.851780Z",
     "shell.execute_reply": "2026-09-25T21:00:55.851000Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.978e-19"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "6.63e-34 * 3.00e8 / 500e-9     # énergie d'un photon de 500 nm, en joules"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0c53325",
   "metadata": {},
   "source": [
    "### Prédis puis exécute\n",
    "Avant d'exécuter la cellule suivante, écris sur ton brouillon ce que tu penses obtenir. Puis vérifie."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "8e851ecf",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:55.853231Z",
     "iopub.status.busy": "2026-09-25T21:00:55.852988Z",
     "iopub.status.idle": "2026-09-25T21:00:55.857204Z",
     "shell.execute_reply": "2026-09-25T21:00:55.856463Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1 + 2 * 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0d404c32",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:55.858512Z",
     "iopub.status.busy": "2026-09-25T21:00:55.858367Z",
     "iopub.status.idle": "2026-09-25T21:00:55.862424Z",
     "shell.execute_reply": "2026-09-25T21:00:55.861695Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(1 + 2) * 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "826e9b1b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:55.864108Z",
     "iopub.status.busy": "2026-09-25T21:00:55.863564Z",
     "iopub.status.idle": "2026-09-25T21:00:55.868076Z",
     "shell.execute_reply": "2026-09-25T21:00:55.867107Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "25.0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "10 / 2 * 5         # 1 ou 25 ? Les opérations de même priorité s'effectuent de gauche à droite"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f2e65630",
   "metadata": {},
   "source": [
    "**À retenir** : en cas de doute, **mets des parenthèses**. Pour calculer $\\dfrac{10}{2 \\times 5}$ il faut écrire `10 / (2 * 5)`.\n",
    "\n",
    "### 1.2 Variables\n",
    "Une **variable** est un nom auquel on associe une valeur avec le signe `=`. Ce signe n'est pas une égalité mathématique : il signifie « **range** la valeur de droite dans la boîte de gauche »."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b3f88823",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:55.869852Z",
     "iopub.status.busy": "2026-09-25T21:00:55.869290Z",
     "iopub.status.idle": "2026-09-25T21:00:55.873848Z",
     "shell.execute_reply": "2026-09-25T21:00:55.873067Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.943"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = 0.250          # masse (kg)\n",
    "g = 9.81           # champ de pesanteur (m/s^2)\n",
    "h = 1.20           # hauteur (m)\n",
    "\n",
    "Ep = m * g * h     # énergie potentielle de pesanteur (J)\n",
    "Ep"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6bb084c9",
   "metadata": {},
   "source": [
    "Choisis des noms **explicites** et indique les **unités** en commentaire : un physicien relit toujours ses unités.\n",
    "\n",
    "### Prédis puis exécute"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "c1119828",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:55.875196Z",
     "iopub.status.busy": "2026-09-25T21:00:55.875055Z",
     "iopub.status.idle": "2026-09-25T21:00:55.879546Z",
     "shell.execute_reply": "2026-09-25T21:00:55.878765Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 5\n",
    "n = n + 1          # que vaut n maintenant ?\n",
    "n = 2 * n\n",
    "n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "41d9b997",
   "metadata": {},
   "source": [
    "### 1.3 Types de données\n",
    "Python distingue plusieurs **types** : les entiers (`int`), les nombres à virgule (`float`), le texte (`str`, entre guillemets) et les booléens (`True` / `False`). La fonction `type` donne le type d'une valeur."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "78187c8a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:55.880822Z",
     "iopub.status.busy": "2026-09-25T21:00:55.880640Z",
     "iopub.status.idle": "2026-09-25T21:00:55.884366Z",
     "shell.execute_reply": "2026-09-25T21:00:55.883641Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'int'> <class 'float'> <class 'str'> <class 'bool'>\n"
     ]
    }
   ],
   "source": [
    "print(type(3), type(3.0), type(\"3\"), type(3 > 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0b57757e",
   "metadata": {},
   "source": [
    "Les nombres à virgule sont stockés avec environ 16 chiffres significatifs : les calculs sont donc parfois **légèrement** inexacts. Prédis puis exécute :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "375df10d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:55.886063Z",
     "iopub.status.busy": "2026-09-25T21:00:55.885536Z",
     "iopub.status.idle": "2026-09-25T21:00:55.889723Z",
     "shell.execute_reply": "2026-09-25T21:00:55.888914Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "0.1 + 0.2 == 0.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "aaf6e8b7",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:55.891415Z",
     "iopub.status.busy": "2026-09-25T21:00:55.890916Z",
     "iopub.status.idle": "2026-09-25T21:00:55.895170Z",
