From c06b8dee8b5af973bb6b2c7916387696f404ba73 Mon Sep 17 00:00:00 2001 From: Sven Riwoldt Date: Sat, 14 Mar 2026 21:48:48 +0100 Subject: [PATCH] Korrektur --- Mathematik für Ingenieure 1.ipynb | 209 ++++++++++++------------------ 1 file changed, 84 insertions(+), 125 deletions(-) diff --git a/Mathematik für Ingenieure 1.ipynb b/Mathematik für Ingenieure 1.ipynb index 90ce7c3..301038c 100644 --- a/Mathematik für Ingenieure 1.ipynb +++ b/Mathematik für Ingenieure 1.ipynb @@ -2,6 +2,7 @@ "cells": [ { "cell_type": "code", + "execution_count": 1, "id": "902e4b59-77b9-4db6-9ec2-3cff55766dd5", "metadata": { "ExecuteTime": { @@ -9,6 +10,15 @@ "start_time": "2026-03-14T20:28:45.240030Z" } }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "5j\n" + ] + } + ], "source": [ "\n", "def abs(c):\n", @@ -28,20 +38,11 @@ "\n", "\n", "print(mul(1+2j, 2+1j))" - ], - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "5j\n" - ] - } - ], - "execution_count": 12 + ] }, { "cell_type": "code", + "execution_count": 2, "id": "3fb82de2-875a-4dac-935a-e64bad48c895", "metadata": { "ExecuteTime": { @@ -49,6 +50,15 @@ "start_time": "2026-03-14T20:28:45.281685Z" } }, + "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", @@ -59,20 +69,11 @@ "\n", "\n", "print(add((2, 1), (3, 4)))\n" - ], - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "(5, 5)\n" - ] - } - ], - "execution_count": 13 + ] }, { "cell_type": "code", + "execution_count": 3, "id": "3a562f0e-162b-4760-ac6b-22587bf0bd60", "metadata": { "ExecuteTime": { @@ -80,6 +81,16 @@ "start_time": "2026-03-14T20:28:45.349987Z" } }, + "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", @@ -95,21 +106,11 @@ "\n", "print(f\"Intervall: {mein_intervall}\")\n", "print(f\"Mengenangabe: {mengen_angabe}\")\n" - ], - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Intervall: Interval.Ropen(2, 5)\n", - "Mengenangabe: (2 <= x) & (x < 5)\n" - ] - } - ], - "execution_count": 14 + ] }, { "cell_type": "code", + "execution_count": 4, "id": "5f024814-9f83-4d5f-a81f-4283e47e22b9", "metadata": { "ExecuteTime": { @@ -117,6 +118,15 @@ "start_time": "2026-03-14T20:28:45.660677Z" } }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Interval.Ropen(2, 5)\n" + ] + } + ], "source": [ "from sympy import Symbol, And\n", "\n", @@ -130,20 +140,11 @@ "\n", "print(intervall) \n", "# Ausgabe: [2, 5)\n" - ], - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Interval.Ropen(2, 5)\n" - ] - } - ], - "execution_count": 15 + ] }, { "cell_type": "code", + "execution_count": 5, "id": "b58b7c16-2c79-46a4-bde0-1d8fcc16cfa9", "metadata": { "ExecuteTime": { @@ -151,6 +152,15 @@ "start_time": "2026-03-14T20:28:45.765958Z" } }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Interval(-2, 2)\n" + ] + } + ], "source": [ "from sympy import Symbol, solve_univariate_inequality\n", "\n", @@ -164,20 +174,11 @@ "\n", "print(intervall)\n", "# Ausgabe: [-2, 2]\n" - ], - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Interval(-2, 2)\n" - ] - } - ], - "execution_count": 16 + ] }, { "cell_type": "code", + "execution_count": 7, "id": "dd0522d3-0612-44f1-9504-1ba48542e37e", "metadata": { "ExecuteTime": { @@ -185,37 +186,34 @@ "start_time": "2026-03-14T20:28:45.792950Z" } }, - "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)" - ], "outputs": [ { - "ename": "AttributeError", - "evalue": "'Symbol' object has no attribute 'real'", - "output_type": "error", - "traceback": [ - "\u001B[31m---------------------------------------------------------------------------\u001B[39m", - "\u001B[31mAttributeError\u001B[39m Traceback (most recent call last)", - "\u001B[36mCell\u001B[39m\u001B[36m \u001B[39m\u001B[32mIn[17]\u001B[39m\u001B[32m, line 6\u001B[39m\n\u001B[32m 3\u001B[39m x = Symbol(\u001B[33m'\u001B[39m\u001B[33mx\u001B[39m\u001B[33m'\u001B[39m)\n\u001B[32m 5\u001B[39m \u001B[38;5;66;03m# Eine Ungleichung definieren\u001B[39;00m\n\u001B[32m----> \u001B[39m\u001B[32m6\u001B[39m ungleichung = \u001B[38;5;28;43mabs\u001B[39;49m\u001B[43m(\u001B[49m\u001B[43mx\u001B[49m\u001B[43m)\u001B[49m<\u001B[32m8\u001B[39m\n\u001B[32m 8\u001B[39m \u001B[38;5;66;03m# Lösen und als Intervall ausgeben lassen (relational=False)\u001B[39;00m\n\u001B[32m 9\u001B[39m intervall = solve_univariate_inequality(ungleichung, x, relational=\u001B[38;5;28;01mFalse\u001B[39;00m)\n", - "\u001B[36mCell\u001B[39m\u001B[36m \u001B[39m\u001B[32mIn[12]\u001B[39m\u001B[32m, line 2\u001B[39m, in \u001B[36mabs\u001B[39m\u001B[34m(c)\u001B[39m\n\u001B[32m 1\u001B[39m \u001B[38;5;28;01mdef\u001B[39;00m\u001B[38;5;250m \u001B[39m\u001B[34mabs\u001B[39m(c):\n\u001B[32m----> \u001B[39m\u001B[32m2\u001B[39m \u001B[38;5;28;01mreturn\u001B[39;00m (\u001B[43mc\u001B[49m\u001B[43m.\u001B[49m\u001B[43mreal\u001B[49m**\u001B[32m2\u001B[39m + c.imag**\u001B[32m2\u001B[39m)**\u001B[32m0.5\u001B[39m\n", - "\u001B[31mAttributeError\u001B[39m: 'Symbol' object has no attribute 'real'" + "name": "stdout", + "output_type": "stream", + "text": [ + "Interval.open(-8, 8)\n" ] } ], - "execution_count": 17 + "source": [ + "from sympy import Symbol, solve_univariate_inequality, Abs\n", + "\n", + "# 1. Symbol als reell definieren\n", + "x = Symbol('x', real=True)\n", + "\n", + "# 2. Die SymPy-eigene Funktion Abs() verwenden\n", + "# Das verhindert, dass Python-Interne Funktionen dazwischenfunken\n", + "ungleichung = Abs(x) < 8\n", + "\n", + "# 3. Lösen\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": { "ExecuteTime": { @@ -223,6 +221,7 @@ "start_time": "2026-03-14T20:30:39.352620Z" } }, + "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "from sympy import Interval\n", @@ -255,66 +254,26 @@ "# Beispiel: [2, 5)\n", "mein_intervall = Interval(2, 5, left_open=False, right_open=True)\n", "plot_interval(mein_intervall, x_range=(0, 7))\n" - ], - "outputs": [ - { - "data": { - "text/plain": [ - "
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" - }, - "metadata": {}, - "output_type": "display_data", - "jetTransient": { - "display_id": null - } - } - ], - "execution_count": 19 + ] }, { + "cell_type": "code", + "execution_count": null, + "id": "cdb0080c9d06840a", "metadata": { "ExecuteTime": { "end_time": "2026-03-14T20:30:39.750872Z", "start_time": "2026-03-14T20:30:39.440529Z" } }, - "cell_type": "code", + "outputs": [], "source": [ "from sympy import symbols, plot_implicit, And\n", "\n", "x = symbols('x')\n", "# Zeichnet den Bereich auf der x-Achse\n", "plot_implicit(And(x >= 2, x < 5), (x, 0, 7))\n" - ], - "id": "cdb0080c9d06840a", - "outputs": [ - { - "data": { - "text/plain": [ - "
" - ], - "image/png": 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