lab test

.gitignore

+_build/
+.ipynb_checkpoints
+*/.ipynb_checkpoints/*

.gitlab-ci.yml

+image: python:latest
+
+# variables:
+#   PIP_CACHE_DIR: "$CI_PROJECT_DIR/.cache/pip"
+
+# cache:
+#   paths:
+#     - .cache/pip
+#     - venv/
+
+# before_script:
+#   - python -V
+# lav venv miljø med venv, ikke virtualenv
+#  - pip install virtualenv
+#  - virtualenv venv
+#  - source venv/bin/activate
+
+pages:
+  script:
+    - pip install -r requirements.txt
+    - jupyter-book build pg_cs
+    - mv pg_cs/_build/html/ public/
+  artifacts:
+    paths:
+      - public
+    expire_in: 4 weeks
+  only:
+    - main

LICENSE

+MIT License
+
+Copyright (c) 2023, Michael Clasen Linderoth
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.

README.md

-init
+# How to create your own Course Site
\ No newline at end of file
+
+This repository is a template for creating your own Course Site, which if you wish, can be embedded into DTU Learn or any other web service, more or less.
+
+To get started it is useful to learn about the very few files and folders included in this template.
+
+## Files and folders 
+
+What files are supported
+
+reference bib file
+
+Table of content: https://jupyterbook.org/customize/toc.html
+
+Draft
+
+Changing folders and structure
+
+## Great, now what? Building the book/website
+
+As currently configured, you basically only have to alter or add files and "commit" these changes. When doing so, the site will build and update itself, within a few minutes.
+
+
+### Building the book
+
+#### Advanced use
+
+You know to create a basic website, then please proceed to dive into the full Jupyter Book documentation, for more advanced use cases: [Jupyter Book Documentation](https://jupyterbook.org/en/stable/intro.html)
+
+#### Credits
+
+This project is created using the excellent open source [Jupyter Book project](https://jupyterbook.org/) in combination with several other open source projects.
+
+

pg_cs/_config.yml

+#######################################################################################
+# A default configuration that will be loaded for all jupyter books
+# See the documentation for help and more options: 
+# https://jupyterbook.org/customize/config.html
+
+#######################################################################################
+# Book settings
+title                       : PG Course site  # The title of the book. Will be placed in the left navbar.
+author                      : DTU Compute  # The author of the book
+copyright                   : "2023"  # Copyright year to be placed in the footer
+logo                        : logo.png  # A path to the book logo
+
+# Only build table of content _toc.yml files
+only_build_toc_files: true
+
+# Information about where the book exists on the web
+repository:
+  url: https://github.com/mclacompute/pgcoursesite  # Online location of your book
+  path_to_book: /pg_cs  # Optional path to your book, relative to the repository root
+  branch: main # Which branch of the repository should be used when creating links (optional)
+
+# Add GitHub buttons to your book
+# See https://jupyterbook.org/customize/config.html#add-a-link-to-your-repository
+html:
+  use_issues_button: true
+  use_repository_button: true
+
+launch_buttons:
+  notebook_interface: "classic" # or  "jupyterlab"
+  # binderhub_url: "https://mybinder.org"
+  colab_url: "https://colab.research.google.com"
+  # thebe                  : true # husk jupyterlite
+
+parse:
+  myst_enable_extensions:
+    - amsmath
+    - colon_fence
+    # - deflist
+    - dollarmath
+    # - html_admonition
+    # - html_image
+    - linkify
+    # - replacements
+    # - smartquotes
+    - substitution
+    - tasklist
+  myst_url_schemes: [mailto, http, https] # URI schemes that will be recognised as external URLs in Markdown links
+  myst_dmath_double_inline: true  # Allow display math ($$) within an inline context
+
+# Force re-execution of notebooks on each build.
+# See https://jupyterbook.org/content/execute.html
+# execute:
+#   execute_notebooks: force
+
+# Add a bibtex file so that we can create citations
+bibtex_bibfiles:
+  - references.bib
+
+# Define the name of the latex output file for PDF builds
+# latex:
+#   latex_documents:
+#     targetname: book.tex