     "shell.execute_reply": "2026-09-25T21:00:55.894410Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.30000000000000004"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "0.1 + 0.2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4bb358bf",
   "metadata": {},
   "source": [
    "**Commentaire (corrigé)** — bonne occasion de dire qu'on ne teste jamais l'égalité de deux flottants, mais `abs(a - b) < tolerance`. On le réutilise dans la dichotomie et les `assert`."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a48d8876",
   "metadata": {},
   "source": [
    "### 1.4 Lire un message d'erreur\n",
    "Se tromper est normal. L'important est de **lire le message d'erreur** : la **dernière ligne** donne le type d'erreur, et une flèche indique la ligne fautive.\n",
    "\n",
    "| Erreur | Signification courante |\n",
    "|---|---|\n",
    "| `SyntaxError` | faute de « grammaire » : parenthèse oubliée, virgule décimale… |\n",
    "| `NameError` | variable inconnue : faute de frappe, ou cellule de définition pas encore exécutée |\n",
    "| `TypeError` | opération impossible entre ces types (par exemple texte + nombre) |\n",
    "| `ZeroDivisionError` | division par zéro |\n",
    "| `IndentationError` | décalage en début de ligne incorrect (voir partie 3) |\n",
    "\n",
    "### Exercice 1.1 — ★☆☆☆ — le chasseur d'erreurs\n",
    "Chacune des quatre cellules suivantes contient **une** erreur. Exécute-la, lis le message, puis corrige-la."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "0837730b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:55.896458Z",
     "iopub.status.busy": "2026-09-25T21:00:55.896309Z",
     "iopub.status.idle": "2026-09-25T21:00:55.900401Z",
     "shell.execute_reply": "2026-09-25T21:00:55.899720Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14.285714285714286"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Cellule A : vitesse moyenne (km/h) d'un coureur qui parcourt 10 km en 42 min\n",
    "v = 10 / (42 / 60)          # SyntaxError : parenthèse non fermée\n",
    "v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "db6e58ea",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:55.902777Z",
     "iopub.status.busy": "2026-09-25T21:00:55.902149Z",
     "iopub.status.idle": "2026-09-25T21:00:55.906546Z",
     "shell.execute_reply": "2026-09-25T21:00:55.905809Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0022727272727272726"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Cellule B : période d'un signal de fréquence 440 Hz\n",
    "frequence = 440\n",
    "T = 1 / frequence           # NameError : faute de frappe dans le nom de la variable\n",
    "T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "223129d3",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:55.907867Z",
     "iopub.status.busy": "2026-09-25T21:00:55.907725Z",
     "iopub.status.idle": "2026-09-25T21:00:55.912183Z",
     "shell.execute_reply": "2026-09-25T21:00:55.911262Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.0"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Cellule C : énergie cinétique d'une masse de 2 kg à 3 m/s\n",
    "m = 2\n",
    "v = 3\n",
    "Ec = 1/2 * m * v**2         # TypeError : ^ n'est pas la puissance en Python\n",
    "Ec"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "a59415cb",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:55.913538Z",
     "iopub.status.busy": "2026-09-25T21:00:55.913389Z",
     "iopub.status.idle": "2026-09-25T21:00:55.917605Z",
     "shell.execute_reply": "2026-09-25T21:00:55.916840Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2700.0"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Cellule D : masse volumique de l'aluminium (kg/m^3)\n",
    "masse = 2.70e3              # avec une virgule, Python crée un couple de nombres : TypeError à la division\n",
    "volume = 1.00\n",
    "rho = masse / volume\n",
    "rho"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "04e5677c",
   "metadata": {},
   "source": [
    "### Exercice 1.2 — ★☆☆☆\n",
    "Un condensateur de capacité $C = 220$ nF est chargé sous une tension $U = 12$ V.\n",
    "Calculer la charge $q = CU$ et l'énergie stockée $W = \\tfrac{1}{2}CU^2$, en définissant des variables `C` et `U` (attention : $1$ nF $= 10^{-9}$ F)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "f1ae0d09",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:55.918948Z",
     "iopub.status.busy": "2026-09-25T21:00:55.918800Z",
     "iopub.status.idle": "2026-09-25T21:00:55.923265Z",
     "shell.execute_reply": "2026-09-25T21:00:55.922470Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.64e-06, 1.584e-05)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C = 220e-9     # F\n",
    "U = 12         # V\n",
    "q = C * U\n",
    "W = 0.5 * C * U**2\n",
    "q, W           # une virgule permet d'afficher plusieurs valeurs"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38a3ed79",
   "metadata": {},
   "source": [
    "---\n",
    "## Partie 2 — Afficher un résultat  *(15 min)*\n",
    "\n",
    "La fonction `print` affiche ce qu'on lui donne. Pour mélanger texte et valeurs, on utilise une **f-string** : un texte précédé de `f`, dans lequel les variables sont placées entre accolades `{ }`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "6dc7a61c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:55.924597Z",
     "iopub.status.busy": "2026-09-25T21:00:55.924451Z",
