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0ddb8af527
...
61b1cabdbb
6 changed files with 34 additions and 631 deletions
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flake.nix
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27
flake.nix
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{
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inputs.nixpkgs.url = "github:NixOS/nixpkgs/nixpkgs-unstable";
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outputs =
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{ nixpkgs, ... }:
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{
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/*
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This example assumes your system is x86_64-linux
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change as neccesary
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*/
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devShells.x86_64-linux =
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let
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pkgs = nixpkgs.legacyPackages.x86_64-linux;
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in
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{
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default = pkgs.mkShell {
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packages = [
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pkgs.typst
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pkgs.typstyle
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pkgs.tinymist
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pkgs.agebox
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];
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};
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};
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};
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}
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@ -1,80 +0,0 @@
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#import "@preview/grape-suite:1.0.0": exercise
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#import exercise: project, task, subtask
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#set text(lang: "de")
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#show: project.with(
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title: [Kettenregel],
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seminar: [Mathe Q2],
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show-outline: true,
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author: "Erik Grobecker",
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date: datetime(day: 18, month: 11, year: 2024),
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show-solutions: false,
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)
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#show heading.where(level: 1): it => {
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counter(math.equation).update(0)
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it
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}
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#show math.equation: set text(font: "New Computer Modern Math")
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= Kettenregel
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$
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f(x)&= underbrace((3/4 x^2 -3), u) dot underbrace(e^(1.4-x^2), v) \
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f'(x)&=u' dot v + u dot v'\
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u'&=3/4 dot 2x^1\ &
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= 3/2 dot x\
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v'&=e^(1.4-x^2)\
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&=e^(overbrace(1.4-x^2, "innere Ableitung")) \
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&=e^(1.4-x^2) dot overbrace((-2x), "innere Ableitung")\
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\
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"Einsetzen:"\
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f'(x)&=u' dot v + u dot v'\
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&=3/2x dot e^(1.4-x^2) + (3/4 x^2 -3) dot e^(1.4-x^2) dot (-2x) #h(2em)&| e "entfernen" \
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&=e^(1.4-x^2) dot (3/2x + (3/4x^2-3) dot (-2x))\
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&=e^(1.4-x^2) dot (3/2x -3/2x^3 + 6x)\
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&=e^(1.4-x^2) dot (-3/2x^3 + 15/2x)
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$
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Innere Ableitung:
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$
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u(x)&=1.4-x^2\
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u'(x)&=2x
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$
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#pagebreak()
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== Aufgabe
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Leite die folgenden Funktionen ab:
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*1)*
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$
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f(x)&=e^(2x)\
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f'(x)&=e^(2x)dot 2\
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&=2e^(2x)
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$
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*2)*
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$
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f(x)&=e^(3x)\
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f'(x)&=e^(3x) dot 3\
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&=3e^(3x)
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$
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*3)*
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$