pg_cs/_toc.yml

+# Table of contents
+# Learn more at https://jupyterbook.org/customize/toc.html
+
+format: jb-book
+root: intro
+parts:
+- caption: 
+  chapters:
+  - file: democontent/demopage
+    sections:
+    - file: democontent/notebooks
+    - file: democontent/Intro-SymPy
+#  - file: democontent/...
+- caption: 
+  chapters:
+  - file: weeks/weeklyplan
+    sections:
+    - file: weeks/week1
+    - file: weeks/week2
+    - file: weeks/week3
+    - file: weeks/week4
+#      sections:
+#      - file: longday
+#        sections:
+#        - file: exl1
+#        - file: exl2
+#      - file: shortday
+#        sections:
+#        - file: exs1
+#        - file: exs2
+- caption:  
+  chapters:
+  - file: enotes/enotes
+

pg_cs/democontent/Demo-E-Uge-12-StoreDag.ipynb

+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Differentialligningssystemer\n",
+    "Demo af Christian Mikkelstrup og Hans Henrik Hermansen"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from sympy import *\n",
+    "init_printing(use_latex='mathjax')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Homogene systemer af første ordens lineære diff-ligninger\n",
+    "\n",
+    "## 1. Systemmatricen har to reelle egenværdier\n",
+    "Givet differentialligningsystemet\n",
+    "\n",
+    "\\begin{gather*}\n",
+    "    \\frac{\\text{d}}{\\text{d}t}x_1(t) = 5x_1(t) - 3x_2(t)\\\\\n",
+    "    \\frac{\\text{d}}{\\text{d}t}x_2(t) = 6x_1(t) - 4x_2(t)\n",
+    "\\end{gather*}"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### a. Simuleret håndregning via diagonaliseringsmetoden\n",
+    "Først løser vi systemet i hånden vha. diagonaliseringsmetoden, dvs. vi opstiller og analyserer systemmatricen"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "t,C1,C2 = symbols(\"t C1:3\")\n",
+    "A = Matrix([[5,-3],[6,-4]])\n",
+    "ev = A.eigenvects()\n",
+    "res = C1 * E ** (ev[0][0]*t) * ev[0][2][0] + C2 * E ** (ev[1][0]*t) * ev[1][2][0]\n",
+    "res"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### b. via dsolve\n",
+    "Vi kan også finde løsningen direkte med dsolve"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x1 = Function(\"x1\")\n",
+    "x2 = Function(\"x2\")\n",
+    "eq1 = Eq(diff(x1(t),t),5 * x1(t) - 3 * x2(t))\n",
+    "eq2 = Eq(diff(x2(t),t),6*x1(t) - 4*x2(t))\n",
+    "\n",
+    "dsolve([eq1, eq2])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 2. Systemmatricen har to komplekse egenværdier\n",
+    "Givet differentialligningssystemet\n",
+    "\\begin{gather*}\n",
+    "    \\frac{\\text{d}}{\\text{d}t}x_1(t) = 2x_1(t) + 2x_2(t)\\\\\n",
+    "    \\frac{\\text{d}}{\\text{d}t}x_2(t) = -x_1(t) + 4x_2(t)\n",
+    "\\end{gather*}"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## a. Simuleret håndregning\n",
+    "Fremgangsmåden her er den samme."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "A = Matrix([[2,2],[-1,4]])\n",
+    "ev = A.eigenvects()\n",
+    "res = C1 * E ** (ev[0][0]*t) * ev[0][2][0] + C2 * E ** (ev[1][0]*t) * ev[1][2][0]\n",