     "iopub.status.idle": "2026-09-25T21:00:55.928810Z",
     "shell.execute_reply": "2026-09-25T21:00:55.928071Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Énergie potentielle : 2.943 J\n",
      "Énergie potentielle : 2.943 J\n"
     ]
    }
   ],
   "source": [
    "m = 0.250\n",
    "g = 9.81\n",
    "h = 1.20\n",
    "Ep = m * g * h\n",
    "print(\"Énergie potentielle :\", Ep, \"J\")      # méthode simple\n",
    "print(f\"Énergie potentielle : {Ep} J\")       # f-string"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34b362a7",
   "metadata": {},
   "source": [
    "Le résultat `2.943` a trop de chiffres par rapport aux données (3 chiffres significatifs). On précise le **format** après deux points :\n",
    "\n",
    "| Format | Effet | `Ep = 2.943` s'affiche |\n",
    "|---|---|---|\n",
    "| `{Ep:.2f}` | 2 chiffres après la virgule | `2.94` |\n",
    "| `{Ep:.3g}` | 3 chiffres significatifs | `2.94` |\n",
    "| `{Ep:.2e}` | écriture scientifique, 2 décimales | `2.94e+00` |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "9aceecc0",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:55.930573Z",
     "iopub.status.busy": "2026-09-25T21:00:55.930054Z",
     "iopub.status.idle": "2026-09-25T21:00:55.934335Z",
     "shell.execute_reply": "2026-09-25T21:00:55.933595Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ep = 2.94 J\n",
      "Ep = 2.94e+00 J\n",
      "Nombre d'Avogadro : 6.022e+23 mol^-1\n"
     ]
    }
   ],
   "source": [
    "print(f\"Ep = {Ep:.3g} J\")\n",
    "print(f\"Ep = {Ep:.2e} J\")\n",
    "N_A = 6.02214076e23\n",
    "print(f\"Nombre d'Avogadro : {N_A:.3e} mol^-1\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83ce6f67",
   "metadata": {},
   "source": [
    "### Exercice 2.1 — ★☆☆☆\n",
    "La lumière met environ 8 min 20 s pour venir du Soleil. Avec $c = 3{,}00\\times10^8$ m/s, calculer la distance Terre-Soleil et l'afficher sous la forme `Distance Terre-Soleil : 1.50e+11 m`.\n",
    "\n",
    "### Exercice 2.2 — ★★☆☆\n",
    "Reprendre l'exercice 1.2 et afficher, en une seule instruction `print`, une phrase du type :\n",
    "`q = 2.64 µC et W = 15.8 µJ` (il faut convertir en micro-unités avant l'affichage)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "75bd3898",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:55.936007Z",
     "iopub.status.busy": "2026-09-25T21:00:55.935483Z",
     "iopub.status.idle": "2026-09-25T21:00:55.939493Z",
     "shell.execute_reply": "2026-09-25T21:00:55.938753Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Distance Terre-Soleil : 1.50e+11 m\n"
     ]
    }
   ],
   "source": [
    "# Exercice 2.1\n",
    "c = 3.00e8\n",
    "duree = 8 * 60 + 20           # s\n",
    "d = c * duree\n",
    "print(f\"Distance Terre-Soleil : {d:.2e} m\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "aa923a03",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:55.941247Z",
     "iopub.status.busy": "2026-09-25T21:00:55.940700Z",
     "iopub.status.idle": "2026-09-25T21:00:55.945006Z",
     "shell.execute_reply": "2026-09-25T21:00:55.944195Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "q = 2.64 µC et W = 15.8 µJ\n"
     ]
    }
   ],
   "source": [
    "# Exercice 2.2\n",
    "C, U = 220e-9, 12\n",
    "q = C * U\n",
    "W = 0.5 * C * U**2\n",
    "print(f\"q = {q*1e6:.3g} µC et W = {W*1e6:.3g} µJ\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc4169fe",
   "metadata": {},
   "source": [
    "---\n",
    "## Partie 3 — Listes et boucles  *(25 min)*\n",
    "\n",
    "### 3.1 Listes\n",
    "Une **liste** regroupe plusieurs valeurs entre crochets. Les éléments sont numérotés **à partir de 0**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "9b028e6b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:55.946706Z",
     "iopub.status.busy": "2026-09-25T21:00:55.946155Z",
     "iopub.status.idle": "2026-09-25T21:00:55.950657Z",
     "shell.execute_reply": "2026-09-25T21:00:55.949921Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.02\n",
      "2.98\n",
      "5.0\n",
      "5\n"
     ]
    }
   ],
   "source": [
    "tensions = [1.02, 2.01, 2.98, 4.05, 5.00]     # (V)\n",
    "\n",
    "print(tensions[0])        # premier élément\n",
    "print(tensions[2])        # troisième élément !\n",
    "print(tensions[-1])       # dernier élément\n",
    "print(len(tensions))      # nombre d'éléments"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "e4cabb68",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:55.952368Z",
     "iopub.status.busy": "2026-09-25T21:00:55.951849Z",
     "iopub.status.idle": "2026-09-25T21:00:55.956193Z",
     "shell.execute_reply": "2026-09-25T21:00:55.955453Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1.02, 2.01, 2.98, 4.05, 5.0, 6.03]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tensions.append(6.03)     # ajouter un élément à la fin\n",
    "tensions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e6daba1d",
   "metadata": {},
   "source": [
    "### Prédis puis exécute"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "57c7e5be",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:55.957915Z",
     "iopub.status.busy": "2026-09-25T21:00:55.957404Z",
     "iopub.status.idle": "2026-09-25T21:00:55.961897Z",