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f(x)&=e^(-x)\
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f'(x)&=e^(-x) dot (-1)\
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&=-e^(-x)
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$
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*4)*
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$
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f(x)&=e^(0.5x)\
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f'(x)&=e^(0.5x) dot 1 / 2\
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&=1 / 2 e^(0.5x)
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$
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@ -1,298 +0,0 @@
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{
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"cells": [
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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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"### **Grundlegende Operatoren und Funktionen**\n",
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"\n",
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"1. **Exponentiation** (Potenz)\n",
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"\n",
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" - `**`: Exponentiation\n",
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" ```python\n",
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" x**2 # x hoch 2\n",
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" ```\n",
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" - `exp(x)`: Exponentielle Funktion \\( e^x \\)\n",
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" ```python\n",
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" from sympy import exp\n",
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" exp(x)\n",
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" ```\n",
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"\n",
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"2. **Logarithmen**\n",
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"\n",
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" - `log(x)`: Natürlicher Logarithmus \\( \\ln(x) \\)\n",
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" ```python\n",
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||||||
" from sympy import log\n",
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" log(x)\n",
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" ```\n",
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" - `log(x, base)`: Logarithmus zur Basis `base`\n",
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" ```python\n",
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" log(x, 10) # Logarithmus zur Basis 10\n",
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" ```\n",
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"\n",
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"3. **Trigonometrische Funktionen**\n",
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"\n",
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" - `sin(x)`: Sinus\n",
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" ```python\n",
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" from sympy import sin\n",
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" sin(x)\n",
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" ```\n",
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" - `cos(x)`: Kosinus\n",
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" ```python\n",
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||||||
" from sympy import cos\n",
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" cos(x)\n",
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" ```\n",
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" - `tan(x)`: Tangens\n",
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" ```python\n",
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||||||
" from sympy import tan\n",
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" tan(x)\n",
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" ```\n",
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||||||
" - `csc(x)`: Kosekans (1/sin(x))\n",
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" ```python\n",
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||||||
" from sympy import csc\n",
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" csc(x)\n",
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" ```\n",
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" - `sec(x)`: Sekans (1/cos(x))\n",
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" ```python\n",
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||||||
" from sympy import sec\n",
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" sec(x)\n",
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" ```\n",
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" - `cot(x)`: Kotangens (1/tan(x))\n",
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" ```python\n",
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" from sympy import cot\n",
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" cot(x)\n",
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" ```\n",
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"\n",
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"4. **Hyperbolische Funktionen**\n",
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"\n",
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" - `sinh(x)`: Sinus hyperbolicus\n",
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" ```python\n",
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" from sympy import sinh\n",
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" sinh(x)\n",
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" ```\n",
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" - `cosh(x)`: Kosinus hyperbolicus\n",
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" ```python\n",