+    "res"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Nu finder vi også den fuldstændige reelle løsning vha. metode 17.5"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "a = re(ev[0][0])\n",
+    "b = im(ev[0][0])\n",
+    "re_ev = re(ev[0][2][0])\n",
+    "im_ev = im(ev[0][2][0])\n",
+    "u1 = E ** (a * t) * (cos(b * t) * re_ev - sin(b * t) * im_ev)\n",
+    "u2 = E ** (a * t) * (sin(b * t) * re_ev + cos(b * t) * im_ev)\n",
+    "C1 * u1 + C2 * u2"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### b. Med dsovle"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "eq1 = Eq(diff(x1(t),t),2*x1(t) + 2*x2(t))\n",
+    "eq2 = Eq(diff(x2(t),t),-x1(t) + 4*x2(t))\n",
+    "\n",
+    "dsolve([eq1, eq2])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Selvom løsningerne ser lidt forskellige ud, så er de lig hinanden."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 3. Betinget løsning med plot\n",
+    "Lad os se på systemet fra eksempel 1 igen.\n",
+    "\\begin{gather*}\n",
+    "    \\frac{\\text{d}}{\\text{d}t}x_1(t) = 5x_1(t) - 3x_2(t)\\\\\n",
+    "    \\frac{\\text{d}}{\\text{d}t}x_2(t) = 6x_2(t) - 4x_2(t)\n",
+    "\\end{gather*}\n",
+    "\n",
+    "Vi kom frem til den fuldstændige løsning\n",
+    "\\begin{gather*}\n",
+    "    \\begin{bmatrix} x_1(t) \\\\ x_2(t) \\end{bmatrix} = C_1 e^{-t} \\begin{bmatrix}1 \\\\ 2\\end{bmatrix} + C_2 e^{2t} \\begin{bmatrix} 1 \\\\ 1 \\end{bmatrix}\n",
+    "\\end{gather*}\n",
+    "\n",
+    "Lad os finde et $C_1$ og $C_2$, der medfører at $x_1(0) = 2$ og $x_2(0) = 3$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### a. Simuleret håndregning\n",
+    "Først finder vi lige løsningen igen"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "t,C1,C2 = symbols(\"t C1:3\")\n",
+    "A = Matrix([[5,-3],[6,-4]])\n",
+    "ev = A.eigenvects()\n",
+    "fuld = C1 * E ** (ev[0][0]*t) * ev[0][2][0] + C2 * E ** (ev[1][0]*t) * ev[1][2][0]\n",
+    "x1_fuld, x2_fuld = fuld[0],fuld[1]\n",
+    "x1_fuld, x2_fuld"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Nu kan løse for $c_1$ og $c_2$\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "solve([Eq(x1_fuld.subs(t,0),2),Eq(x2_fuld.subs(t,0),3)])\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Vi kunne også gøre dette med $\\text{dsolve}$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "eq1 = Eq(diff(x1(t),t),5 * x1(t) - 3 * x2(t))\n",
+    "eq2 = Eq(diff(x2(t),t),2*x1(t) - 4*x2(t))\n",
+    "\n",
+    "dsolve([eq1, eq2],ics={x1(0) : 2, x2(0) : 3})"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Nu, hvor vi har fundet $c_1$ og $c_2$, kan vi plotte vores løsning."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "plot(x1_fuld.subs([(C1,2),(C2,1)]),x2_fuld.subs([(C1,2),(C2,1)]),xlim=(-1,1),ylim=(0,8),legend=True)"
+   ]
+  }
+ ],
+ "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": "3.9.16"
+  },
+  "vscode": {
+   "interpreter": {
+    "hash": "e7370f93d1d0cde622a1f8e1c04877d8463912d04d973331ad4851f04de6915a"
+   }
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

