mirror of
https://github.com/vale981/TUD_MATH_BA
synced 2025-03-06 10:01:39 -05:00
669 lines
No EOL
19 KiB
TeX
669 lines
No EOL
19 KiB
TeX
\RequirePackage{ifluatex,ifpdf}
|
|
\documentclass[ngerman,a4paper]{report}
|
|
\usepackage[left=2.1cm,right=3.1cm,bottom=3cm]{geometry}
|
|
\usepackage[ngerman]{babel}
|
|
\ifpdf
|
|
\usepackage[utf8]{inputenc} %not recommended with lualatex
|
|
\fi
|
|
|
|
\usepackage{zref-base}
|
|
\usepackage{etoolbox}
|
|
\usepackage{xparse}%better macros
|
|
\usepackage{chngcntr}
|
|
\usepackage{calc}
|
|
|
|
\usepackage{scalerel,stackengine}
|
|
|
|
\usepackage[T1]{fontenc}
|
|
\ifluatex
|
|
\usepackage{fontspec}
|
|
\fi
|
|
|
|
\usepackage[texindy]{imakeidx}
|
|
\indexsetup{
|
|
level=\chapter*
|
|
}
|
|
\makeindex
|
|
\makeindex[name=semester1,title={Symbolverzeichnis (1. Semester)}]
|
|
\makeindex[name=semester2,title={Symbolverzeichnis (2. Semester)}]
|
|
\makeindex[name=symbols,title=Symbolverzeichnis]
|
|
|
|
\usepackage[xindy,acronym]{glossaries}
|
|
\makeglossaries
|
|
|
|
\usepackage[title,titletoc]{appendix}
|
|
|
|
\usepackage{amsmath}
|
|
\usepackage{amssymb}
|
|
\usepackage{amsfonts}
|
|
\usepackage{mathtools}
|
|
\usepackage{latexsym}
|
|
\usepackage{marvosym} %lighning
|
|
\usepackage{bbm} %unitary matrix 1
|
|
\usepackage{cancel}
|
|
\usepackage{xfrac}%sfrac -> fractions e.g. 3/4
|
|
|
|
\usepackage[table]{xcolor}
|
|
\usepackage{graphicx}
|
|
\usepackage{pgfplots}
|
|
\pgfplotsset{compat=1.10}
|
|
\usepgfplotslibrary{fillbetween}
|
|
\usepackage{pgf}
|
|
\usepackage{tikz}
|
|
\usetikzlibrary{patterns,arrows,calc,decorations.pathmorphing}
|
|
\usetikzlibrary{matrix}
|
|
\usepackage{color}
|
|
\usepackage{wasysym}
|
|
|
|
\usepackage{enumerate}
|
|
\usepackage{enumitem} %customize label
|
|
\usepackage{stmaryrd} % Lightning symbol
|
|
|
|
\usepackage{tabularx}
|
|
\usepackage{multirow}
|
|
\usepackage{booktabs}
|
|
|
|
\usepackage{ulem} %better underlines
|
|
|
|
\usepackage{parskip}%split paragraphs by vspace instead of intendations
|
|
\usepackage{tocloft}
|
|
\usepackage{fancyhdr}
|
|
\usepackage{titlesec}%customize titles
|
|
\usepackage{marginnote}
|
|
|
|
\usepackage[amsmath,amsthm,thmmarks,hyperref]{ntheorem}%customize theorem-environments more effectively
|
|
\usepackage[ntheorem,framemethod=TikZ]{mdframed}
|
|
|
|
\usepackage[unicode,bookmarks=true]{hyperref}
|
|
\hypersetup{
|
|
colorlinks,
|
|
citecolor=green,
|
|
filecolor=green,
|
|
linkcolor=blue,
|
|
urlcolor=green
|
|
}
|
|
\usepackage{cleveref}
|
|
\usepackage{bookmark}
|
|
|
|
\newcommand{\coloredRule}[3][black]{\textcolor{#1}{\rule{#2}{#3}}}
|
|
\newlength{\blacktrianglewidth}
|
|
\settowidth{\blacktrianglewidth}{$\blacktriangleright$}
|
|
|
|
\definecolor{lightgrey}{gray}{0.91}
|
|
\definecolor{lightred}{rgb}{1,0.6,0.6}
|
|
\definecolor{darkgrey}{gray}{0.6}
|
|
\definecolor{darkgreen}{rgb}{0,0.6,0}
|
|
|
|
%numbered theorems
|
|
\theoremstyle{break}
|
|
