mirror of
https://github.com/vale981/TUD_MATH_BA
synced 2025-03-06 10:01:39 -05:00
568 lines
No EOL
16 KiB
TeX
568 lines
No EOL
16 KiB
TeX
\RequirePackage{ifluatex}
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\documentclass[ngerman,a4paper]{report}
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%\usepackage[top=2cm,bottom=2cm,left=1cm,right=1cm]{geometry}
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\usepackage[ngerman]{babel}
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%\usepackage[utf8]{inputenc} %not recommended with lualatex
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\usepackage{zref-base}
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\usepackage{etoolbox}
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\usepackage{xparse}%better macros
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\usepackage{chngcntr}
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\usepackage[T1]{fontenc}
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\ifluatex
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\usepackage{fontspec}
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\fi
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\usepackage[texindy]{imakeidx}
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\makeindex[name=semester1,title={Symbolverzeichnis (1. Semester)}]
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\makeindex[name=semester2,title={Symbolverzeichnis (2. Semester)}]
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\makeindex[name=symbols,title=Symbolverzeichnis]
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\usepackage[xindy,acronym]{glossaries}
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\makeglossaries
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\usepackage{amsmath}
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\usepackage{amssymb}
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\usepackage{amsfonts}
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\usepackage{latexsym}
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\usepackage{marvosym} %lighning
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\usepackage{bbm} %unitary matrix 1
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\usepackage{cancel}
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\usepackage{xfrac}%sfrac -> fractions e.g. 3/4
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\usepackage[table]{xcolor}
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\usepackage{graphicx}
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\usepackage{enumerate}
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\usepackage{enumitem} %customize label
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\usepackage{tabularx}
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\usepackage{multirow}
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\usepackage{booktabs}
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\usepackage{ulem} %better underlines
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\usepackage{parskip}%split paragraphs by vspace instead of intendations
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\usepackage{tocloft}
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\usepackage{fancyhdr}
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\usepackage{titlesec}%customize titles
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\usepackage{marginnote}
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\usepackage{tikz}
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\usetikzlibrary{patterns,arrows,calc,decorations.pathmorphing}
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\usepackage[amsthm,thmmarks,hyperref]{ntheorem}%customize theorem-environments more effectively
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\usepackage[ntheorem,framemethod=TikZ]{mdframed}
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\usepackage[bookmarks=true]{hyperref}
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\hypersetup{
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colorlinks,
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citecolor=green,
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filecolor=green,
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linkcolor=blue,
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urlcolor=green
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}
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\usepackage{cleveref}
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\usepackage{bookmark}
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\definecolor{lightgrey}{gray}{0.91}
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\definecolor{lightred}{rgb}{1,0.6,0.6}
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\definecolor{darkgrey}{gray}{0.6}
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\definecolor{darkgreen}{rgb}{0,0.6,0}
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\newlength{\blacktrianglewidth}
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\settowidth{\blacktrianglewidth}{$\blacktriangleright$}
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%numbered theorems
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\theoremstyle{break}
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\theorembodyfont{}
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\mdfdefinestyle{boxedtheorem}{%
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outerlinewidth=3pt,%
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skipabove=5pt,%
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skipbelow=10pt,%
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frametitlefont=\normalfont\bfseries\color{black},%
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}
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\newmdtheoremenv[%
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style=boxedtheorem,%
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innertopmargin=\topskip,%
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innerbottommargin=\topskip,%
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linecolor=darkgrey,%
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backgroundcolor=lightgrey,%
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]{theorem}{Theorem}[section]
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\newmdtheoremenv[%
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style=boxedtheorem,%
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linecolor=darkgrey,%
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topline=false,%
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rightline=false,%
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bottomline=false,%
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innertopmargin=\topskip,%
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innerbottommargin=\topskip,%
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backgroundcolor=lightgrey,%
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]{proposition}[theorem]{Satz}
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\newmdtheoremenv[%
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style=boxedtheorem,%
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linecolor=darkgrey,%
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topline=false,%
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rightline=false,%
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bottomline=false,%
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backgroundcolor=lightgrey,%
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innertopmargin=\topskip,%
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innerbottommargin=\topskip,%
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]{lemma}[theorem]{Lemma}
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\newmdtheoremenv[%
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style=boxedtheorem,%
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linecolor=red,%
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topline=false,%
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rightline=false,%
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bottomline=false,%
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innertopmargin=0,%