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" from sympy import cosh\n",
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" cosh(x)\n",
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" ```\n",
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" - `tanh(x)`: Tangens hyperbolicus\n",
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" ```python\n",
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||||||
" from sympy import tanh\n",
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||||||
" tanh(x)\n",
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" ```\n",
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"\n",
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"5. **Trigonometrische Inverse Funktionen**\n",
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" - `asin(x)`: Arkussinus (Inverser Sinus)\n",
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" ```python\n",
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||||||
" from sympy import asin\n",
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" asin(x)\n",
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" ```\n",
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" - `acos(x)`: Arkuskosinus (Inverser Kosinus)\n",
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" ```python\n",
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" from sympy import acos\n",
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" acos(x)\n",
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" ```\n",
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" - `atan(x)`: Arkustangens (Inverser Tangens)\n",
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" ```python\n",
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" from sympy import atan\n",
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" atan(x)\n",
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" ```\n",
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"\n",
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||||||
"---\n",
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"\n",
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"### **Algebraische Operationen**\n",
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"\n",
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"1. **Addition, Subtraktion, Multiplikation, Division**\n",
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"\n",
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" - `+`, `-`, `*`, `/`\n",
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" ```python\n",
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" x + y # Addition\n",
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" x - y # Subtraktion\n",
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" x * y # Multiplikation\n",
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" x / y # Division\n",
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" ```\n",
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"\n",
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"2. **Exponenten**\n",
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"\n",
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" - `**`: Potenz\n",
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" ```python\n",
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" x**2 # x hoch 2\n",
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" ```\n",
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"\n",
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"3. **Wurzeln**\n",
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" - `sqrt(x)`: Quadratwurzel\n",
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" ```python\n",
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" from sympy import sqrt\n",
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" sqrt(x)\n",
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" ```\n",
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"\n",
|
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||||||
"---\n",
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"\n",
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"### **Integral- und Ableitungsoperationen**\n",
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"\n",
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"1. **Ableitungen**\n",
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"\n",
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" - `diff(f, x)`: Erste Ableitung von `f` nach `x`\n",
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" ```python\n",
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" from sympy import diff\n",
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" diff(f, x)\n",
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" ```\n",
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"\n",
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"2. **Integrale**\n",
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" - `integrate(f, x)`: Unbestimmtes Integral von `f` nach `x`\n",
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" ```python\n",
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||||||
" from sympy import integrate\n",
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" integrate(f, x)\n",
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" ```\n",
|
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||||||
" - `integrate(f, (x, a, b))`: Bestimmtes Integral von `f` von `a` bis `b`\n",
|
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" ```python\n",
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" integrate(f, (x, 0, 1))\n",
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" ```\n",
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"\n",
|
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||||||
"---\n",
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||||||
"\n",
|
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"### **Summen, Produkte und Faktorisierung**\n",
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"\n",
