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Diffstat (limited to 'exams/mathe2/hauptklausur/definitions.tex')
| -rw-r--r-- | exams/mathe2/hauptklausur/definitions.tex | 152 |
1 files changed, 152 insertions, 0 deletions
diff --git a/exams/mathe2/hauptklausur/definitions.tex b/exams/mathe2/hauptklausur/definitions.tex new file mode 100644 index 0000000..1f9cca4 --- /dev/null +++ b/exams/mathe2/hauptklausur/definitions.tex @@ -0,0 +1,152 @@ +%%%% START OF PREAMBLE +% Copyright (c) 2021 Frederik, Franz, Marvin +% Copyright (c) 2022 Linus, Benny, Marvin +\usepackage[a4paper, inner=1cm, outer=1cm, top=2cm, bottom=2cm, bindingoffset=0cm]{geometry} +\usepackage{amsmath,amsthm,amssymb,amsfonts} +\usepackage{mathrsfs} +\usepackage{braket} +\usepackage{enumitem} +\usepackage{csquotes} +\usepackage{colortbl} +\usepackage{environ} +\usepackage{graphicx,tikz,xcolor,color,float,titlesec} +\usepackage{pgfplots} +\usepackage{fancyhdr} +\usepackage{gauss} +\usepackage{polynom} +\usepackage{bm} +\usepackage[ngerman=ngerman-x-latest]{hyphsubst} +\usepackage[ngerman]{babel} +\usetikzlibrary{matrix,shapes,trees} +\usepgfplotslibrary{fillbetween} +\pgfplotsset{compat=1.18} +\setlength\parindent{0pt} +\definecolor{ochsblau}{RGB}{26,122,219} +\definecolor{ochsgelb}{RGB}{245,209,168} +\definecolor{ochsorange}{RGB}{243,92,43} +\renewcommand{\headrulewidth}{2pt} +\let\oldheadrule\headrule +\renewcommand{\headrule}{\color{ochsgelb}\oldheadrule} +\newcommand\bracketify[1]{\lbrack#1\rbrack} +\titleformat{\section}{\normalfont\large\bfseries\color{ochsblau}}{Aufgabe \thesection.\ }{0em}{\bracketify} +%%%% END OF PREAMBLE + +%\usepackage{background} +%\backgroundsetup{ +% position=current page.east, +% angle=-90, +% nodeanchor=east, +% vshift=-5mm, +% hshift=1cm, +% opacity=1, +% scale=3, +% contents=Entwurf +%} + +\newcommand\namesnstuff{ + \pagestyle{fancy} + \fancyhf{} + \fancyhead[L,LO]{\textcolor{ochsblau}{\textbf{Name:}}} + \fancyhead[C,CO]{\textcolor{ochsblau}{\textbf{MFI2 - SS22}}} + \fancyhead[R,RO]{\textcolor{ochsblau}{\textbf{Hauptklausur}}} + \fancyfoot[C,CO]{\thepage} + \setlength{\headheight}{13.6pt} + + \vspace{-2.0cm} + \noindent\includegraphics[width=0.2\textwidth]{../ochs_logo.png} + \begin{minipage}[b]{0.6\textwidth} + \centering + \textcolor{ochsblau}{\textbf{\Large Mathematik 2 für Informatik}}\\ + \vspace{3mm} + Peter Ochs, Tobias Nordgauer\\ + \vspace{3mm} + Sommersemester 2022 + \end{minipage} + \noindent\includegraphics[width=0.2\textwidth]{../uni_logo.png}\\ + \begin{center}\textcolor{ochsblau}{\textbf{Hauptklausur Gedächtnisprotokoll}}\end{center} +} + +\newcommand\refiff[1]{\stackrel{\text{#1}}{\iff}} +\newcommand\refimp[1]{\stackrel{\text{#1}}{\implies}} +\newcommand\refeq[1]{\stackrel{\text{#1}}{=}} +\newcommand\refless[1]{\stackrel{\text{#1}}{<}} +\newcommand\refleads[1]{\stackrel{\text{#1}}{\leadsto}} + +\newcommand\NR{\textbf{Nebenrechnung: }} +\newcommand\proposition{\textbf{Behauptung: }} +\newcommand\toprove{\textbf{Zu zeigen: }} +\newcommand\task{\textbf{Aufgabe: }} +\newcommand\defi{\textbf{Definition: }} + +% denglish ftw +\newcommand\da{\text{ da }} +\newcommand\with{\text{ mit }} +\newcommand\und{\text{ und }} +\newcommand\oder{\text{ oder }} +\newcommand\for{\text{ für }} +\newcommand\when{\text{ wenn }} +\newcommand\sei{\text{ sei }} + +\newcommand\Real{\mathrm{Re}} % Realteil +\newcommand\Imag{\mathrm{Im}} % Imaginärteil + +\newcommand\N{\mathbb{N}} +\newcommand\R{\mathbb{R}} +\newcommand\Z{\mathbb{Z}} +\newcommand\C{\mathbb{C}} +\newcommand\Q{\mathbb{Q}} +\renewcommand\P{\mathbb{P}} +\renewcommand\O{\mathcal{O}} +\newcommand\pot{\mathcal{P}} + +\newcommand\rank{\mathrm{rank}} +\newcommand\lin{\mathrm{Lin}} +\renewcommand\det{\mathrm{det}} +\renewcommand\dim{\mathrm{dim}} + +\renewcommand\u{\boldsymbol{u}} +\renewcommand\v{\boldsymbol{v}} +\newcommand\w{\boldsymbol{w}} + +% for vertical line in gmatrix +\usepackage{etoolbox} +\makeatletter +\patchcmd\g@matrix + {\vbox\bgroup} + {\vbox\bgroup\normalbaselines} + {}{} +\makeatother +\newcommand{\gvline}{% + \hspace{-\arraycolsep}% + \strut\vrule + \hspace{-\arraycolsep}% +} + +% lol +\makeatletter +\renewenvironment{proof}[1][\proofname] {\par\pushQED{\qed}\normalfont\topsep6\p@\@plus6\p@\relax\trivlist\item[\hskip\labelsep\bfseries#1\@addpunct{.}]\ignorespaces}{\popQED\endtrivlist\@endpefalse} +\makeatother +\def\qedsymbol{\sc q.e.d.} % hmm? + +\newenvironment{induktion}{\renewcommand*{\proofname}{Beweis durch vollständige Induktion}\begin{proof}$ $\newline}{\end{proof}} +\newcommand\IA[1]{\textbf{Induktionsanfang ($#1$):}} +\newcommand\IV[1]{\textbf{Induktionsvoraussetzung:} Die Behauptung gelte für ein beliebiges aber festes $#1$.\\} +\newcommand\IS[1]{\textbf{Induktionsschritt ($#1$):}} + +\newenvironment{gegenbeweis}{\renewcommand*{\proofname}{Beweis durch Gegenbeweis}\begin{proof}}{\end{proof}} +\newenvironment{gegenbeispiel}{\renewcommand*{\proofname}{Beweis durch Gegenbeispiel}\begin{proof}}{\end{proof}} + +\NewEnviron{splitty}{\begin{displaymath}\begin{split}\BODY\end{split}\end{displaymath}} +\newcolumntype{C}{>{$}c<{$}} % math-mode column + +\DeclareMathOperator{\ggT}{ggT} + +\newlist{abc}{enumerate}{10} +\setlist[abc]{label=(\alph*)} + +\newlist{num}{enumerate}{10} +\setlist[num]{label=\arabic*.} + +\newlist{rom}{enumerate}{10} +\setlist[rom]{label=(\roman*)} + |