\theorembodyfont{}
|
|
|
|
\mdfdefinestyle{boxedtheorem}{%
|
|
outerlinewidth=3pt,%
|
|
skipabove=5pt,%
|
|
skipbelow=10pt,%
|
|
frametitlefont=\normalfont\bfseries\color{black},%
|
|
}
|
|
|
|
\newmdtheoremenv[%
|
|
style=boxedtheorem,%
|
|
innertopmargin=\topskip,%
|
|
innerbottommargin=\topskip,%
|
|
linecolor=darkgrey,%
|
|
backgroundcolor=lightgrey,%
|
|
]{theorem}{Theorem}[section]
|
|
|
|
\newmdtheoremenv[%
|
|
style=boxedtheorem,%
|
|
linecolor=darkgrey,%
|
|
topline=false,%
|
|
rightline=false,%
|
|
bottomline=false,%
|
|
innertopmargin=\topskip,%
|
|
innerbottommargin=\topskip,%
|
|
backgroundcolor=lightgrey,%
|
|
]{proposition}[theorem]{Satz}
|
|
|
|
\newmdtheoremenv[%
|
|
style=boxedtheorem,%
|
|
linecolor=darkgrey,%
|
|
topline=false,%
|
|
rightline=false,%
|
|
bottomline=false,%
|
|
backgroundcolor=lightgrey,%
|
|
innertopmargin=\topskip,%
|
|
innerbottommargin=\topskip,%
|
|
]{lemma}[theorem]{Lemma}
|
|
|
|
\newmdtheoremenv[%
|
|
style=boxedtheorem,%
|
|
linecolor=red,%
|
|
topline=false,%
|
|
rightline=false,%
|
|
bottomline=false,%
|
|
innertopmargin=0,%
|
|
innerbottommargin=-3pt,%
|
|
]{definition}[theorem]{Definition}
|
|
|
|
\newmdtheoremenv[%
|
|
outerlinewidth=3pt,%
|
|
linecolor=black,%
|
|
topline=false,%
|
|
rightline=false,%
|
|
bottomline=false,%
|
|
innertopmargin=0pt,%
|
|
innerbottommargin=-0pt,%
|
|
frametitlefont=\normalfont\bfseries\color{black},%
|
|
skipabove=5pt,%
|
|
skipbelow=10pt,%
|
|
]{conclusion}[theorem]{Folgerung}
|
|
|
|
\newmdtheoremenv[%
|
|
hidealllines=true,%
|
|
frametitlefont=\normalfont\bfseries\color{black},%
|
|
innerleftmargin=0pt,%
|
|
skipabove=5pt,%
|
|
innerleftmargin=10pt,%
|
|
]{remark}[theorem]{\hspace*{-10pt}$\blacktriangleright$\hspace*{\dimexpr 10pt - \blacktrianglewidth\relax}Bemerkung}
|
|
|
|
\newmdtheoremenv[%
|
|
hidealllines=true,%
|
|
frametitlefont=\normalfont\bfseries\color{black},%
|
|
innerleftmargin=10pt,%
|
|
]{example}[theorem]{\hspace*{-10pt}\rule{5pt}{5pt}\hspace*{5pt}Beispiel}
|
|
|
|
%unnumbered theorems
|
|
\theoremstyle{nonumberbreak}
|
|
\theoremindent0cm
|
|
\newmdtheoremenv[%
|
|
style=boxedtheorem,%
|
|
linecolor=red,%
|
|
topline=false,%
|
|
rightline=false,%
|
|
bottomline=false,%
|
|
innertopmargin=1pt,%
|
|
innerbottommargin=1pt,%
|
|
]{*definition}{Definition}
|
|
|
|
\newmdtheoremenv[%
|
|
hidealllines=true,%
|
|
frametitlefont=\normalfont\bfseries\color{black},%
|
|
skipabove=5pt,%
|
|
innerleftmargin=10pt,%
|
|
]{*remark}{\hspace*{-10pt}$\blacktriangleright$\hspace*{\dimexpr 10pt - \blacktrianglewidth\relax}Bemerkung}
|
|
|
|
\newmdtheoremenv[%
|
|
hidealllines=true,%
|
|
innerleftmargin=10pt,%
|
|
]{*example}{\hspace*{-10pt}\rule{5pt}{5pt}\hspace*{5pt}Beispiel}
|
|
\newtheorem{overview}[theorem]{Überblick}
|
|
|
|
\newmdtheoremenv[%
|
|
style=boxedtheorem,%
|
|
topline=false,%
|
|
rightline=false,%
|
|
leftline=false,
|
|
bottomline=false,%
|
|
innertopmargin=\topskip,%