     "shell.execute_reply": "2026-09-25T21:00:55.960960Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "60"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L = [10, 20, 30, 40]\n",
    "L[1] + L[-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1f774d3c",
   "metadata": {},
   "source": [
    "### 3.2 La boucle `for`\n",
    "Une boucle **répète** des instructions. `for x in L:` donne successivement à `x` chacune des valeurs de `L`.\n",
    "\n",
    "⚠️ Les instructions répétées sont **décalées vers la droite** (indentation de 4 espaces, obtenue avec la touche `Tab`). C'est ce décalage qui indique à Python ce qui fait partie de la boucle. Ne pas oublier les **deux points** à la fin de la ligne `for`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "94ea656b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:55.963219Z",
     "iopub.status.busy": "2026-09-25T21:00:55.963078Z",
     "iopub.status.idle": "2026-09-25T21:00:55.967439Z",
     "shell.execute_reply": "2026-09-25T21:00:55.966582Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "U = 1.02 V  ->  I = 10.2 mA\n",
      "U = 2.01 V  ->  I = 20.1 mA\n",
      "U = 2.98 V  ->  I = 29.8 mA\n",
      "U = 4.05 V  ->  I = 40.5 mA\n",
      "U = 5.00 V  ->  I = 50.0 mA\n",
      "Fin de la boucle\n"
     ]
    }
   ],
   "source": [
    "tensions = [1.02, 2.01, 2.98, 4.05, 5.00]     # (V)\n",
    "R = 100                                        # (ohm)\n",
    "\n",
    "for U in tensions:\n",
    "    I = U / R\n",
    "    print(f\"U = {U:.2f} V  ->  I = {I*1e3:.1f} mA\")\n",
    "\n",
    "print(\"Fin de la boucle\")       # pas décalé : exécuté une seule fois, après la boucle"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "129653dd",
   "metadata": {},
   "source": [
    "La fonction `range(n)` fournit les entiers $0, 1, \\dots, n-1$ : c'est pratique pour répéter $n$ fois, ou pour parcourir les **indices** d'une liste."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "33843cbb",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:55.968751Z",
     "iopub.status.busy": "2026-09-25T21:00:55.968571Z",
     "iopub.status.idle": "2026-09-25T21:00:55.972342Z",
     "shell.execute_reply": "2026-09-25T21:00:55.971519Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "1\n",
      "2\n",
      "3\n"
     ]
    }
   ],
   "source": [
    "for i in range(4):\n",
    "    print(i)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e74e7b09",
   "metadata": {},
   "source": [
    "### 3.3 Construire une liste avec une boucle\n",
    "On part d'une liste vide `[]` et on la remplit avec `append`. On peut aussi **accumuler** une somme dans une variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "428eef78",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:55.973767Z",
     "iopub.status.busy": "2026-09-25T21:00:55.973584Z",
     "iopub.status.idle": "2026-09-25T21:00:55.977974Z",
     "shell.execute_reply": "2026-09-25T21:00:55.977179Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.0102, 0.020099999999999996, 0.0298, 0.0405, 0.05]\n",
      "tension moyenne : 3.01 V\n"
     ]
    }
   ],
   "source": [
    "tensions = [1.02, 2.01, 2.98, 4.05, 5.00]     # (V)\n",
    "R = 100\n",
    "\n",
    "intensites = []              # liste vide\n",
    "somme = 0                    # accumulateur\n",
    "for U in tensions:\n",
    "    intensites.append(U / R)\n",
    "    somme = somme + U\n",
    "\n",
    "print(intensites)\n",
    "print(f\"tension moyenne : {somme / len(tensions):.2f} V\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21cc4b14",
   "metadata": {},
   "source": [
    "### Application guidée — ★☆☆☆\n",
    "Des élèves ont mesuré la période d'oscillation d'un pendule 6 fois. Compléter pour calculer la moyenne **avec une boucle**, puis afficher la plus grande et la plus petite valeur avec les fonctions `max` et `min`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "b860fe3b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:55.979584Z",
     "iopub.status.busy": "2026-09-25T21:00:55.979085Z",
     "iopub.status.idle": "2026-09-25T21:00:55.983604Z",
     "shell.execute_reply": "2026-09-25T21:00:55.982869Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "moyenne : 1.800 s ; min : 1.78 s ; max : 1.82 s\n"
     ]
    }
   ],
   "source": [
    "periodes = [1.79, 1.81, 1.80, 1.78, 1.82, 1.80]    # (s)\n",
    "\n",
    "somme = 0\n",
    "for T in periodes:\n",
    "    somme = somme + T\n",
    "moyenne = somme / len(periodes)\n",
    "\n",
    "print(f\"moyenne : {moyenne:.3f} s ; min : {min(periodes)} s ; max : {max(periodes)} s\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a687c7a3",
   "metadata": {},
   "source": [
    "### Exercice 3.1 — ★★☆☆\n",
    "Les longueurs d'onde (en nm) de quatre raies visibles de l'hydrogène sont `[656.3, 486.1, 434.0, 410.2]`.\n",
    "Construire la liste des fréquences correspondantes $\\nu = c/\\lambda$, puis afficher pour chaque raie une ligne du type\n",
    "`656.3 nm  ->  4.57e+14 Hz`.\n",
    "\n",
    "### Exercice 3.2 — ★★☆☆ — Bonus\n",
    "Une balle rebondit : à chaque rebond, elle remonte à 70 % de sa hauteur précédente. Elle est lâchée de 2,0 m.\n",
    "Avec une boucle `for`, afficher la hauteur atteinte après chacun des 10 premiers rebonds.\n",