pg_cs/democontent/Demo-F-Uge-1-StoreDag2.ipynb

+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Partielle afledede, Gradienter, Retningsafledede\n",
+    "\n",
+    "Demo af Christian Mikkelstrup og Hans Henrik Hermansen"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from sympy import *\n",
+    "from dtumathtools import *\n",
+    "from IPython import get_ipython\n",
+    "%matplotlib widget\n",
+    "init_printing()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Velkommen tilbage efter jul og januar, og velkommen til foråret i mat1. Der kommer til at være en helt masse nyt pensum, og blandt andet en helt masse 3D-plots! Til dette har vi udviklet ``dtumathtools``, som vil følge jer i løbet af foråret. Den indeholder ``dtuplot`` som skal bruges til at plotte, samt flere gode hjælpefunktioner. Det kan hentes fra terminalen, hvor man så skal skrive ``pip install dtumathtools`` (tilsvarende med ``pip3``). Det tager op til ~5 minutter før den er helt færdig og tillader dig igen at skrive i terminalen. Efter dette kan resten af demoen nydes."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Partielt afledte ved brug af ``diff``\n",
+    "\n",
+    "I dag introducerer vi partielle afledte, samt hvordan vi kan benytte dem. For at vise hvordan man kan få de partielt afledte, kan vi kigge på funktionen"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x, y = symbols('x y')\n",
+    "f = x*y**2+x\n",
+    "f"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "og finde de afledte med kommandoen som vi også brugte sidste semester"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "f.diff(x), f.diff(y)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "På samme måde kan man finde de afledte *af anden orden*"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "f.diff(x,2), f.diff(y,2), f.diff(x,y), f.diff(y,x)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Vi kan så indsætte værdier i denne, for eksempel $\\frac{\\partial}{\\partial x}f(x,y)$ taget i $(-2,3)$ ved"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "f.diff(x).subs({x:-2,y:3})"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Eller $\\frac{\\partial}{\\partial x\\partial y}f(x,y)$, taget i $(5,-13)$ ved"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "f.diff(x,y).subs({x:5,y:-13})"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Grafer og niveaukurver\n",
+    "\n",
+    "Vi skal nu, for første gang til at plotte funktioner af flere variable, og altså i 3D! Her er et valg man skal tage, for man har nemlig mulighed for at rotere et plot rundt, så man kan se det fra flere vinkler. \n",
+    "\n",
+    "Hvis man ikke gør noget aktivt (eller hvis man bruger kommandoen ``%matplotlib inline``), kommer plots som I er vant til fra efteråret (som også kommer med hvis man eksporterer til pdf),"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "f = 4-x**2-y**2\n",
+    "\n",
+    "p=dtuplot.plot3d(f, (x,-3,3),(y,-3,3))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Ovenstående kommando laver plottet som en **statisk** PNG-fil, hvilket er smart hvis man skal printe Notebook'en eller eksportere til PDF. Hvis man i stedet kører ``%matplotlib qt`` (i den følgende blok udkommenteret, men prøv at fjerne udkommenteringen \\#), aktiverer man **interaktive** plots. Alle efterfølgende plots \"popper\" nu ud af VS Code, hvorefter man man rotere plottet rundt og se det fra flere vinkler! Prøv derefter at plotte 3D plottet igen!"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    " # %matplotlib widget"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Om interaktive plots"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Bemærk: `%matplotlib qt` virker normalt kun hvis man kører fx VS Code på egen laptop. Hvis man fx kører Python på en online server i browseren som Google Colab, vil `%matplotlib qt` ikke virke. Her kan man prøve widgets i stedet for: `%matplotlib ipympl`. Det kører at man lige installerer pakken `ipympl`. Samlet oversigt:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Fjern udkommentering for den backend der ønskes brugt\n",
+    "# %matplotlib inline        # statisk plots\n",
+    "# %matplotlib qt            # QT (cute) interaktivt pop-ud plots\n",
+    "# %matplotlib ipympl        # Widget/ipynpl interaktivt inline plots (ikke så stabil som QT og kan kræve restart af kernel)\n",
+    "# %matplotlib --list        # liste over alle backends  "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Vi kan også plotte højdelinjer, altså et 2D plot over en 3D struktur ved:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "dtuplot.plot_contour(f, (x,-3,3),(y,-3,3), is_filled=False)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Og hvis vi vil bestemme hvilke højder der vises, kan vi bruge,"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "zvals = [-2,-1,0,1]\n",
+    "dtuplot.plot_contour(f, (x,-3,3),(y,-3,3), rendering_kw={\"levels\":zvals, \"alpha\":0.5}, is_filled=False)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "I ovenstående plot er der brugt ``rendering_kw={....}`` som argument, og det kan se lidt underligt ud. Dette er blot hvilke æstetiske (rendering) indstillinger der skal bruges, eksempelvis ``color``, ``alpha``, osv. Man kan også i det fleste tilfælde \"bare\" skrive ``{....}``, og så ved den godt at det er det æstetiske, men det er mere tydeligt at skrive det med.\n",