|
|
innerbottommargin=\topskip,%
|
|
backgroundcolor=lightgrey,%
|
|
]{*anmerkung}{Anmerkung}
|
|
|
|
%Hinweis-Theoremstyle and environment
|
|
%To get rid of the parentheses, a new theorem style is neccessary (definition of nonumberbreak from ntheorem.sty)
|
|
%to achieve the underlining, this needed to put in the theoremstyle definition
|
|
\theoremheaderfont{\mdseries}
|
|
\theoremseparator{:}
|
|
\theorempostskip{0pt}
|
|
\makeatletter
|
|
\newtheoremstyle{noparentheses}%
|
|
{\item[\rlap{\vbox{\hbox{\hskip\labelsep \theorem@headerfont
|
|
\underline{##1}\theorem@separator}\hbox{\strut}}}]}%
|
|
{\item[\rlap{\vbox{\hbox{\hskip\labelsep \theorem@headerfont
|
|
\underline{##1\ ##3\theorem@separator}}\hbox{\strut}}}]}
|
|
\newtheoremstyle{underlinedPlain}%
|
|
{\item[\hskip\labelsep \uline{\theorem@headerfont ##1\theorem@separator}]}%
|
|
{\item[\hskip\labelsep \uline{\theorem@headerfont ##1\ \theorem@headerfont(##3)\theorem@separator}]}
|
|
\newtheoremstyle{underlinedEnvironment}{}%
|
|
{\item[\hskip\labelsep \uline{##1\theorem@headerfont ##3\theorem@separator}]}
|
|
\newtheoremstyle{proofstyle}%
|
|
{\item[\hskip\labelsep {\theorem@headerfont ##1}\theorem@separator]}%
|
|
{\item[\hskip\labelsep {\theorem@headerfont ##1}\ (##3)\theorem@separator]}
|
|
\makeatother
|
|
|
|
\theoremstyle{noparentheses}
|
|
\newmdtheoremenv[%
|
|
hidealllines=true,%
|
|
innerleftmargin=1em,%
|
|
innerbottommargin=0pt,%
|
|
innerrightmargin=0,%
|
|
skipbelow=0pt,%
|
|
]{interpretation}{\hspace*{\dimexpr - \mdflength{innerleftmargin}\relax}Interpretation}
|
|
\theoremstyle{underlinedPlain}
|
|
\newmdtheoremenv[%
|
|
hidealllines=true,%
|
|
innerleftmargin=1em,%
|
|
innerrightmargin=0,%
|
|
skipbelow=0pt,%
|
|
]{hint}{\hspace*{\dimexpr - \mdflength{innerleftmargin}\relax}Hinweis}
|
|
|
|
\theoremstyle{underlinedEnvironment}
|
|
\newmdtheoremenv[%
|
|
hidealllines=true,%
|
|
innerleftmargin=1em,%
|
|
innerrightmargin=0,%
|
|
skipbelow=0pt,%
|
|
]{underlinedenvironment}{\hspace*{\dimexpr -\mdflength{innerleftmargin}\relax}}
|
|
|
|
\theoremstyle{proofstyle}
|
|
\theoremheaderfont{\normalfont\normalsize\itshape}
|
|
\theorembodyfont{\normalfont\small}
|
|
\theoremseparator{.}
|
|
\theorempreskip{5pt}
|
|
\theorempostskip{5pt}
|
|
\theoremsymbol{$\square$}
|
|
\renewtheorem{proof}{Beweis}
|
|
|
|
%for \cref: printed environment names
|
|
\crefname{theorem}{Theorem}{Theoreme}
|
|
\crefname{proposition}{Satz}{Sätze}
|
|
\crefname{lemma}{Lemma}{Lemmata}
|
|
\crefname{conclusion}{Folgerung}{Folgerungen}
|
|
\crefname{definition}{Definition}{Definitionen}
|
|
\crefname{remark}{Bemerkung}{Bemerkungen}
|
|
\crefname{example}{Beispiel}{Beispiele}
|
|
\crefname{*definition}{Definition}{Definitionen}
|
|
\crefname{*remark}{Bemerkung}{Bemerkungen}
|
|
\crefname{*example}{Beispiel}{Beispiele}
|
|
|
|
\makeatletter
|
|
\newcommand*{\rom}[1]{\expandafter\@slowromancap\romannumeral #1@}
|
|