    "Puis, avec une boucle `while` (qui se répète **tant qu'**une condition est vraie : `while h > 0.01:`), déterminer le nombre de rebonds au bout duquel la hauteur devient inférieure à 1 cm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "eb89124b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:55.985098Z",
     "iopub.status.busy": "2026-09-25T21:00:55.984845Z",
     "iopub.status.idle": "2026-09-25T21:00:55.989351Z",
     "shell.execute_reply": "2026-09-25T21:00:55.988524Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "656.3 nm  ->  4.57e+14 Hz\n",
      "486.1 nm  ->  6.17e+14 Hz\n",
      "434.0 nm  ->  6.91e+14 Hz\n",
      "410.2 nm  ->  7.31e+14 Hz\n"
     ]
    }
   ],
   "source": [
    "# Exercice 3.1\n",
    "c = 3.00e8\n",
    "raies = [656.3, 486.1, 434.0, 410.2]      # nm\n",
    "frequences = []\n",
    "for lam in raies:\n",
    "    frequences.append(c / (lam * 1e-9))\n",
    "for i in range(len(raies)):\n",
    "    print(f\"{raies[i]} nm  ->  {frequences[i]:.2e} Hz\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "3e81e3f4",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:55.990737Z",
     "iopub.status.busy": "2026-09-25T21:00:55.990488Z",
     "iopub.status.idle": "2026-09-25T21:00:55.995137Z",
     "shell.execute_reply": "2026-09-25T21:00:55.994410Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rebond 1 : h = 1.400 m\n",
      "rebond 2 : h = 0.980 m\n",
      "rebond 3 : h = 0.686 m\n",
      "rebond 4 : h = 0.480 m\n",
      "rebond 5 : h = 0.336 m\n",
      "rebond 6 : h = 0.235 m\n",
      "rebond 7 : h = 0.165 m\n",
      "rebond 8 : h = 0.115 m\n",
      "rebond 9 : h = 0.081 m\n",
      "rebond 10 : h = 0.056 m\n",
      "moins de 1 cm après 15 rebonds\n"
     ]
    }
   ],
   "source": [
    "# Exercice 3.2\n",
    "h = 2.0\n",
    "for n in range(1, 11):\n",
    "    h = 0.7 * h\n",
    "    print(f\"rebond {n} : h = {h:.3f} m\")\n",
    "\n",
    "h = 2.0\n",
    "n = 0\n",
    "while h > 0.01:\n",
    "    h = 0.7 * h\n",
    "    n = n + 1\n",
    "print(f\"moins de 1 cm après {n} rebonds\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0fe6248d",
   "metadata": {},
   "source": [
    "---\n",
    "## Partie 4 — Fonctions  *(20 min)*\n",
    "\n",
    "### 4.1 Utiliser des fonctions existantes\n",
    "Les fonctions mathématiques (racine, sinus, exponentielle…) ne sont pas disponibles immédiatement : elles se trouvent dans des **bibliothèques** qu'il faut **importer**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "50adcef2",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:55.996939Z",
     "iopub.status.busy": "2026-09-25T21:00:55.996368Z",
     "iopub.status.idle": "2026-09-25T21:00:56.001165Z",
     "shell.execute_reply": "2026-09-25T21:00:56.000257Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.4142135623730951\n",
      "3.141592653589793\n",
      "-1.0\n",
      "2.718281828459045\n",
      "1.0\n",
      "3.0\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "print(math.sqrt(2))          # racine carrée\n",
    "print(math.pi)               # la constante pi\n",
    "print(math.cos(math.pi))     # les angles sont en RADIANS\n",
    "print(math.exp(1))           # exponentielle\n",
    "print(math.log(math.e))      # logarithme népérien (ln)\n",
    "print(math.log10(1000))      # logarithme décimal"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98b5dbd1",
   "metadata": {},
   "source": [
    "### 4.2 Écrire ses propres fonctions\n",
    "Une fonction regroupe un calcul que l'on veut **réutiliser**. On la définit avec `def`, elle reçoit des **arguments** entre parenthèses et **renvoie** un résultat avec `return`. Comme pour les boucles : deux points et indentation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "174774c2",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:56.002556Z",
     "iopub.status.busy": "2026-09-25T21:00:56.002416Z",
     "iopub.status.idle": "2026-09-25T21:00:56.006407Z",
     "shell.execute_reply": "2026-09-25T21:00:56.005633Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.0060666807106475\n",
      "1.0030333403553238\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "def periode_pendule(l):\n",
    "    # renvoie la période (s) d'un pendule simple de longueur l (m), petites oscillations\n",
    "    g = 9.81\n",
    "    return 2 * math.pi * math.sqrt(l / g)\n",
    "\n",
    "print(periode_pendule(1.0))\n",
    "print(periode_pendule(0.25))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a784c94",
   "metadata": {},
   "source": [
    "⚠️ **Définir** une fonction n'affiche rien : il faut ensuite l'**appeler** avec des valeurs. Et `return` n'est pas `print` : `return` rend la valeur au programme, qui peut la réutiliser dans un calcul."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "f7a06bb1",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:56.007708Z",
     "iopub.status.busy": "2026-09-25T21:00:56.007530Z",
     "iopub.status.idle": "2026-09-25T21:00:56.011352Z",
     "shell.execute_reply": "2026-09-25T21:00:56.010603Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "quadrupler la longueur multiplie la période par 2.00\n"
     ]
    }
   ],
   "source": [
    "T1 = periode_pendule(1.0)\n",
    "T2 = periode_pendule(4.0)\n",
    "print(f\"quadrupler la longueur multiplie la période par {T2 / T1:.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4b99966",
   "metadata": {},
   "source": [
    "### Application guidée — ★☆☆☆\n",