+    "\n",
+    "Her er samme plot vist, nu med højder som farver, i 3D,"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "p=dtuplot.plot3d(f, (x,-3,3),(y,-3,3), use_cm=True, legend=True)\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Gradientvektorfelter\n",
+    "\n",
+    "Vi kigger nu på vektorfeltet \n",
+    "\n",
+    "\\begin{equation}\n",
+    "f(x,y)=\\cos(x)+\\sin(y).\n",
+    "\\end{equation}\n",
+    "\n",
+    "Gradienten for $f$ taget i punktet $(x,y)$ er en vektor, som har symbolet $\\nabla f(x,y)$ ($\\nabla$ kaldes *nabla*). Den er sammensat af de to partielt afledte,\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "f = cos(x)+sin(y)\n",
+    "nf = Matrix([f.diff(x), f.diff(y)])\n",
+    "nf"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Som let plottes ved,"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "dtuplot.plot_vector(nf, (x,-pi/2,3/2*pi),(y,0,2*pi),scalar=False)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Eller hvis det skal være lidt flottere (her er ``rendering_kw`` splittet, så man kan specificere for pile og contours seperat),"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "dtuplot.plot_vector(nf, (x,-pi/2,3/2*pi),(y,0,2*pi),\n",
+    "    quiver_kw={\"color\":\"black\"},\n",
+    "    contour_kw={\"cmap\": \"Blues_r\", \"levels\": 20},\n",
+    "    grid=False, xlabel=\"x\", ylabel=\"y\",n=15)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Som i 3D visualiseres ved"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# \"camera\" Juster hvorfra man skal se på grafen\n",
+    "# meget brugbart, hvis man vil have bestemt\n",
+    "# rotation med i pdf-filen\n",
+    "p = dtuplot.plot3d(f, (x,-pi/2,3/2*pi),(y,0,2*pi),use_cm=True, camera={\"elev\":45, \"azim\":-65}, legend=True)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Retningsafledt af funktion af to variable\n",
+    "\n",
+    "Vi betragter funktionen"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "f = 1-x**2/2-y**2/2\n",
+    "f"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Vi ønsker nu den retningsafledte af $f$ fra punktet $(1,-1)$ i retningen givet ved enhedsvektoren,"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x0 = Matrix([1,-1])\n",
+    "e = Matrix([-1,-2]).normalized()\n",
+    "e, N(e)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "p1 = dtuplot.scatter(x0, rendering_kw={\"markersize\":10,\"color\":'r'}, xlim=[-2,2],ylim=[-2,2],show=False)\n",
+    "p1.extend(dtuplot.quiver(x0,e,show=False))\n",
+    "p1.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Vi får gradienten i punktet $x_0$ ved"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "Nabla = Matrix([diff(f,x),diff(f,y)]).subs({x:x0[0],y:x0[1]})\n",
+    "Nabla"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Hvorefter den retningsafledte, $f'((1,-1), e)$, findes ved"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "a = e.dot(Nabla)\n",
+    "a"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Dette viser, at *f aftager* fra punktet $(1,-1)$ i retningen $e$. Dette er fordi den retningsafledte angiver raten, hvormed $f$ aftager."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Parameterkurve i (x,y)-planen og dens tangenter\n",
+    "\n",
+    "Vi betragter spiralen, givet ved parameterfremstillingen,"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "u, t = symbols('u t', real=True)\n",
+    "r = Matrix([u*cos(u), u*sin(u)])\n",
+    "r"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Tangentvektoren i et vilkårligt punkt fåes nu til"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "rd = diff(r,u)\n",
+    "rd"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Vi finder nu en parameterfremstilling for tangenten til spiralen i røringspunktet $((0,-\\frac{3\\pi}{2}))$, svarende til parameterværdien $u_0=\\frac{3\\pi}{2}$, som ses ved,"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "u0 = 3*pi/2\n",
+    "rdu0 = rd.subs(u,u0)\n",
+    "ru0 = r.subs(u,u0)\n",
+    "ru0"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Parameterfremstillingen for tangenten i $u_0$ findes ved"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "T = ru0 + t*rdu0\n",
+    "T"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Det hele kan nu visualiseres ved"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "p = dtuplot.plot_parametric(r[0], r[1],(u,0,4*pi),rendering_kw={\"color\":\"red\"},use_cm=False,show=False)\n",
+    "p.extend(dtuplot.plot_parametric(T[0],T[1],(t,-1.5,1.5),rendering_kw={\"color\":\"royalblue\"},use_cm=False,show=False))\n",
+    "p.extend(dtuplot.scatter(ru0,rendering_kw={\"markersize\":10,\"color\":'black'}, show=False))\n",
+    "p.extend(dtuplot.quiver(ru0,rdu0,rendering_kw={\"color\":\"black\"},show=False))\n",
+    "\n",
+    "p.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "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": "3.9.16"
+  },
+  "vscode": {
+   "interpreter": {
+    "hash": "949777d72b0d2535278d3dc13498b2535136f6dfe0678499012e853ee9abcab1"
+   }
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