\newcommand*{\proplbl}[1]{%
|
|
\@bsphack
|
|
\begingroup
|
|
\label{#1}%
|
|
\zref@setcurrent{default}{\arabic{chapter}}%
|
|
% \zref@wrapper@immediate{%
|
|
\zref@labelbyprops{#1@chapter}{default}
|
|
% }
|
|
\endgroup
|
|
\@esphack
|
|
}
|
|
\newcommand*{\propref}[1]{%
|
|
\ifcsdef{r@#1}%in first compilation the label may not be defined yet
|
|
{%
|
|
\zref@refused{#1@chapter}%
|
|
\ifnumcomp{\value{chapter}}{=}{\zref@extractdefault{#1@chapter}{default}{0}}%
|
|
{%same chapter
|
|
\ifmmode
|
|
\cref{#1}%
|
|
\else
|
|
\mbox{\cref{#1}}%
|
|
\fi
|
|
}%
|
|
{%otherwise
|
|
\def\propositionref@current@type{}%
|
|
\cref@gettype{#1}{\propositionref@current@type}%get the environment's name
|
|
%example for following line:
|
|
%\crefformat{truetheorem}{\cref@truetheorem@name~##2\rom{\zref@extractdefault{#1}{#1chapter}{1}}.##1##3}
|
|
%this changes the format used by \cref to <environtment name> <chapter-number>.<section-number>.<theorem number>
|
|
\crefformat{\propositionref@current@type}{%
|
|
\csname cref@\propositionref@current@type @name\endcsname ~##2\rom{\zref@extractdefault{#1@chapter}{default}{1}}.##1##3%
|
|
}%
|
|
\ifmmode
|
|
\cref{#1}%
|
|
\else
|
|
\mbox{\cref{#1}}%
|
|
\fi
|
|
\crefformat{\propositionref@current@type}{%
|
|
\csname cref@\propositionref@current@type @name\endcsname~##2##1##3%
|
|
}%
|
|
}%
|
|
}%
|
|
{??}%similar to \ref\cref: question marks in case of undefined labels
|
|
}
|
|
\makeatother
|
|
|
|
\NewDocumentCommand{\begriff}{s O{} m O{}}{%
|
|
\IfBooleanTF{#1}%
|
|
{\index{#2#3#4}}%
|
|
{%
|
|
\uline{#3}%
|
|
\ifnumcomp{\value{section}}{<}{16}%
|
|
{\index[semester1]{#2#3#4}}%
|
|
{\index[semester2]{#2#3#4}}%
|
|
\index{#2#3#4}%
|
|
}%
|
|
}
|
|
\NewDocumentCommand{\mathsymbol}{s O{} m m O{}}{%
|
|
\IfBooleanTF{#1}%
|
|
{\index[symbols]{#2#3@\detokenize{#4}#5}}%
|
|
{#4\index[symbols]{#2#3@\detokenize{#4}#5}}%
|
|
}
|
|
\NewDocumentCommand{\zeroAmsmathAlignVSpaces}{s s O{0 pt} O{0 pt}}{%
|
|
\IfBooleanTF{#1}%
|
|
{%
|
|
\IfBooleanTF{#2}%
|
|
{\setlength{\belowdisplayskip}{#4}}%
|
|
{\setlength{\abovedisplayskip}{#3}}%
|
|
}%
|
|
{%
|
|
\setlength{\abovedisplayskip}{#3}%
|
|
\setlength{\belowdisplayskip}{#4}%
|
|
}%
|
|
}
|
|
|
|
\NewDocumentCommand{\transpose}{m}{\ensuremath{#1^\mathsf{T}}}
|
|
|
|
\NewDocumentCommand{\itemEq}{s m}{%
|
|
\begingroup%
|
|
\setlength{\abovedisplayskip}{\dimexpr -\parskip + 1pt\relax}%
|
|
\setlength{\belowdisplayskip}{0pt}%
|
|
\IfBooleanTF{#1}%
|
|
{\parbox[c]{\linewidth}{\begin{flalign*}#2&&\end{flalign*}}}%}
|
|
{\parbox[c]{\linewidth}{\begin{flalign}#2&&\end{flalign}}}%}
|
|
\endgroup%
|
|
}
|
|
\newcommand\equalhat{\mathrel{\stackon[1.5pt]{=}{\stretchto{%
|
|
\scalerel*[\widthof{=}]{\wedge}{\rule{1ex}{3ex}}}{0.5ex}}}}
|
|
|
|
\makeatletter
|
|
\newcommand{\leqnos}{\tagsleft@true\let\veqno\@@leqno}
|
|
\newcommand{\reqnos}{\tagsleft@false\let\veqno\@@eqno}
|
|
\reqnos
|
|
\makeatother
|
|
|
|
%General newcommands!