    "Écrire une fonction `energie_cinetique(m, v)` puis l'utiliser pour une voiture de 1,2 t roulant à 50 km/h, puis à 130 km/h (attention aux unités !)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "df79fa34",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:56.013192Z",
     "iopub.status.busy": "2026-09-25T21:00:56.012580Z",
     "iopub.status.idle": "2026-09-25T21:00:56.017247Z",
     "shell.execute_reply": "2026-09-25T21:00:56.016432Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "50 km/h : 116 kJ\n",
      "130 km/h : 782 kJ\n"
     ]
    }
   ],
   "source": [
    "def energie_cinetique(m, v):\n",
    "    return 0.5 * m * v**2\n",
    "\n",
    "v1 = 50 / 3.6          # 50 km/h en m/s\n",
    "v2 = 130 / 3.6         # 130 km/h en m/s\n",
    "print(f\"50 km/h : {energie_cinetique(1.2e3, v1)/1e3:.0f} kJ\")\n",
    "print(f\"130 km/h : {energie_cinetique(1.2e3, v2)/1e3:.0f} kJ\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e60e802",
   "metadata": {},
   "source": [
    "### Exercice 4.1 — ★★☆☆\n",
    "Écrire une fonction `R_serie(R1, R2)` et une fonction `R_parallele(R1, R2)` donnant la résistance équivalente de deux résistances. Les tester avec $R_1 = 1$ kΩ et $R_2 = 2{,}2$ kΩ (attendu : 3200 Ω et 687,5 Ω).\n",
    "Utiliser ensuite ces deux fonctions pour calculer la résistance équivalente de l'association : $R_1$ en série avec ($R_2$ en parallèle avec $R_3 = 3{,}3$ kΩ).\n",
    "\n",
    "### Exercice 4.2 — ★★☆☆ — Bonus\n",
    "Écrire une fonction `hauteur_max(v0, angle_deg)` qui renvoie la hauteur maximale $\\dfrac{(v_0\\sin\\alpha)^2}{2g}$ atteinte par un projectile lancé à la vitesse $v_0$ avec un angle $\\alpha$ donné **en degrés** (penser à `math.radians`). Afficher, avec une boucle, la hauteur maximale pour les angles 15°, 30°, 45°, 60°, 75° et 90°, avec $v_0 = 10$ m/s."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "2b396cff",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:56.018925Z",
     "iopub.status.busy": "2026-09-25T21:00:56.018388Z",
     "iopub.status.idle": "2026-09-25T21:00:56.022989Z",
     "shell.execute_reply": "2026-09-25T21:00:56.022233Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3200.0 687.5\n",
      "R_eq = 2320 ohm\n"
     ]
    }
   ],
   "source": [
    "# Exercice 4.1\n",
    "def R_serie(R1, R2):\n",
    "    return R1 + R2\n",
    "\n",
    "def R_parallele(R1, R2):\n",
    "    return R1 * R2 / (R1 + R2)\n",
    "\n",
    "print(R_serie(1e3, 2.2e3), R_parallele(1e3, 2.2e3))\n",
    "print(f\"R_eq = {R_serie(1e3, R_parallele(2.2e3, 3.3e3)):.0f} ohm\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "a7d81e00",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:56.024296Z",
     "iopub.status.busy": "2026-09-25T21:00:56.024143Z",
     "iopub.status.idle": "2026-09-25T21:00:56.029083Z",
     "shell.execute_reply": "2026-09-25T21:00:56.028212Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "15° : 0.34 m\n",
      "30° : 1.27 m\n",
      "45° : 2.55 m\n",
      "60° : 3.82 m\n",
      "75° : 4.76 m\n",
      "90° : 5.10 m\n"
     ]
    }
   ],
   "source": [
    "# Exercice 4.2\n",
    "import math\n",
    "\n",
    "def hauteur_max(v0, angle_deg):\n",
    "    alpha = math.radians(angle_deg)\n",
    "    return (v0 * math.sin(alpha))**2 / (2 * 9.81)\n",
    "\n",
    "for a in [15, 30, 45, 60, 75, 90]:\n",
    "    print(f\"{a:2d}° : {hauteur_max(10, a):.2f} m\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e34fdacb",
   "metadata": {},
   "source": [
    "---\n",
    "## Partie 5 — Premier graphique  *(20 min)*\n",
    "\n",
    "Pour tracer des courbes, on utilise deux bibliothèques qui nous serviront toute l'année :\n",
    "- `numpy` (importée sous le nom `np`) : calcul sur des **tableaux** de nombres, sans écrire de boucle ;\n",
    "- `matplotlib.pyplot` (importée sous le nom `plt`) : tracé de graphiques.\n",
    "\n",
    "### 5.1 Les tableaux `numpy`\n",
    "`np.linspace(debut, fin, N)` crée un tableau de $N$ valeurs régulièrement espacées, **fin incluse**. Les opérations et les fonctions `np.sin`, `np.exp`… s'appliquent **à toutes les cases à la fois**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "0ae4c007",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:56.030916Z",
     "iopub.status.busy": "2026-09-25T21:00:56.030319Z",
     "iopub.status.idle": "2026-09-25T21:00:56.095354Z",
     "shell.execute_reply": "2026-09-25T21:00:56.094242Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.   0.25 0.5  0.75 1.  ]\n",
      "[0.  0.5 1.  1.5 2. ]\n",
      "[0.     0.0625 0.25   0.5625 1.    ]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "t = np.linspace(0, 1, 5)\n",
    "print(t)\n",
    "print(2 * t)          # chaque valeur est multipliée par 2\n",
    "print(t ** 2)         # chaque valeur est élevée au carré"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa976f7b",
   "metadata": {},
   "source": [
    "### Prédis puis exécute\n",
    "Que va afficher la cellule suivante ? Et que donnerait le même calcul avec une **liste** `[0, 1, 2]` au lieu d'un tableau `numpy` ? Essaie !"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "3eefb24c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:56.097011Z",
     "iopub.status.busy": "2026-09-25T21:00:56.096481Z",
     "iopub.status.idle": "2026-09-25T21:00:56.101524Z",