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||||||
"1. **Summe**\n",
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"\n",
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" - `sum(iterable)`: Summe über eine Reihe oder Liste\n",
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" ```python\n",
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" from sympy import Sum, symbols\n",
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" n = symbols('n')\n",
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" Sum(n, (n, 1, 10))\n",
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|
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" ```\n",
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"\n",
|
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"2. **Produkt**\n",
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"\n",
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" - `product(iterable)`: Produkt über eine Reihe oder Liste\n",
|
|
||||||
" ```python\n",
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||||||
" from sympy import Product\n",
|
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||||||
" Product(n, (n, 1, 10))\n",
|
|
||||||
" ```\n",
|
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||||||
"\n",
|
|
||||||
"3. **Faktorisierung**\n",
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"\n",
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|
||||||
" - `factor(x)`: Faktorisieren eines Polynoms\n",
|
|
||||||
" ```python\n",
|
|
||||||
" from sympy import factor\n",
|
|
||||||
" factor(x**2 - 4)\n",
|
|
||||||
" ```\n",
|
|
||||||
"\n",
|
|
||||||
"4. **Entwicklung in Reihen**\n",
|
|
||||||
" - `series(f, x)`: Taylor-Reihe von `f` um `x`\n",
|
|
||||||
" ```python\n",
|
|
||||||
" from sympy import series\n",
|
|
||||||
" series(f, x)\n",
|
|
||||||
" ```\n",
|
|
||||||
"\n",
|
|
||||||
"---\n",
|
|
||||||
"\n",
|
|
||||||
"### **Matrixoperationen**\n",
|
|
||||||
"\n",
|
|
||||||
"1. **Matrix**\n",
|
|
||||||
"\n",
|
|
||||||
" - `Matrix([[1, 2], [3, 4]])`: Erstellen einer Matrix\n",
|
|
||||||
" ```python\n",
|
|
||||||
" from sympy import Matrix\n",
|
|
||||||
" A = Matrix([[1, 2], [3, 4]])\n",
|
|
||||||
" ```\n",
|
|
||||||
"\n",
|
|
||||||
"2. **Determinante**\n",
|
|
||||||
"\n",
|
|
||||||
" - `det(A)`: Determinante einer Matrix\n",
|
|
||||||
" ```python\n",
|
|
||||||
" A.det()\n",
|
|
||||||
" ```\n",
|
|
||||||
"\n",
|
|
||||||
"3. **Inverses einer Matrix**\n",
|
|
||||||
" - `inv(A)`: Inverse der Matrix `A`\n",
|
|
||||||
" ```python\n",
|
|
||||||
" A.inv()\n",
|
|
||||||
" ```\n",
|
|
||||||
"\n",
|
|
||||||
"---\n",
|
|
||||||
"\n",
|
|
||||||
"### **Grenzwerte und Limes**\n",
|
|
||||||
"\n",
|
|
||||||
"1. **Grenzwert (Limit)**\n",
|
|
||||||
"\n",
|
|
||||||
" - `limit(f, x, c)`: Grenzwert von `f` für `x → c`\n",
|
|
||||||
" ```python\n",
|
|
||||||
" from sympy import limit\n",
|
|
||||||
" limit(f, x, 0)\n",
|
|
||||||
" ```\n",
|
|
||||||
"\n",
|
|
||||||
"2. **Unendlicher Grenzwert**\n",
|
|
||||||
" - `limit(f, x, oo)`: Grenzwert für `x → ∞`\n",
|
|
||||||
" ```python\n",
|
|
||||||
" limit(f, x, float('inf'))\n",
|
|
||||||
" ```\n",
|
|
||||||
"\n",
|
|
||||||
"---\n",
|
|
||||||
"\n",
|
|
||||||
"### **Differentialgleichungen**\n",
|
|
||||||
"\n",
|
|
||||||
"1. **Lösen von Differentialgleichungen**\n",
|
|
||||||
" - `dsolve(eq, func)`: Lösen einer gewöhnlichen Differentialgleichung\n",
|
|
||||||
" ```python\n",
|
|
||||||
" from sympy import Function, dsolve, Derivative\n",
|
|
||||||
" f = Function('f')\n",
|
|
||||||
" dsolve(Derivative(f(x), x) - f(x), f(x))\n",
|
|
||||||
" ```\n",
|
|
||||||
"\n",
|
|
||||||
"---\n",
|
|
||||||
"\n",
|
|
||||||
"### **Sonstige nützliche Funktionen**\n",
|
|
||||||
"\n",
|
|
||||||
"1. **Ganze Zahlen (Modulararithmetik)**\n",
|
|
||||||
"\n",
|
|
||||||
" - `mod(x, y)`: Modulo-Operation\n",
|
|
||||||
" ```python\n",
|
|
||||||
" from sympy import mod\n",
|
|
||||||
" mod(x, y)\n",
|
|
||||||
" ```\n",
|
|
||||||
"\n",
|
|
||||||
"2. **Boden- und Deckenfunktion**\n",
|
|
||||||
" - `floor(x)`: Abrunden auf die nächste ganze Zahl\n",
|
|
||||||
" ```python\n",
|
|
||||||
" from sympy import floor\n",
|
|
||||||
" floor(x)\n",
|
|
||||||
" ```\n",
|
|
||||||
" - `ceiling(x)`: Aufrunden auf die nächste ganze Zahl\n",
|
|
||||||
" ```python\n",
|
|
||||||
" from sympy import ceiling\n",
|
|
||||||
" ceiling(x)\n",
|
|
||||||
" ```\n",
|
|
||||||
"\n",
|
|
||||||
"---\n",
|
|
||||||
"\n",
|
|
||||||
"### **Zusammenfassung der wichtigsten Funktionen**\n",
|
|
||||||
"\n",
|
|
||||||
"| **Funktion** | **SymPy-Befehl** | **Beschreibung** |\n",
|
|
||||||
"| --------------------------- | --------------------------------------------- | -------------------------------------- |\n",
|
|
||||||
"| Exponentiation | `exp(x)` | \\( e^x \\) |\n",
|
|
||||||
"| Trigonometrische Funktionen | `sin(x)`, `cos(x)`, `tan(x)` | Sinus, Kosinus, Tangens |\n",
|
|
||||||
"| Ableitung | `diff(f, x)` | Ableitung von `f` nach `x` |\n",
|
|
||||||
"| Integral | `integrate(f, x)` | Unbestimmtes Integral von `f` nach `x` |\n",
|
|
||||||
"| Summe | `Sum(expression, (variable, start, end))` | Summe über eine Reihe |\n",
|
|
||||||
"| Produkt | `Product(expression, (variable, start, end))` | Produkt über eine Reihe |\n",
|
|
||||||
"| Faktorisierung | `factor(f)` | Faktorisierung von `f` |\n",
|
|
||||||
"| Grenzwert | `limit(f, x, c)` | Grenzwert von `f` für `x → c` |\n",
|
|
||||||
"| Matrixoperationen | `Matrix([[1, 2], [3, 4]])` | Erstellen von Matrizen |\n",
|
|
||||||
"| Differentialgleichung lösen | `dsolve(eq, func)` | Lösen von Differentialgleichungen |\n",
|
|
||||||
"\n",
|
|
||||||
"---\n",
|
|
||||||
"\n",
|
|
||||||
"\n",
|
|
||||||
"<!--->siehe https://chatgpt.com/share/673b2049-b010-8013-a3d7-9552c03da480</--->\n"
|
|
||||||
]
|
|
||||||
}
|
|
||||||
],
|
|
||||||
"metadata": {
|
|
||||||
"language_info": {
|
|
||||||
"name": "python"
|
|
||||||
}
|
|
||||||
},
|
|
||||||
"nbformat": 4,
|
|
||||||
"nbformat_minor": 2
|
|
||||||
}
|
|
||||||
Binary file not shown.