pg_cs/democontent/demopage.md

+# PG demo Content
+
+## Question 1
+  
+````{card}
+A smooth function $f$ of one variable fulfills that $\,f(2)=1\,$ and $\,f'(2)=1\,.$ Its approximating second-degree polynomial with development point $\,x_0=2\,$ fulfills $\,P_2(1)=1\,.$ Determine $\,P_2(x)\,$.
+
+````
+  
+```{admonition} Hint for question
+:class: dropdown
+In this exercise we are testing in particular the following differentiation rules:
+
+- The product rule used when differentiating the product of two functions.
+- The chain rule used when differentiating a composite function ("a function within a function").
+
+\begin{gather*}
+a_1=b_1+c_1\\
+a_2=b_2+c_2-d_2+e_2
+\end{gather*}
+
+```
+
+```{admonition} Answer
+:class: tip, dropdown
+
+$$
+  \int_0^\infty \frac{x^3}{e^x-1}\,dx = \frac{\pi^4}{15}
+$$
+
+```
+
+We will compute the volume of the parallelepiped that is spanned by three geometric vectors in a standard coordinate system in 3D space
+
+:::{important}
+Remember to readTheorem 10.54 in eNote 10.
+:::
+
+## Question 2
+  
+````{card}
+A smooth function $f$ of one variable fulfills that $\,f(2)=1\,$ and $\,f'(2)=1\,.$ Its approximating second-degree polynomial with development point $\,x_0=2\,$ fulfills $\,P_2(1)=1\,.$ Determine $\,P_2(x)\,$.
+
+````
+
+```{admonition} Hint for question
+:class: dropdown
+In this exercise we are testing in particular the following differentiation rules:
+
+- The product rule used when differentiating the product of two functions.
+- The chain rule used when differentiating a composite function ("a function within a function").
+
+\begin{gather*}
+a_1=b_1+c_1\\
+a_2=b_2+c_2-d_2+e_2
+\end{gather*}
+
+```
+
+```{admonition} Answer
+:class: tip, dropdown
+
+$$
+  \int_0^\infty \frac{x^3}{e^x-1}\,dx = \frac{\pi^4}{15}
+$$
+
+```

pg_cs/democontent/markdown-notebooks.md

+---
+jupytext:
+  cell_metadata_filter: -all
+  formats: md:myst
+  text_representation:
+    extension: .md
+    format_name: myst
+    format_version: 0.13
+    jupytext_version: 1.11.5
+kernelspec:
+  display_name: Python 3
+  language: python
+  name: python3
+---
+
+# Notebooks with MyST Markdown
+
+Jupyter Book also lets you write text-based notebooks using MyST Markdown.
+See [the Notebooks with MyST Markdown documentation](https://jupyterbook.org/file-types/myst-notebooks.html) for more detailed instructions.
+This page shows off a notebook written in MyST Markdown.
+
+## An example cell
+
+With MyST Markdown, you can define code cells with a directive like so:
+
+```{code-cell}
+print(2 + 2)
+```
+
+```{code-cell}
+import numpy as np
+import matplotlib.pyplot as plt
+plt.ion()
+
+data = np.random.randn(2, 100)
+fig, ax = plt.subplots()
+ax.scatter(*data, c=data[1], s=100*np.abs(data[0]));
+```
+
+When your book is built, the contents of any `{code-cell}` blocks will be
+executed with your default Jupyter kernel, and their outputs will be displayed
+in-line with the rest of your content.
+
+```{seealso}
+Jupyter Book uses [Jupytext](https://jupytext.readthedocs.io/en/latest/) to convert text-based files to notebooks, and can support [many other text-based notebook files](https://jupyterbook.org/file-types/jupytext.html).
+```
+
+## Create a notebook with MyST Markdown
+
+MyST Markdown notebooks are defined by two things:
+
+1. YAML metadata that is needed to understand if / how it should convert text files to notebooks (including information about the kernel needed).
+   See the YAML at the top of this page for example.
+2. The presence of `{code-cell}` directives, which will be executed with your book.
+
+That's all that is needed to get started!
+
+## Quickly add YAML metadata for MyST Notebooks
+
+If you have a markdown file and you'd like to quickly add YAML metadata to it, so that Jupyter Book will treat it as a MyST Markdown Notebook, run the following command:
+
+```
+jupyter-book myst init path/to/markdownfile.md
+```

pg_cs/democontent/markdown.md

+# Markdown Files
+
+Whether you write your book's content in Jupyter Notebooks (`.ipynb`) or
+in regular markdown files (`.md`), you'll write in the same flavor of markdown
+called **MyST Markdown**.
+This is a simple file to help you get started and show off some syntax.
+
+## What is MyST?
+
+MyST stands for "Markedly Structured Text". It
+is a slight variation on a flavor of markdown called "CommonMark" markdown,
+with small syntax extensions to allow you to write **roles** and **directives**
+in the Sphinx ecosystem.