     "shell.execute_reply": "2026-09-25T21:00:56.100723Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 3, 6])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([0, 1, 2])\n",
    "x * 3"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d62d59f4",
   "metadata": {},
   "source": [
    "**Commentaire (corrigé)** — avec une liste, `[0, 1, 2] * 3` donne `[0, 1, 2, 0, 1, 2, 0, 1, 2]` (répétition) : c'est la raison principale d'utiliser `numpy` pour les calculs."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "275328aa",
   "metadata": {},
   "source": [
    "### 5.2 Tracer une courbe\n",
    "Exemple : la position d'un objet en chute libre, $x(t) = \\tfrac{1}{2}gt^2$, pendant 2 s.\n",
    "Un graphique scientifique a **toujours** des axes légendés avec leurs unités."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "26e01d8b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:56.103342Z",
     "iopub.status.busy": "2026-09-25T21:00:56.102805Z",
     "iopub.status.idle": "2026-09-25T21:00:56.507932Z",
     "shell.execute_reply": "2026-09-25T21:00:56.506959Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "g = 9.81\n",
    "t = np.linspace(0, 2, 100)       # 100 instants entre 0 et 2 s\n",
    "x = 0.5 * g * t**2               # 100 positions, calculées d'un coup\n",
    "\n",
    "plt.figure()                     # nouvelle figure\n",
    "plt.plot(t, x)                   # courbe x en fonction de t\n",
    "plt.xlabel(\"t (s)\")              # légende de l'axe horizontal\n",
    "plt.ylabel(\"x (m)\")              # légende de l'axe vertical\n",
    "plt.title(\"Chute libre\")\n",
    "plt.grid()                       # quadrillage\n",
    "plt.show()                       # affichage"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c71b5ff",
   "metadata": {},
   "source": [
    "Pour tracer des **mesures**, on représente des **points** que l'on ne relie pas : on ajoute un marqueur, par exemple `'o'` ou `'+'`. Pour superposer plusieurs courbes, on appelle `plt.plot` plusieurs fois, avec un `label` pour la légende."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "4967ef02",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:56.509960Z",
     "iopub.status.busy": "2026-09-25T21:00:56.509306Z",
     "iopub.status.idle": "2026-09-25T21:00:56.589387Z",
     "shell.execute_reply": "2026-09-25T21:00:56.588388Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t_mes = [0.0, 0.2, 0.4, 0.6, 0.8, 1.0]           # (s)\n",
    "x_mes = [0.00, 0.21, 0.77, 1.78, 3.12, 4.93]     # (m)\n",
    "\n",
    "t = np.linspace(0, 1, 100)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(t_mes, x_mes, 'o', label=\"mesures\")\n",
    "plt.plot(t, 0.5 * 9.81 * t**2, 'r-', label=\"modèle\")\n",
    "plt.xlabel(\"t (s)\")\n",
    "plt.ylabel(\"x (m)\")\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba54fdd0",
   "metadata": {},
   "source": [
    "### Application guidée — ★☆☆☆\n",
    "Tracer la tension $u(t) = U_m\\cos(2\\pi f t)$ du secteur ($U_m = 325$ V, $f = 50$ Hz) sur trois périodes, avec l'axe des temps en millisecondes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "c68a8acc",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:56.591298Z",
     "iopub.status.busy": "2026-09-25T21:00:56.590724Z",
     "iopub.status.idle": "2026-09-25T21:00:56.666186Z",
     "shell.execute_reply": "2026-09-25T21:00:56.665197Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "Um = 325\n",
    "f = 50\n",
    "T = 1 / f                            # période (s)\n",
    "t = np.linspace(0, 3 * T, 500)       # trois périodes\n",
    "u = Um * np.cos(2 * np.pi * f * t)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(t * 1e3, u)                 # t * 1e3 : temps en ms\n",
    "plt.xlabel(\"t (ms)\")\n",
    "plt.ylabel(\"u (V)\")\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe7ced5c",
   "metadata": {},
   "source": [
    "### Exercice 5.1 — ★★☆☆\n",
    "Tracer sur un même graphique la charge d'un condensateur $u(t) = E\\left(1 - e^{-t/\\tau}\\right)$ pour $E = 5$ V et $\\tau = 1$ ms, et la droite horizontale $u = E$ (on peut utiliser `plt.axhline(5, color='k', linestyle='--')`), sur l'intervalle $[0 ; 5\\tau]$. Ajouter une légende.\n",
    "Lire sur le graphique la valeur de $u$ à $t = \\tau$ et vérifier qu'elle vaut environ 63 % de $E$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "7a297f90",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:56.667647Z",
     "iopub.status.busy": "2026-09-25T21:00:56.667489Z",
     "iopub.status.idle": "2026-09-25T21:00:56.749610Z",
     "shell.execute_reply": "2026-09-25T21:00:56.748736Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "u(tau) = 3.16 V, soit 63% de E\n"
     ]
    }
   ],
   "source": [
    "E, tau = 5.0, 1e-3\n",
    "t = np.linspace(0, 5 * tau, 300)\n",
    "plt.figure()\n",
    "plt.plot(t * 1e3, E * (1 - np.exp(-t / tau)), label=\"u(t)\")\n",
    "plt.axhline(E, color='k', linestyle='--', label=\"u = E\")\n",
    "plt.axvline(tau * 1e3, color='g', linestyle=':', label=\"t = tau\")\n",
    "plt.xlabel(\"t (ms)\"); plt.ylabel(\"u (V)\"); plt.legend(); plt.grid(); plt.show()\n",
    "print(f\"u(tau) = {E * (1 - np.exp(-1)):.2f} V, soit {1 - np.exp(-1):.0%} de E\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fabc33c8",
   "metadata": {},
   "source": [