|
|
@ -1,236 +0,0 @@
|
||||||
{
|
|
||||||
"cells": [
|
|
||||||
{
|
|
||||||
"cell_type": "code",
|
|
||||||
"execution_count": null,
|
|
||||||
"metadata": {},
|
|
||||||
"outputs": [],
|
|
||||||
"source": [
|
|
||||||
"import sympy"
|
|
||||||
]
|
|
||||||
},
|
|
||||||
{
|
|
||||||
"cell_type": "code",
|
|
||||||
"execution_count": 1,
|
|
||||||
"metadata": {},
|
|
||||||
"outputs": [
|
|
||||||
{
|
|
||||||
"data": {
|
|
||||||
"image/png": "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",
|
|
||||||
"text/plain": [
|
|
||||||
"<Figure size 640x480 with 1 Axes>"
|
|
||||||
]
|
|
||||||
},
|
|
||||||
"metadata": {},
|
|
||||||
"output_type": "display_data"
|
|
||||||
}
|
|
||||||
],
|
|
||||||
"source": [
|
|
||||||
"import matplotlib.pyplot as plt\n",
|
|
||||||
"from sympy import symbols, latex\n",
|
|
||||||
"\n",
|
|
||||||
"x = symbols('x')\n",
|
|
||||||
"expr = x**2 + 2*x + 1\n",
|
|
||||||
"\n",
|
|
||||||
"# LaTeX-String erstellen\n",
|
|
||||||
"latex_code = latex(expr)\n",
|
|
||||||
"\n",
|
|
||||||
"# Plot erstellen\n",
|
|
||||||
"plt.text(0.5, 0.5, f\"${latex_code}$\", fontsize=12, ha='center')\n",
|
|
||||||
"plt.axis('off')\n",
|
|
||||||
"plt.show()\n"
|
|
||||||
]
|
|
||||||
},
|
|
||||||
{
|
|
||||||
"cell_type": "code",
|
|
||||||
"execution_count": 2,
|
|
||||||
"metadata": {},
|
|
||||||
"outputs": [
|
|
||||||
{
|
|
||||||
"name": "stdout",
|
|
||||||
"output_type": "stream",
|
|
||||||
"text": [
|
|
||||||
"x^{2} + 2 x + 1\n"
|
|
||||||
]
|
|
||||||
}
|
|
||||||
],
|
|
||||||
"source": [
|
|
||||||
"from sympy import symbols, latex\n",
|
|
||||||
"\n",
|
|
||||||
"x = symbols('x')\n",
|
|
||||||
"expr = x**2 + 2*x + 1\n",
|
|
||||||
"\n",
|
|
||||||
"# LaTeX-String erzeugen\n",
|
|
||||||
"latex_code = latex(expr)\n",
|
|
||||||
"print(latex_code)\n"
|
|
||||||
]
|
|
||||||
},
|
|
||||||
{
|
|
||||||
"cell_type": "code",
|
|
||||||
"execution_count": 3,
|
|
||||||
"metadata": {},
|
|
||||||
"outputs": [
|
|
||||||
{
|
|
||||||
"name": "stdout",
|
|
||||||
"output_type": "stream",
|
|
||||||
"text": [
|
|
||||||
"3 x^{2} + 2\n",
|
|
||||||
"\\frac{x^{4}}{4} + x^{2} + x\n"
|
|
||||||
]
|
|
||||||
}
|
|
||||||
],
|
|
||||||
"source": [
|
|
||||||
"from sympy import diff, integrate, symbols, latex\n",
|
|
||||||
"\n",
|
|
||||||
"x = symbols('x')\n",
|
|
||||||
"f = x**3 + 2*x + 1\n",
|
|
||||||
"\n",
|
|
||||||
"# Ableitung\n",
|
|
||||||
"derivative = diff(f)\n",
|
|
||||||