|
|
\newcommand{\comp}{\mathbb{C}} % complex set C
|
|
\newcommand{\real}{\mathbb{R}} % real set R
|
|
\newcommand{\whole}{\mathbb{Z}} % whole number Symbol
|
|
\newcommand{\natur}{\mathbb{N}} % natural number Symbol
|
|
\newcommand{\ratio}{\mathbb{Q}} % rational number symbol
|
|
\newcommand{\field}{\mathbb{K}} % general field for the others above!
|
|
\newcommand{\diff}{\mathrm{d}} % differential d
|
|
\newcommand{\s}{\,\,} % space after the function in the intergral
|
|
\newcommand{\cont}{\mathcal{C}} % Contour C
|
|
\newcommand{\fuk}{f(z) \s\diff z} % f(z) dz
|
|
\newcommand{\diffz}{\s\diff z}
|
|
\newcommand{\subint}{\int\limits} % lower boundaries for the integral
|
|
\newcommand{\poly}{\mathcal{P}} % special P - polygon
|
|
\newcommand{\defi}{\mathcal{D}} % D for the domain of a function
|
|
\newcommand{\cover}{\mathcal{U}} % cover for a set
|
|
\newcommand{\setsys}{\mathcal{M}} % set system M
|
|
\newcommand{\setnys}{\mathcal{N}} % set system N
|
|
\newcommand{\zetafunk}{f(\zeta)\s\diff \zeta} %f(zeta) d zeta
|
|
\newcommand{\ztfunk}{f(\zeta)} % f(zeta)
|
|
\newcommand{\bocirc}{S_r(z)}
|
|
\newcommand{\prop}{\,|\,}
|
|
\newcommand*{\QEDA}{\hfill\ensuremath{\blacksquare}} %tombstone
|
|
\newcommand{\emptybra}{\{\varnothing\}} % empty set with set-bracket
|
|
\newcommand{\realpos}{\real_{>0}}
|
|
\newcommand{\realposr}{\real_{\geq0}}
|
|
\newcommand{\naturpos}{\natur_{>0}}
|
|
\newcommand{\Imag}{\operatorname{Im}} % Imaginary symbol
|
|
\newcommand{\Realz}{\operatorname{Re}} % Real symbol
|
|
\newcommand{\norm}{\Vert \cdot \Vert}
|
|
\newcommand{\metric}{\vert \cdot \vert}
|
|
\newcommand{\foralln}{\forall n} %all n
|
|
\newcommand{\forallnset}{\forall n \in \natur} %all n € |N
|
|
\newcommand{\forallnz}{\forall n \geq _0} % all n >= n_0
|
|
\newcommand{\conjz}{\overline{z}} % conjugated z
|
|
\newcommand{\tildz}{\tilde{z}} % different z
|
|
\newcommand{\lproofar}{"`$ \Leftarrow $"'} % "`<="'
|
|
\newcommand{\rproofar}{"`$ \Rightarrow $"'} % "`=>"'
|
|
\newcommand{\beha}{\Rightarrow \text{ Behauptung}}
|
|
\newcommand{\powerset}{\mathcal{P}}
|
|
\newcommand{\person}[1]{\textsc{#1}}
|
|
\newcommand{\highlight}[1]{\emph{#1}}
|
|
\newcommand{\realz}{\mathfrak{Re}}
|
|
\newcommand{\imagz}{\mathfrak{Im}}
|
|
\renewcommand{\epsilon}{\varepsilon}
|
|
\renewcommand{\phi}{\varphi}
|
|
\newcommand{\lebesque}{\person{Lebesgue}}
|
|
\renewcommand{\Re}{\mathfrak{Re}}
|
|
\renewcommand{\Im}{\mathfrak{Im}}
|
|
|
|
% Math Operators
|
|