pg_cs/democontent/math.ipynb

+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "bc47e68d",
+   "metadata": {},
+   "source": [
+    "(myst-content/math)=\n",
+    "# Math and equations\n",
+    "\n",
+    "Jupyter Book uses [MathJax](http://docs.mathjax.org/) for typesetting math in your HTML book build.\n",
+    "This allows you to have LaTeX-style mathematics in your online content.\n",
+    "This page shows you a few ways to control this.\n",
+    "\n",
+    ":::{seealso}\n",
+    "For more information about equation numbering,\n",
+    "see the [MathJax equation numbering documentation](http://docs.mathjax.org/en/v2.7-latest/tex.html#automatic-equation-numbering).\n",
+    ":::\n",
+    "\n",
+    ":::{tip}\n",
+    "\n",
+    "By default MathJax version 2 is currently used.\n",
+    "If you are using a lot of math, you may want to try using version 3, which claims to improve load speeds by 60 - 80%:\n",
+    "\n",
+    "```yaml\n",
+    "sphinx:\n",
+    "  config:\n",
+    "    mathjax_path: https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js\n",
+    "```\n",
+    "\n",
+    "See the [Sphinx documentation](sphinx:sphinx.ext.mathjax) for details.\n",
+    "\n",
+    ":::\n",
+    "\n",
+    "## In-line math\n",
+    "\n",
+    "To insert in-line math use the `$` symbol within a Markdown cell.\n",
+    "For example, the text `$this_{is}^{inline}$` will produce: $this_{is}^{inline}$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fb8cd4ec",
+   "metadata": {},
+   "source": [
+    "## Math blocks\n",
+    "\n",
+    "You can also include math blocks for separate equations. This allows you to focus attention\n",
+    "on more complex or longer equations, as well as link to them in your pages. To use a block\n",
+    "equation, wrap the equation in either `$$` or `\\begin` statements.\n",
+    "\n",
+    "For example,\n",
+    "\n",
+    "```latex\n",
+    "$$\n",
+    "  \\int_0^\\infty \\frac{x^3}{e^x-1}\\,dx = \\frac{\\pi^4}{15}\n",
+    "$$\n",
+    "```\n",
+    "\n",
+    "results in:\n",
+    "\n",
+    "$$\n",
+    "  \\int_0^\\infty \\frac{x^3}{e^x-1}\\,dx = \\frac{\\pi^4}{15}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a8f88cc6",
+   "metadata": {},
+   "source": [
+    "(math:latex)=\n",
+    "### Latex-style math\n",
+    "\n",
+    "You can enable parsing LaTeX-style math blocks with the `amsmath` MyST extension. Enable it by adding the following to `_config.yml`\n",
+    "\n",
+    "```yaml\n",
+    "parse:\n",
+    "  myst_enable_extensions:\n",
+    "    # don't forget to list any other extensions you want enabled,\n",
+    "    # including those that are enabled by default!\n",
+    "    - amsmath\n",
+    "```\n",
+    "\n",
+    "Once enabled, you can define math blocks like so:\n",
+    "\n",
+    "```latex\n",
+    "\\begin{gather*}\n",
+    "a_1=b_1+c_1\\\\\n",
+    "a_2=b_2+c_2-d_2+e_2\n",
+    "\\end{gather*}\n",
+    "\n",
+    "\\begin{align}\n",
+    "a_{11}& =b_{11}&\n",
+    "  a_{12}& =b_{12}\\\\\n",
+    "a_{21}& =b_{21}&\n",
+    "  a_{22}& =b_{22}+c_{22}\n",
+    "\\end{align}\n",
+    "```\n",
+    "\n",
+    "which results in:\n",
+    "\n",
+    "\\begin{gather*}\n",
+    "a_1=b_1+c_1\\\\\n",
+    "a_2=b_2+c_2-d_2+e_2\n",
+    "\\end{gather*}\n",
+    "\n",
+    "\\begin{align}\n",
+    "a_{11}& =b_{11}&\n",
+    "  a_{12}& =b_{12}\\\\\n",
+    "a_{21}& =b_{21}&\n",
+    "  a_{22}& =b_{22}+c_{22}\n",
+    "\\end{align}\n",
+    "\n",
+    ":::{seealso}\n",
+    "The MyST guides to [dollar math syntax](myst-parser:syntax/math), [LaTeX math syntax](myst-parser:syntax/amsmath), and [how MyST-Parser works with MathJax](myst-parser:syntax/mathjax).\n",