"print(latex(derivative)) # Ausgabe: 3 x^{2} + 2\n",
|
|
||||||
"\n",
|
|
||||||
"# Integral\n",
|
|
||||||
"integral = integrate(f)\n",
|
|
||||||
"print(latex(integral)) # Ausgabe: \\frac{x^{4}}{4} + x^{2} + x\n"
|
|
||||||
]
|
|
||||||
},
|
|
||||||
{
|
|
||||||
"cell_type": "markdown",
|
|
||||||
"metadata": {},
|
|
||||||
"source": [
|
|
||||||
"$$\n",
|
|
||||||
"3 x^{2} + 2\n",
|
|
||||||
"\\frac{x^{4}}{4} + x^{2} + x\n",
|
|
||||||
"$$"
|
|
||||||
]
|
|
||||||
},
|
|
||||||
{
|
|
||||||
"cell_type": "code",
|
|
||||||
"execution_count": 4,
|
|
||||||
"metadata": {},
|
|
||||||
"outputs": [
|
|
||||||
{
|
|
||||||
"name": "stdout",
|
|
||||||
"output_type": "stream",
|
|
||||||
"text": [
|
|
||||||
"-2\n",
|
|
||||||
"2\n"
|
|
||||||
]
|
|
||||||
}
|
|
||||||
],
|
|
||||||
"source": [
|
|
||||||
"from sympy import solve\n",
|
|
||||||
"\n",
|
|
||||||
"eq = x**2 - 4\n",
|
|
||||||
"solution = solve(eq)\n",
|
|
||||||
"\n",
|
|
||||||
"# Lösungen anzeigen\n",
|
|
||||||
"for sol in solution:\n",
|
|
||||||
" print(latex(sol)) # Ausgabe: -2 und 2\n"
|
|
||||||
]
|
|
||||||
},
|
|
||||||
{
|
|
||||||
"cell_type": "code",
|
|
||||||
"execution_count": 5,
|
|
||||||
"metadata": {},
|
|
||||||
"outputs": [
|
|
||||||
{
|
|
||||||
"data": {
|
|
||||||
"image/png": "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",
|
|
||||||
"text/latex": [
|
|
||||||
"$\\displaystyle \\left[ -2, \\ 2\\right]$"
|
|
||||||
],
|
|
||||||
"text/plain": [
|
|
||||||
"[-2, 2]"
|
|
||||||
]
|
|
||||||
},
|
|
||||||
"metadata": {},
|
|
||||||
"output_type": "display_data"
|
|
||||||
}
|
|
||||||
],
|
|
||||||
"source": [
|
|
||||||
"from sympy import symbols, solve, init_printing\n",
|
|
||||||
"from IPython.display import display\n",
|
|
||||||
"\n",
|
|
||||||
"# SymPy-Darstellung aktivieren\n",
|
|
||||||
"init_printing()\n",
|
|
||||||
"\n",
|
|
||||||
"x = symbols('x')\n",
|
|
||||||
"eq = x**2 - 4\n",
|
|
||||||
"\n",
|
|
||||||
"# Gleichung lösen und anzeigen\n",
|
|
||||||
"solutions = solve(eq)\n",
|
|
||||||
"display(solutions)\n"
|
|
||||||
]
|
|
||||||
},
|
|
||||||
{
|
|
||||||
"cell_type": "code",
|
|
||||||
"execution_count": 7,
|
|
||||||
"metadata": {},
|
|
||||||
"outputs": [
|
|
||||||
{
|
|
||||||
"name": "stdout",
|
|
||||||
"output_type": "stream",
|
|
||||||
"text": [
|
|
||||||
"Ableitung von f(x) = exp(0.5*x):\n",
|
|
||||||
"0.5*exp(0.5*x)\n"
|
|
||||||
]
|
|
||||||
},
|
|
||||||
{
|
|
||||||
"data": {
|
|
||||||