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innerbottommargin=-3pt,%
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]{definition}[theorem]{Definition}
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\newmdtheoremenv[%
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outerlinewidth=3pt,%
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linecolor=black,%
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topline=false,%
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rightline=false,%
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bottomline=false,%
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innertopmargin=0pt,%
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innerbottommargin=-3pt,%
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frametitlefont=\normalfont\bfseries\color{black},%
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skipabove=5pt,%
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skipbelow=10pt,%
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]{conclusion}[theorem]{Folgerung}
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\newmdtheoremenv[%
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hidealllines=true,%
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frametitlefont=\normalfont\bfseries\color{black},%
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innerleftmargin=0pt,%
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skipabove=5pt,%
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innerleftmargin=10pt,%
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]{remark}[theorem]{\hspace*{-10pt}$\blacktriangleright$\hspace*{\dimexpr \mdflength{innerleftmargin} - \blacktrianglewidth\relax}Bemerkung}
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\newmdtheoremenv[%
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hidealllines=true,%
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frametitlefont=\normalfont\bfseries\color{black},%
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innerleftmargin=10pt,%
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]{example}[theorem]{\hspace*{-\mdflength{innerleftmargin}}\rule{5pt}{5pt}\hspace*{5pt}Beispiel}
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%unnumbered theorems
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\theoremstyle{nonumberbreak}
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\theoremindent0cm
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\newmdtheoremenv[%
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style=boxedtheorem,%
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linecolor=red,%
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topline=false,%
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rightline=false,%
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bottomline=false,%
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innertopmargin=0,%
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innerbottommargin=-3pt,%
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]{*definition}{Definition}
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\newmdtheoremenv[%
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hidealllines=true,%
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frametitlefont=\normalfont\bfseries\color{black},%
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innerleftmargin=0pt,%
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skipabove=5pt,%
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innerleftmargin=10pt,%
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]{*remark}{\hspace*{-10pt}$\blacktriangleright$\hspace*{\dimexpr \mdflength{innerleftmargin} - \blacktrianglewidth\relax}Bemerkung}
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\newmdtheoremenv[%
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hidealllines=true,%
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innerleftmargin=10pt,%
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]{*example}{\hspace*{-\mdflength{innerleftmargin}}\rule{5pt}{5pt}\hspace*{5pt}Beispiel}
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%Hinweis-Theoremstyle and environment
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%To get rid of the parentheses, a new theorem style is neccessary (definition of nonumberbreak from ntheorem.sty)
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%to achieve the underlining, this needed to put in the theoremstyle definition
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\theoremheaderfont{\mdseries}
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\theoremseparator{:}
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\theorempostskip{0pt}
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\makeatletter
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\newtheoremstyle{noparentheses}%
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{\item[\rlap{\vbox{\hbox{\hskip\labelsep \theorem@headerfont
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\uline{##1}\theorem@separator}\hbox{\strut}}}]}%
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{\item[\rlap{\vbox{\hbox{\hskip\labelsep \theorem@headerfont
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\uline{##1\ ##3\theorem@separator}}\hbox{\strut}}}]}
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\newtheoremstyle{underlinedPlain}%
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{\item[\hskip\labelsep \underline{\theorem@headerfont ##1\theorem@separator}]}%
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{\item[\hskip\labelsep \underline{\theorem@headerfont ##1\ (##3)\theorem@separator}]}
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\makeatother
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\theoremstyle{noparentheses}
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\newmdtheoremenv[%
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hidealllines=true,%
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innerleftmargin=1em,%
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]{interpretation}{\hspace*{\dimexpr - \mdflength{innerleftmargin}\relax}Interpretation}
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\theoremstyle{underlinedPlain}
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\newmdtheoremenv[%
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hidealllines=true,%
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innerleftmargin=1em,%
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innerrightmargin=0,%
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skipbelow=0pt,%
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]{hint}{\hspace*{\dimexpr - \mdflength{innerleftmargin}\relax}Hinweis}
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\theoremheaderfont{\normalfont}
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\theorembodyfont{\itshape\small}
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\theoremseparator{:}
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\theoremsymbol{$\blacksquare$}
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\renewtheorem{proof}{Beweis}
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%for \cref: printed environment names
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\crefname{theorem}{Theorem}{Theoreme}
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\crefname{proposition}{Satz}{Sätze}
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\crefname{lemma}{Lemma}{Lemmata}
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\crefname{conclusion}{Folgerung}{Folgerungen}
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\crefname{definition}{Definition}{Definitionen}
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\crefname{remark}{Bemerkung}{Bemerkungen}
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\crefname{example}{Beispiel}{Beispiele}
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\crefname{*definition}{Definition}{Definitionen}
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\crefname{*remark}{Bemerkung}{Bemerkungen}
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\crefname{*example}{Beispiel}{Beispiele}
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\makeatletter
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\newcommand*{\rom}[1]{\expandafter\@slowromancap\romannumeral #1@}