    "---\n",
    "## Partie 6 — Mini-projet de synthèse  *(10 min, à terminer à la maison si besoin)* — ★★★☆\n",
    "\n",
    "**Chute libre du haut de monuments célèbres.** On lâche une bille sans vitesse initiale et on néglige les frottements.\n",
    "\n",
    "1. Écrire une fonction `duree_chute(h)` qui renvoie la durée de chute (s) d'une hauteur `h` (m), sachant que $h = \\tfrac{1}{2}g t^2$.\n",
    "2. Écrire une fonction `vitesse_impact(h)` qui renvoie la vitesse (en km/h) au moment de toucher le sol, sachant que $v = g\\,t$.\n",
    "3. Avec une boucle, afficher un tableau propre pour les monuments ci-dessous, du type\n",
    "   `Tour Eiffel      :  h = 300 m   t = 7.8 s   v = 276 km/h`\n",
    "   (le format `{nom:15s}` aligne un texte sur 15 caractères).\n",
    "4. Tracer, sur un même graphique, la position $x(t)$ pendant la chute depuis chacun des monuments, chaque courbe s'arrêtant à l'impact.\n",
    "5. *Bonus* : en réalité, une bille de 1 cm dans l'air atteint une vitesse limite d'environ 100 km/h. Pour quels monuments le modèle de la chute libre est-il manifestement faux ? (Le cas de la chute avec frottement sera traité plus tard dans l'année.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "2e36d2d4",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T21:00:56.751518Z",
     "iopub.status.busy": "2026-09-25T21:00:56.750966Z",
     "iopub.status.idle": "2026-09-25T21:00:56.863999Z",
     "shell.execute_reply": "2026-09-25T21:00:56.863068Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Capitole        :  h =  30 m   t =  2.5 s   v =   87 km/h\n",
      "Tour Eiffel     :  h = 300 m   t =  7.8 s   v =  276 km/h\n",
      "Burj Khalifa    :  h = 828 m   t = 13.0 s   v =  459 km/h\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "noms = [\"Capitole\", \"Tour Eiffel\", \"Burj Khalifa\"]\n",
    "hauteurs = [30, 300, 828]      # (m) — le Capitole : hauteur approximative de la façade\n",
    "g = 9.81\n",
    "\n",
    "# 1. et 2. Les fonctions\n",
    "def duree_chute(h):\n",
    "    return np.sqrt(2 * h / g)\n",
    "\n",
    "def vitesse_impact(h):\n",
    "    return g * duree_chute(h) * 3.6          # m/s -> km/h\n",
    "\n",
    "# 3. Le tableau\n",
    "for i in range(len(noms)):\n",
    "    h = hauteurs[i]\n",
    "    print(f\"{noms[i]:15s} :  h = {h:3d} m   t = {duree_chute(h):4.1f} s   v = {vitesse_impact(h):4.0f} km/h\")\n",
    "\n",
    "# 4. Le graphique\n",
    "plt.figure()\n",
    "for i in range(len(noms)):\n",
    "    t = np.linspace(0, duree_chute(hauteurs[i]), 200)\n",
    "    plt.plot(t, 0.5 * g * t**2, label=noms[i])\n",
    "plt.xlabel(\"t (s)\")\n",
    "plt.ylabel(\"distance parcourue (m)\")\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()\n",
    "\n",
    "# 5. La vitesse d'impact dépasse 100 km/h pour la tour Eiffel et Burj Khalifa : le modèle est faux,\n",
    "#    les frottements ne sont plus négligeables. Pour le Capitole (~87 km/h), il reste acceptable en ordre de grandeur."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16bcbb98",
   "metadata": {},
   "source": [
    "**Commentaire (corrigé)** — la vitesse limite de 100 km/h est un ordre de grandeur (bille d'acier de 1 cm : environ 100 à 120 km/h). Le prolongement naturel est l'exercice 6 du notebook 4 (chute avec frottement quadratique, méthode d'Euler)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "092910e4",
   "metadata": {},
   "source": [
    "---\n",
    "## Bilan — ce que je sais faire\n",
    "\n",
    "Coche mentalement chaque ligne : si l'une d'elles n'est pas acquise, reprends la partie correspondante, puis entraîne-toi avec le notebook « 0. Bases de Python ».\n",
    "\n",
    "| Je sais… | Partie |\n",
    "|---|---|\n",
    "| exécuter une cellule, relancer tout le notebook dans l'ordre | 0 |\n",
    "| écrire un calcul avec `**`, des parenthèses et la notation `6.02e23` | 1 |\n",
    "| lire un message d'erreur et trouver la ligne fautive | 1 |\n",
    "| afficher un résultat avec un nombre adapté de chiffres significatifs | 2 |\n",
    "| accéder à un élément d'une liste, la parcourir avec `for`, la remplir avec `append` | 3 |\n",
    "| importer une bibliothèque et définir une fonction avec `def` et `return` | 4 |\n",
    "| créer un tableau avec `np.linspace` et tracer une courbe avec axes légendés et unités | 5 |\n",
    "\n",
    "**Aide-mémoire de la séance**\n",
    "\n",
    "```python\n",
    "import math                      # fonctions mathématiques sur des nombres\n",
    "import numpy as np               # calcul sur des tableaux\n",
    "import matplotlib.pyplot as plt  # graphiques\n",
    "\n",
    "x = 2.5e-3                       # variable (point décimal, notation scientifique)\n",
    "print(f\"x = {x:.2e} m\")          # affichage formaté\n",
    "\n",
    "L = [1, 2, 3]                    # liste ; L[0] premier élément, len(L) longueur\n",
    "for valeur in L:                 # boucle : deux points + indentation\n",
    "    print(valeur)\n",
    "\n",
    "def carre(a):                    # fonction\n",
    "    return a**2\n",
    "\n",
    "t = np.linspace(0, 1, 100)       # 100 valeurs de 0 à 1\n",
    "plt.plot(t, carre(t)); plt.xlabel(\"t (s)\"); plt.ylabel(\"...\"); plt.grid(); plt.show()\n",
    "```"
   ]
  }
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