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Mathematik für Ingenieure 1.ipynb

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+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "id": "902e4b59-77b9-4db6-9ec2-3cff55766dd5",
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-14T20:09:28.272005Z",
+     "start_time": "2026-03-14T20:09:28.181811Z"
+    }
+   },
+   "source": [
+    "\n",
+    "def abs(c):\n",
+    "    return (c.real**2 + c.imag**2)**0.5\n",
+    "\n",
+    "def add(c1, c2):\n",
+    "    return complex(c1.real + c2.real, c1.imag + c2.imag)\n",
+    "\n",
+    "def sub(c1, c2):\n",
+    "    # (a+bi) - (c+di) = (a-c) + (b-d)i\n",
+    "    return complex(c1.real - c2.real, c1.imag - c2.imag)\n",
+    "\n",
+    "def mul(c1, c2):\n",
+    "    # (a+bi)(c+di) = (ac-bd) + (ad+bc)i\n",
+    "    return complex(c1.real * c2.real - c1.imag * c2.imag, c1.real * c2.imag + c1.imag * c2.real)\n",
+    "\n",
+    "\n",
+    "\n",
+    "print(mul(1+2j, 2+1j))"
+   ],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "5j\n"
+     ]
+    }
+   ],
+   "execution_count": 1
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "3fb82de2-875a-4dac-935a-e64bad48c895",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(5, 5)\n"
+     ]
+    }
+   ],
+   "source": [
+    "def add(v1, v2):\n",
+    "    return (v1[0] + v2[0], v1[1] + v2[1])\n",
+    "\n",
+    "def sub(v1, v2):\n",
+    "    return (v1[0] - v2[0], v1[1] - v2[1])\n",
+    "\n",
+    "\n",
+    "\n",
+    "print(add((2, 1), (3, 4)))\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "3a562f0e-162b-4760-ac6b-22587bf0bd60",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Intervall: Interval.Ropen(2, 5)\n",
+      "Mengenangabe: (2 <= x) & (x < 5)\n"
+     ]
+    }
+   ],
+   "source": [
+    "from sympy import Interval, Symbol\n",
+    "\n",
+    "# 1. Variable definieren\n",
+    "x = Symbol('x')\n",
+    "\n",
+    "# 2. Intervall erstellen (z.B. [2, 5) - links abgeschlossen, rechts offen)\n",
+    "# left_open=False (Standard) bedeutet inklusive 2, right_open=True bedeutet exklusive 5\n",
+    "mein_intervall = Interval(2, 5, left_open=False, right_open=True)\n",
+    "\n",
+    "# 3. In Mengenangabe / Ungleichung umwandeln\n",
+    "mengen_angabe = mein_intervall.as_relational(x)\n",
+    "\n",
+    "print(f\"Intervall: {mein_intervall}\")\n",
+    "print(f\"Mengenangabe: {mengen_angabe}\")\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "5f024814-9f83-4d5f-a81f-4283e47e22b9",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Interval.Ropen(2, 5)\n"
+     ]
+    }
+   ],
+   "source": [
+    "from sympy import Symbol, And\n",
+    "\n",
+    "x = Symbol('x')\n",
+    "\n",
+    "# Eine Mengenangabe als logische Verknüpfung (2 <= x < 5)\n",
+    "mengen_angabe = And(x >= 2, x < 5)\n",
+    "\n",
+    "# Umwandlung in ein Intervall-Objekt\n",
+    "intervall = mengen_angabe.as_set()\n",
+    "\n",
+    "print(intervall) \n",
+    "# Ausgabe: [2, 5)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "b58b7c16-2c79-46a4-bde0-1d8fcc16cfa9",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Interval(-2, 2)\n"
+     ]
+    }
+   ],
+   "source": [
+    "from sympy import Symbol, solve_univariate_inequality\n",
+    "\n",
+    "x = Symbol('x')\n",
+    "\n",
+    "# Eine Ungleichung definieren\n",
+    "ungleichung = x**2 <= 4\n",
+    "\n",
+    "# Lösen und als Intervall ausgeben lassen (relational=False)\n",
+    "intervall = solve_univariate_inequality(ungleichung, x, relational=False)\n",
+    "\n",
+    "print(intervall)\n",
+    "# Ausgabe: [-2, 2]\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "dd0522d3-0612-44f1-9504-1ba48542e37e",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Interval.open(-8, 8)\n"
+     ]
+    }
+   ],
+   "source": [
+    "from sympy import Symbol, solve_univariate_inequality\n",
+    "\n",
+    "x = Symbol('x')\n",
+    "\n",
+    "# Eine Ungleichung definieren\n",
+    "ungleichung = abs(x)<8\n",
+    "\n",
+    "# Lösen und als Intervall ausgeben lassen (relational=False)\n",
+    "intervall = solve_univariate_inequality(ungleichung, x, relational=False)\n",
+    "\n",
+    "print(intervall)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "99ed5f78-8032-40eb-99ce-988de647549b",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "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": "3.13.11"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}