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\newcommand*{\proplbl}[1]{%
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\@bsphack
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\begingroup
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\label{#1}%
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\zref@setcurrent{default}{\arabic{chapter}}%
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\zref@wrapper@immediate{%
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\zref@labelbyprops{#1@chapter}{default}
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}
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\endgroup
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\@esphack
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}
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\newcommand*{\propref}[1]{%
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\zref@refused{#1@chapter}%
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\ifnumcomp{\value{chapter}}{=}{\zref@extractdefault{#1@chapter}{default}{1}}%
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{%same chapter
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\mbox{\cref{#1}}%
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}%
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{%otherwise
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\ifcsdef{r@#1}%in first compilation the label may not be defined yet
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{%
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\def\propositionref@current@type{}%
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\cref@gettype{#1}{\propositionref@current@type}%get the environment's name
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%example for following line:
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%\crefformat{truetheorem}{\cref@truetheorem@name~##2\rom{\zref@extractdefault{#1}{#1chapter}{1}}.##1##3}
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%this changes the format used by \cref to <environtment name> <chapter-number>.<section-number>.<theorem number>
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\crefformat{\propositionref@current@type}{%
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\csname cref@\propositionref@current@type @name\endcsname ~##2\rom{\zref@extractdefault{#1@chapter}{default}{1}}.##1##3%
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}%
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\mbox{\cref{#1}}%mbox neccessary due to cleveref <-> ulem
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\crefformat{\propositionref@current@type}{%
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\csname cref@\propositionref@current@type @name\endcsname~##2##1##3%
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}%
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}%
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{??}%similar to \ref\cref: question marks in case of undefined labels
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}%
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}
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\makeatother
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\NewDocumentCommand{\begriff}{s O{} m O{}}{%
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\IfBooleanTF{#1}%
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{\index{#2#3#4}}%
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{%
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\uline{#3}%
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\ifnumcomp{\value{chapter}}{<}{16}%
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{\index[semester1]{#2#3#4}}%
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{\index[semester2]{#2#3#4}}%
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}%
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}
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\NewDocumentCommand{\mathsymbol}{s O{} m m O{}}{%
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\IfBooleanTF{#1}%
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{\index[symbols]{#2#3@\detokenize{#4}#5}}%
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{#4\index[symbols]{#2#3@\detokenize{#4}#5}}%
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}
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\NewDocumentCommand{\zeroAmsmathAlignVSpaces}{s s O{0 pt} O{0 pt}}{%
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\IfBooleanTF{#1}%
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{%
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\IfBooleanTF{#2}%
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{\setlength{\belowdisplayskip}{#4}}%
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{\setlength{\abovedisplayskip}{#3}}%
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}%
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{%
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\setlength{\abovedisplayskip}{#3}%
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\setlength{\belowdisplayskip}{#4}%
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}%
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}
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\NewDocumentCommand{\itemEq}{s m}{%
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\begingroup%
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\setlength{\abovedisplayskip}{\dimexpr -\parskip + 1pt\relax}%
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\setlength{\belowdisplayskip}{0pt}%
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\IfBooleanTF{#1}%
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{\parbox[c]{\linewidth}{\begin{flalign*}#2&&\end{flalign*}}}%
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{\parbox[c]{\linewidth}{\begin{flalign}#2&&\end{flalign}}}%
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\endgroup%
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}
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\newcommand{\person}[1]{\textsc{#1}}
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\newcommand{\highlight}[1]{\emph{#1}}
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\newcommand{\realz}{\mathfrak{Re}}
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\newcommand{\imagz}{\mathfrak{Im}}
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\renewcommand{\epsilon}{\varepsilon}
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%change headings:
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\titlelabel{\thetitle.\quad}%. behind section/sub... (3. instead of 3)
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\counterwithout{section}{chapter}
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\renewcommand{\thechapter}{\Roman{chapter}}
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%italic chapters (due to titlesec package some more stuff)
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\titleformat{\chapter}[display]{\huge\bfseries\itshape}{\chaptername\;\thechapter:}{-5pt}{\huge\bfseries}
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\titlespacing{\chapter}{0pt}{0pt}{10pt}
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\titleformat{\section}[hang]{\bfseries\Large}{\thesection.}{8pt}{\Large\bfseries}
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%change header:
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\renewcommand{\headrulewidth}{0.75pt}
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\renewcommand{\footrulewidth}{0.3pt}
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\lhead{\rightmark}%left: section-number. section-title
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\rhead{\leftmark}%right: chapter chapternumber: chapter-title
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%change appearence of heading of toc: 0 space above, bold, italic huge toc-heading
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\renewcommand{\cftbeforetoctitleskip}{0pt}
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\renewcommand{\cfttoctitlefont}{\itshape\Huge\bfseries}
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\pagestyle{fancy}
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\pagenumbering{arabic}