"image/png": "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",
|
|
||||||
"text/latex": [
|
|
||||||
"$\\displaystyle 0.5 e^{0.5 x}$"
|
|
||||||
],
|
|
||||||
"text/plain": [
|
|
||||||
" 0.5⋅x\n",
|
|
||||||
"0.5⋅ℯ "
|
|
||||||
]
|
|
||||||
},
|
|
||||||
"metadata": {},
|
|
||||||
"output_type": "display_data"
|
|
||||||
}
|
|
||||||
],
|
|
||||||
"source": [
|
|
||||||
"from sympy import symbols, diff, exp, init_printing\n",
|
|
||||||
"from IPython.display import display\n",
|
|
||||||
"init_printing()\n",
|
|
||||||
"\n",
|
|
||||||
"# Symbol für die Variable x definieren\n",
|
|
||||||
"x = symbols('x')\n",
|
|
||||||
"\n",
|
|
||||||
"# Funktion definieren: f(x) = e^(0.5x)\n",
|
|
||||||
"f = exp(0.5 * x)\n",
|
|
||||||
"\n",
|
|
||||||
"# Ableitung berechnen\n",
|
|
||||||
"f_derivative = diff(f, x)\n",
|
|
||||||
"\n",
|
|
||||||
"# Ergebnis anzeigen\n",
|
|
||||||
"print(f\"Ableitung von f(x) = {f}:\")\n",
|
|
||||||
"print(f_derivative)\n",
|
|
||||||
"display(f_derivative)"
|
|
||||||
]
|
|
||||||
}
|
|
||||||
],
|
|
||||||
"metadata": {
|
|
||||||
"kernelspec": {
|
|
||||||
"display_name": "Python (Nix)",
|
|
||||||
"language": "python",
|
|
||||||
"name": "nix-python"
|
|
||||||
},
|
|
||||||
"language_info": {
|
|
||||||
"codemirror_mode": {
|
|
||||||
"name": "ipython",
|
|
||||||
"version": 3
|
|
||||||
},
|
|
||||||
"file_extension": ".py",
|
|
||||||
"mimetype": "text/x-python",
|
|
||||||
"name": "python",
|
|
||||||
"nbconvert_exporter": "python",
|
|
||||||
"pygments_lexer": "ipython3",
|
|
||||||
"version": "3.12.7"
|
|
||||||
}
|
|
||||||
},
|
|
||||||
"nbformat": 4,
|
|
||||||
"nbformat_minor": 2
|
|
||||||
}
|
|
||||||
24
shell.nix
24
shell.nix
|
|
@ -1,22 +1,12 @@
|
||||||
{ pkgs ? import <nixpkgs> {} }:
|
{ pkgs ? import <nixpkgs> {} }:
|
||||||
|
|
||||||
pkgs.mkShell {
|
pkgs.mkShell {
|
||||||
packages = with pkgs; [
|
packages = [
|
||||||
typst
|
pkgs.typst
|
||||||
typstyle
|
pkgs.typstyle
|
||||||
tinymist
|
pkgs.tinymist
|
||||||
tdf
|
pkgs.tdf
|
||||||
agebox
|
pkgs.agebox
|
||||||
mermaid-cli
|
pkgs.mermaid-cli
|
||||||
|
|
||||||
# for math
|
|
||||||
python312
|
|
||||||
python312Packages.sympy
|
|
||||||
python312Packages.numpy
|
|
||||||
python312Packages.matplotlib
|
|
||||||
python312Packages.scipy
|
|
||||||
python312Packages.pandas
|
|
||||||
python312Packages.jupyter
|
|
||||||
python312Packages.ipykernel
|
|
||||||
];
|
];
|
||||||
}
|
}
|
||||||
|
|
|
||||||
Loading…
Add table
Reference in a new issue