\DeclareMathOperator{\inn}{int} % Set of inner points
|
|
\DeclareMathOperator{\ext}{ext} % Set of outer points
|
|
\DeclareMathOperator{\cl}{cl} % Closure
|
|
\DeclareMathOperator{\grad}{grad}
|
|
\DeclareMathOperator{\D}{d}
|
|
\DeclareMathOperator{\id}{id}
|
|
\DeclareMathOperator{\graph}{graph}
|
|
\DeclareMathOperator{\Int}{int}
|
|
\DeclareMathOperator{\Ext}{ext}
|
|
\DeclareMathOperator{\diam}{diam}
|
|
|
|
%change headings:
|
|
\titlelabel{\thetitle.\quad}%. behind section/sub... (3. instead of 3)
|
|
\counterwithout{section}{chapter}
|
|
\renewcommand{\thechapter}{\Roman{chapter}}
|
|
\renewcommand{\thepart}{\Alph{part}}
|
|
%italic chapters (due to titlesec package some more stuff)
|
|
%\titleformat{command}[shape]{format}{label}{sep}{before-code}[after-code]
|
|
\titleformat{\chapter}[display]{\bfseries}{\Large\chaptername\;\thechapter}{-5pt}{\huge\bfseries\itshape}
|
|
\titlespacing{\chapter}{0pt}{0pt}{10pt}
|
|
\titleformat{\section}[hang]{\bfseries\Large}{\thesection.}{8pt}{\Large\bfseries}
|
|
%\titlespacing{command}{left}{before-sep}{after-sep}
|
|
\titlespacing{\subsection}{0pt}{0pt}{5pt}
|
|
|
|
%change appearence of heading of toc: 0 space above, bold, italic huge toc-heading
|
|
\renewcommand{\cftbeforetoctitleskip}{0pt}
|
|
\renewcommand{\cfttoctitlefont}{\itshape\Huge\bfseries}
|
|
%change indentations due to width of capital roman numbers
|
|
\renewcommand{\cftchapnumwidth}{2.5em}
|
|
\renewcommand{\cftsecindent}{2.5em}
|
|
%\renewcommand{\cftsecnumwidth}{3.3em}
|
|
\renewcommand{\cftsubsecindent}{4.8em}
|
|
%\renewcommand{\cftsubsecnumwidth}{4.2em}
|
|
|
|
%change header:
|
|
\renewcommand{\headrulewidth}{0.75pt}
|
|
\renewcommand{\footrulewidth}{0.3pt}
|
|
\lhead{\rightmark}%left: section-number. section-title
|
|
\rhead{\leftmark}%right: chapter chapternumber: chapter-title
|
|
|
|
% Add new page-style (just footer), patch \chapter command to use this page style
|
|
\fancypagestyle{plainChapter}{%
|
|
\fancyhf{}%
|
|
\fancyfoot[C]{\thepage}%
|
|
\renewcommand{\headrulewidth}{0pt}% Line at the header invisible
|
|
\renewcommand{\footrulewidth}{0.4pt}% Line at the footer visible
|
|
}
|
|
\patchcmd{\chapter}{\thispagestyle{plain}}{\thispagestyle{plainChapter}}{}{}
|
|
|
|
\pagestyle{fancy}
|
|
\pagenumbering{arabic}
|
|
%remember chapter-title in \leftmark and \rightmark
|
|
\renewcommand{\chaptermark}[1]{%
|
|
\markboth{\chaptername
|
|
\ \thechapter:\ #1}{}}
|
|
%remember section title in \leftmark
|
|
\renewcommand{\sectionmark}[1]{%