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%remember chapter-title in \leftmark and \rightmark
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\renewcommand{\chaptermark}[1]{%
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\markboth{\chaptername
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\ \thechapter:\ #1}{}}
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%remember section title in \leftmark, overwrites chapter-title there
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\renewcommand{\sectionmark}[1]{%
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\markright{\thesection.\ #1}{}}
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%change numbering of equations to be section by section
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\counterwithout{equation}{section}
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\author{Dozent: Prof. F. Schuricht}
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\title{Analysis Grundlagen 1 \& 2} % add WS & SS
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\date{Updated: \today}
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\begin{document}
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\pagenumbering{roman}
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\pagestyle{plain}
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\maketitle
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\tableofcontents
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\pagebreak
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\pagestyle{fancy}
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\pagenumbering{arabic}
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%remember chapter-title in \leftmark and \rightmark
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%\renewcommand{\chaptermark}[1]{%
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% \markboth{\chaptername
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% \ \thechapter:\ #1}{}}
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%remember section title in \leftmark
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%\renewcommand{\sectionmark}[1]{%
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% \markright{\thesection.\ #1}{}}
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\chapter{Funktionen und Stetigkeit}
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\section{Anwendungen}
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\begin{theorem}[Mit Titel]
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test
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\end{theorem}
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\begin{proposition}[Incl. Titel]
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Und Inhalt.
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\end{proposition}
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\begin{interpretation}[von Gleichung (1)]
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Und hier der spannende Text...
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\end{interpretation}
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\subsection{Partialbruchzerlegung}
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\begin{theorem}[Mit Titel]
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\proplbl{eintheorem}
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test
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\end{theorem}
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\begin{proposition}[Incl. Titel]
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Und Inhalt.\propref{eintheorem}
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\end{proposition}
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\section{Noch mehr Anwendungen}
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\begin{definition}[Und Name]
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Tada
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\end{definition}
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\begin{example}[Einschließlich Überschrift]
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Verständnisfördernd...
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\end{example}
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\begin{conclusion}[Ergänzung]
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Einfache Schlussfolgerung
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\end{conclusion}
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\begin{lemma}
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nur Müll
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\end{lemma}
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\begin{lemma}[Kurze, aber wichtige, Aussage]
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Klein aber fein.
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\end{lemma}
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\begin{remark}[Hossa]
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Dumdidum
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\end{remark}
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\begin{example}[Test]
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LOhne Nummer
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\end{example}
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\begin{proof}[\cref{einzweitestheorem}]
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Ein Beweis unter Ausnutzung von \propref{einzweitestheorem}
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\begin{align}
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f = f(x) \text{ (mit Formelnnummer)}
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\end{align}
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und inline-math $\hbar$.
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\end{proof}
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\chapter{Its you}
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\section{Or me?}
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\begin{theorem}[Mit Titel]
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\proplbl{einzweitestheorem}
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test
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\end{theorem}
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\begin{proposition}[Incl. Titel]
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Und Inhalt.
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\end{proposition}
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\begin{definition}[Und Name]
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Tada
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\end{definition}
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\begin{example}[Einschließlich Überschrift]
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Verständnisfördernd...
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\end{example}
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\begin{conclusion}[Ergänzung]
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Einfache Schlussfolgerung
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\end{conclusion}
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\begin{lemma}[Kurze Aussage]
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Klein aber fein.
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\end{lemma}
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\begin{remark}[Hossa]
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Dumdidum
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\end{remark}
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\begin{*example}[Test]
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Ohne Nummer
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\end{*example}
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\begin{proof}[]
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Ein Beweis. Siehe auch \propref{eintheorem} und \propref{einzweitestheorem}.
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\begin{align}
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f = f(x) \text{ (mit Formelnnummer)}
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\end{align}
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und inline-math $\hbar$.