+    "\n",
+    "For advanced use, also see how to [define MathJax TeX Macros](sphinx/tex-macros).\n",
+    ":::"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b2e67170",
+   "metadata": {},
+   "source": [
+    "### Numbering equations\n",
+    "\n",
+    "If you'd like to number equations so that you can refer to them later, use the **math directive**.\n",
+    "It looks like this:\n",
+    "\n",
+    "````md\n",
+    "```{math}\n",
+    ":label: my_label\n",
+    "my_math\n",
+    "```\n",
+    "````\n",
+    "\n",
+    "For example, the following code:\n",
+    "\n",
+    "````md\n",
+    "```{math}\n",
+    ":label: my_label\n",
+    "w_{t+1} = (1 + r_{t+1}) s(w_t) + y_{t+1}\n",
+    "```\n",
+    "````\n",
+    "\n",
+    "will generate\n",
+    "\n",
+    "```{math}\n",
+    ":label: my_label\n",
+    "w_{t+1} = (1 + r_{t+1}) s(w_t) + y_{t+1}\n",
+    "```\n",
+    "\n",
+    "Alternatively you can use the dollar math syntax with a prefixed label:\n",
+    "\n",
+    "```md\n",
+    "$$\n",
+    "  w_{t+1} = (1 + r_{t+1}) s(w_t) + y_{t+1}\n",
+    "$$ (my_other_label)\n",
+    "```\n",
+    "\n",
+    "which generates\n",
+    "\n",
+    "$$\n",
+    "  w_{t+1} = (1 + r_{t+1}) s(w_t) + y_{t+1}\n",
+    "$$ (my_other_label)\n",
+    "\n",
+    ":::{note}\n",
+    "Labels cannot start with an integer, or they won't be able to be referenced and\n",
+    "will throw a warning message if referenced. For example, `:label: 1` and `:label: 1eq` cannot\n",
+    "be referenced.\n",
+    ":::\n",
+    "\n",
+    "### Linking to equations\n",
+    "\n",
+    "If you have created an equation with a label, you can link to it from within your text\n",
+    "(and across pages!).\n",
+    "\n",
+    "You can refer to the equation using the label that you've provided by using\n",
+    "the `{eq}` role. For example:\n",
+    "\n",
+    "```md\n",
+    "- A link to an equation directive: {eq}`my_label`\n",
+    "- A link to a dollar math block: {eq}`my_other_label`\n",
+    "```\n",
+    "\n",
+    "results in\n",
+    "\n",
+    "- A link to an equation directive: {eq}`my_label`\n",
+    "- A link to a dollar math block: {eq}`my_other_label`\n",
+    "\n",
+    ":::{note}\n",
+    "`\\labels` inside LaTeX environment are not currently identified, and so cannot be referenced.\n",
+    "We hope to implement this in a future update (see [executablebooks/MyST-Parser#202](https://github.com/executablebooks/MyST-Parser/issues/202))!\n",
+    ":::"
+   ]
+  }
+ ],
+ "metadata": {
+  "jupytext": {
+   "text_representation": {
+    "extension": ".md",
+    "format_name": "myst"
+   }
+  },
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.8.15"
+  },
+  "source_map": [
+   10,
+   44,
+   66,
+   117
+  ]
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
\ No newline at end of file

pg_cs/democontent/test.ipynb

+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "6e94e772",
+   "metadata": {},
+   "source": [
+    "# Min overskrift"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a32ec2c9",
+   "metadata": {},
+   "source": [
+    "\\begin{gather*}\n",
+    "    \\frac{\\text{d}}{\\text{d}t}x_1(t) = 5x_1(t) - 3x_2(t)\\\\\n",
+    "    \\frac{\\text{d}}{\\text{d}t}x_2(t) = 6x_1(t) - 4x_2(t)\n",
+    "\\end{gather*}"
+   ]
+  }
+ ],
+ "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": "3.9.16"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}

pg_cs/drafts/exl1.md

+# exl1
+

pg_cs/drafts/exl2.md

+# exl2
+

pg_cs/drafts/exs1.md

+# exs1
+

pg_cs/drafts/exs2.md

+# exs2
+