|
|
\markright{\thesection.\ #1}{}}
|
|
|
|
%change numbering of equations to be section by section
|
|
\counterwithout{equation}{section}
|
|
|
|
\newacronym{gdw}{gdw.}{genau dann wenn}
|
|
\newacronym{fa}{fa.}{fast alle}
|
|
\newacronym{fü}{f.ü.}{fast überall}
|
|
\newacronym{obda}{oBdA}{ohne Beschränkung der Allgemeinheit}
|
|
\newacronym{tf}{TF}{\begriff{Teilfolge}}
|
|
\newacronym{hw}{Hw}{\begriff{Häufungswert}}
|
|
\newacronym{cf}{CF}{\begriff{\person{Cauchy}-Folge}}
|
|
\newacronym{hp}{HP}{\begriff{Häufungspunkt}}
|
|
\newacronym{vr}{VR}{Vektorraum}
|
|
\newacronym{diffbar}{diffbar}{differenzierbar}
|
|
\newacronym{differenzierbar}{differenzierbar}{differenzierbar}
|
|
\newacronym{mws}{MWS}{Mittelwertsatz}
|
|
|
|
\title{\textbf{Analysis 2. Semester (SS2018)}}
|
|
\author{Dozent: Prof. Dr. Friedemann Schuricht\\
|
|
Kursassistenz: Moritz Schönherr}
|
|
|
|
\makeatletter
|
|
\makeatletter
|
|
\let\sv@endpart\@endpart
|
|
\def\@endpart{\thispagestyle{empty}\sv@endpart}
|
|
\makeatother
|
|
\makeatother
|
|
|
|
\begin{document}
|
|
\pagenumbering{roman}
|
|
\pagestyle{plain}
|
|
|
|
\maketitle
|
|
|
|
\hypertarget{tocpage}{}
|
|
\tableofcontents
|
|
\bookmark[dest=tocpage,level=1]{Inhaltsverzeichnis}
|
|
|
|
\pagebreak
|
|
\pagestyle{fancy}
|
|
\pagenumbering{arabic}
|
|
|
|
\part{1. Semester}
|
|
\pagestyle{fancy}
|
|
\chapter{Zahlenbereiche}
|
|
\input{./TeX_files/Grundbegriffe_Logik}
|
|
\include{./TeX_files/Natuerliche_Zahlen}
|
|
%\include{./TeX_files/Ganze_und_Rationale_Zahlen}
|
|
%\include{./TeX_files/Reelle_Zahlen}
|
|
%\include{./TeX_files/Komplexe_Zahlen}
|
|
%
|
|
%\chapter{Metrische Räume und Konvergenz}
|
|
%\input{./TeX_files/Grundlegende_Ungleichungen}
|
|
%\include{./TeX_files/Metrische_Raeume}
|
|
%\include{./TeX_files/Konvergenz}
|
|
%\include{./TeX_files/Vollstaendigkeit_und_Kompaktheit}
|
|
%\include{./TeX_files/Reihen}
|
|
%
|
|
%\chapter{Funktionen und Stetigkeit}
|
|
%\input{./TeX_files/Funktionen}
|
|
%\include{./TeX_files/Stetigkeit}
|
|
%\include{./TeX_files/Anwendungen}
|
|
\begin{proposition}
|
|
\proplbl{aeqv_norm}
|
|
\proplbl{chap_15_5}
|
|
\proplbl{defLinearFunction}
|
|
\proplbl{einseitige_grenzwerte}
|
|
\proplbl{lemma_13_10}
|
|
\proplbl{additionstheoreme}
|
|
\proplbl{chap_5}
|
|
\proplbl{satz_von_weierstrass}
|
|
\proplbl{chap_15_3}
|
|
\proplbl{satz_15_8}
|
|
\proplbl{satz_15_1}
|
|
\proplbl{zwischenwertsatz}
|
|
\proplbl{chap_15_20}
|
|
\proplbl{chap_14_19}
|
|
Test für Labels.