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\begin{itemize}
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\item \itemEq{f(x) = m\cdot x + n}
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Eine Formel auf Höhe des Itemize-Punktes \emph{mit} Numerierung (\verb|\itemEq*{\dotsc}| ohne Nummerierung)
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\end{itemize}
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Eventuell ist es mal praktisch, \zeroAmsmathAlignVSpaces \begin{align*}
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f(x) = m\cdot x + n
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\end{align*}
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\verb|align| ohne Abstände einzubauen. Das geht auch einseitig mit \verb|\zeroAmsmathAlignVSpaces*| (nur oben Ändern) bzw. \verb|\zeroAmsmathAlignVSpaces**| (nur unten ändern).\marginnote{Hinweis am Rand!}
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\end{proof}
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\begin{*definition}[Aber Name]
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Ohne Nummer
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\end{*definition}
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\begin{*remark}
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Bemerkung sowieso
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\end{*remark}
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\renewcommand*\textcircled[1]{\tikz[baseline=(char.base)]{
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\node [shape=circle,draw,inner sep=1pt] (char) {#1};}}
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\begin{tikzpicture}
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% variables for pn-junction diagram:
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% all parameters are in tikz scale
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% p-side of the junction is here on the right
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\def\V{1.5} % junction polarisation (0=flat band)
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\def\EG{3} % band gap of semiconductor
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\def\EF{1.5} % vertical Fermi level position
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\def\EFn{3.3} % pseudo fermi level for electrons
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\def\EFp{1.8} % pseudo fermi level for holes
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\def\DZCE{4} % start position on the left for space charge region (SCR)
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\def\LZCE{2} % SCR width
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\def\PN{10} % total lentgh of the junction
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% calculations
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\pgfmathsetmacro\EC{\EG+\V};% conduction band heigth (without polarisation)
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\pgfmathsetmacro\FZCE{\DZCE+\LZCE};% SCR end position
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% valence and conduction band drawing:
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\draw (0,0) node [left]{$E_V$} -- (\DZCE,0)
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to[out=0, in=180, looseness=0.75] (\FZCE,\V) -- (\PN,\V); % EV
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\draw (0,\EG) node [left] {$E_C$} -- (\DZCE,\EG)
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to[out=0, in=180, looseness=0.75] (\FZCE,\EC) -- (\PN,\EC); % EC
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% fermi level drawing (if needed):
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% \draw [dashed](0,\EF) -- ({\PN-0.5},\EF) node [right]{$E_F$}; % EF
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% quasi fermi levels drawing (if needed) :
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\draw [dashed] (0,\EFn) -- (\PN,\EFn)
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node [right] {$E_{Fn}$}; % EFn for electron
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\draw [dashed] (0,\EFp) -- ({\PN},\EFp)
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node [right] {$E_{Fp}$}; % EFp for holes
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% electric field in SCR drawing :
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\draw [->] (\DZCE, {\V+\EG+1}) --
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node [above] {$\vec{E}_{ZCE}$} (\FZCE, {\V+\EG+1}) ; % E vector
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% excess carriers
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\foreach \x in {1,2,...,7}
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\draw ({\FZCE+1+\x/3},{\EC+0.2}) node {$\bullet$}; % p side : electrons
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\foreach \x in {1,2,...,7}
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\draw ({1+\x/3},{-0.2}) node {$\circ$}; % n side : holes
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% photon injection and carrier generation
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% p side : carrier generation:
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\draw [->, loosely dashed] ({\FZCE+3}, \V) --
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node [right] {\textcircled{1}}({\FZCE+3}, \EC);
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% the textcircled{number} option is used in several places
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% to describe the physical mechanisms.
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% It can be safely removed if not needed
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% photon wave injection in the bandgap on p-side :
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\draw [decorate, decoration={snake}, ->] ({\PN+1},{\EC+1}) --
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node [below,sloped]{$h\nu$} ({\FZCE+3}, \EG);
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% excess carriers diffusion, with diffusion length :
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% electrons on p side :
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\draw [->] ({\FZCE+1},{\EC+0.2}) -- node [above] {$L_{Dn}$}
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node [below=6pt] {\textcircled{2}}({\FZCE},{\EC+0.2})
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node [left] {$\bullet$} ;
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\draw [->] ({\FZCE-0.3},{\EC+0.2}) to [out=200, in=0, looseness=0.75]
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node [above left] {\textcircled{3}} ({\DZCE},{\EG+0.2})
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node [left] {$\bullet$} node [above left=3pt] {\textcircled{4}};
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% holes on n side :
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\draw [->] ({1.2+7/3},{-0.2}) -- node [below] {$L_{Dp}$} ({\DZCE},{-0.2})
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node [right]{$\circ$} ;
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\draw [->] ({\DZCE+0.3},-0.2) to [out=20, in=180, looseness=0.75]
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({\FZCE},{\V-0.2}) node [right]{$\circ$};
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\end{tikzpicture}
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\theoremlisttype{allname}
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\listtheorems{theorem}
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\end{document} |