|
|
\end{proposition}
|
|
|
|
\part{2. Semester}
|
|
\pagestyle{fancy}
|
|
\setcounter{section}{15}
|
|
\setcounter{chapter}{4}
|
|
|
|
%\chapter{Differentiation}
|
|
%\input{./TeX_files/Wiederholung_und_Motivation}
|
|
%\include{./TeX_files/Ableitung}
|
|
%\include{./TeX_files/Richtungsableitung}
|
|
%\include{./TeX_files/Mittelwertsatz}
|
|
%\include{./TeX_files/Stammfunktion}
|
|
%
|
|
%\chapter{Integration}
|
|
%\input{./TeX_files/Integration}
|
|
%\include{./TeX_files/Messbarkeit}
|
|
%\include{./TeX_files/Integral}
|
|
%\include{./TeX_files/Integral_R}
|
|
%\include{./TeX_files/Fubini}
|
|
%
|
|
%\chapter{Differentiation II}
|
|
%\input{./TeX_files/Taylor}
|
|
%\include{./TeX_files/Extremwerte}
|
|
%\include{./TeX_files/Inverse_implizite_Funktionen}
|
|
%\include{./TeX_files/Funktionsfolgen}
|
|
|
|
|
|
\appendix
|
|
\part*{Anhang}
|
|
\addcontentsline{toc}{part}{Anhang}
|
|
\patchcmd{\chapter}{\thispagestyle{plainChapter}}{\thispagestyle{fancy}}{}{}
|
|
%\titleformat{command}[shape]{format}{label}{sep}{before-code}[after-code]
|
|
%\titlespacing{command}{left}{before-sep}{after-sep}
|
|
\renewcommand{\chaptername}{Anhang}
|
|
\renewcommand{\thechapter}{\Alph{chapter}}
|
|
\titleformat{\chapter}[hang]{\bfseries}{\LARGE\chaptername\ \thechapter:}{0.5em}{\LARGE\bfseries}
|
|
\titlespacing{\chapter}{0pt}{-0.75cm}{0pt}
|
|
\renewcommand{\thesection}{\Alph{chapter}.\arabic{section}}
|
|
|
|
%\def\thm@@thmline@name#1#2#3#4#5{%
|
|
% \ifx\\#5\\%
|
|
% \@dottedtocline{-2}{0em}{2.3em}%
|
|
% {#1 \protect\numberline{#2}#3}%
|
|
% {#4}
|
|
% \else
|
|
% \ifHy@linktocpage\relax\relax
|
|
% \@dottedtocline{-2}{0em}{2.3em}%
|
|
% {#1 \protect\numberline{#2}#3}%
|
|
% {\hyper@linkstart{link}{#5}{#4}\hyper@linkend}%
|
|
% \else
|
|
% \@dottedtocline{-2}{0em}{2.3em}%
|
|
% {\hyper@linkstart{link}{#5}%
|
|
% {#1 \protect\numberline{#2}#3}\hyper@linkend}%
|
|
% {#4}%
|
|
% \fi
|
|
% \fi
|
|
%}
|
|
|
|
\makeatletter
|
|
\renewcommand{\thm@@thmline@name}[5]{%
|
|
\def\thm@@thmline@name@tmp{%
|
|
\if\relax\detokenize{#3}\relax%
|
|
\relax%
|
|
\else%
|
|
{:\hspace*{1em}#3}%
|
|
\fi%
|
|
}%
|
|
\ifx\\#5\\%
|
|
\@dottedtocline{-2}{0em}{2.3em}%
|
|
{#1 \protect\numberline{#2}{\thm@@thmline@name@tmp}}%
|
|
{#4}
|
|
\else
|
|
\ifHy@linktocpage\relax\relax
|
|
\@dottedtocline{-2}{0em}{2.3em}%
|
|
{#1 \protect\numberline{#2}{\thm@@thmline@name@tmp}}%
|
|
{\hyper@linkstart{link}{#5}{#4}\hyper@linkend}%
|
|
\else
|
|
\@dottedtocline{-2}{0em}{2.3em}%
|
|
{%
|
|
{#1 \protect\numberline{#2}{\thm@@thmline@name@tmp}}}%
|
|
{\hyper@linkstart{link}{#5}{#4}\hyper@linkend}%
|
|
\fi
|
|
\fi
|
|
}
|
|
\makeatother
|
|
|
|
\chapter{Listen}
|
|
\section{Liste der Theoreme}
|
|
\theoremlisttype{allname}
|
|
\listtheorems{theorem}
|
|
|
|
\pagebreak
|
|
\section{Liste der benannten Sätze}
|
|
\theoremlisttype{optname}
|
|
\listtheorems{proposition}
|
|
|
|
\printglossary[type=\acronymtype]
|
|
\addcontentsline{toc}{chapter}{Akronyme}
|
|
|
|
\printindex
|
|
\addcontentsline{toc}{chapter}{Index}
|
|
|
|
\printindex[symbols]
|
|
\addcontentsline{toc}{chapter}{Symbolverzeichnis}
|
|
|
|
\end{document} |