2023-05-25 18:11:02 +02:00
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Required packages and command changes %
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% required base packages %
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% language and encoding
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\RequirePackage[utf8]{inputenc}
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\RequirePackage[T1]{fontenc}
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\RequirePackage[ngerman]{babel}
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% BibLaTeX
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2023-05-26 22:38:39 +02:00
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\RequirePackage[hyperref,style=authoryear]{biblatex}
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2023-05-25 18:11:02 +02:00
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% math packages
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\RequirePackage{amsmath} % general math
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\RequirePackage{amsthm} % theorems
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\RequirePackage{amssymb} % math symbols
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\RequirePackage{mathtools} % coloneqq: nice ligatures of := and =:
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\RequirePackage{stmaryrd} % lightning symbol
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\RequirePackage{aligned-overset} % proper alignment with oversets
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% other packages
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\RequirePackage{enumerate} % for alphanumeric enumeration: (i), (ii), ...
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\RequirePackage{csquotes} % language dependent correct quote signs
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\RequirePackage[parfill]{parskip}
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% use sans-serif font Computer Modern Bright
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\RequirePackage{cmbright} % sans-serif fonts looking cleaner
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\RequirePackage[lm]{sfmath} % bold math symbols in Latin Modern
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\DeclareRobustCommand{\sm@ller}{%
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\dimen@\f@size\p@
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\ifdim \dimen@ > 12\p@
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4
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\dimen@=0.83333\dimen@
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\else
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\advance \dimen@ -2\p@
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\fi
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\math@fontsfalse
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\fontsize{\the\dimen@}\z@
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\selectfont
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}
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\newcommand{\textc}[1]{{\sm@ller\uppercase{#1}}}
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% load late
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\RequirePackage{hyperref} % hyperref package for refs
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\hypersetup{
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pdftitle={
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2023-05-30 20:03:14 +02:00
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Berechnung der Matrixexponentialfunktion und
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Anwendung auf homogene lineare Differentialgleichungssysteme mit konstanten Koeffizienten
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2023-05-25 18:11:02 +02:00
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},
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pdfsubject={Skript zum Vortrag im Proseminar Algebra},
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pdfauthor={Niklas Birk},
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pdfkeywords={mathematics, calculus, analysis, linear algebra, ordinary differential equations, lecture notes, university}
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}
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\DeclareTextFontCommand{\emph}{\boldmath\bfseries}
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2023-05-30 19:36:58 +02:00
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\allowdisplaybreaks
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% new commands and math operatos %
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% common set symbols
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\newcommand{\NN}{\mathbb{N}}
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\newcommand{\RR}{\mathbb{R}}
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\newcommand{\CC}{\mathbb{C}}
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% common symbols
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\renewcommand{\i}{\mathrm{i}}
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\newcommand{\e}{\mathrm{e}}
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\renewcommand{\d}{\mathrm{d}}
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\renewcommand{\Re}{\mathrm{Re}\,}
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\renewcommand{\Im}{\mathrm{Im}\,}
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\DeclareMathOperator{\diag}{diag}
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\renewcommand{\vec}[1]{\mathfrak{#1}}
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% use the more common variants of greek letters
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\renewcommand{\phi}{\varphi}
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\renewcommand{\epsilon}{\varepsilon}
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% symbols for differentiation and integral
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\newcommand{\dx}[1][x]{\ \d #1} % differential
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\newcommand{\dfdx}[2]{\frac{\d #1}{\d #2}} % 1st derivative
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\newcommand{\ddfdx}[3]{\frac{\d^{#3} #1}{\d #2^{#3}}} % nth derivative
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% sets of the form {...; ...}
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\newcommand{\set}[2]{\left\lbrace #1\ \middle|\ #2 \right\rbrace}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% theorems, definitions, etc. %
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% style for definitions, unnumbered theorems: "Definition ([additional name]) \newline"
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\newtheoremstyle{break*}{}{}{\itshape}{}{\bfseries}{}{\newline}{\thmname{#1}~\thmnote{(#3)}}
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\theoremstyle{break*}
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\newtheorem*{definition}{Definition}
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% style for theorems, lemmata, propositions, corollary: "<counter> Theorem ([additional name]) \newline"
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\newtheoremstyle{break}{}{}{\itshape}{}{\bfseries}{}{\newline}{\thmname{#1}~\thmnumber{#2}~\thmnote{(#3)}}
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\theoremstyle{break}
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\newtheorem{theorem}{Satz}[section]
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\newtheorem{lemma}[theorem]{Lemma}
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\newtheorem{corollary}[theorem]{Folgerung}
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% style for examples: "Beispiel:"
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\newtheoremstyle{nobreak*}{}{}{\normalfont}{}{\bfseries}{}{ }{}
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\theoremstyle{nobreak*}
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\newtheorem*{remark*}{Bemerkung:}
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\newtheorem*{example*}{Beispiel:}
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% proofs with bold name and qed at end
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\renewenvironment{proof}[1][\proofname]{\textbf{#1.} }{\nobreak\hfill\ensuremath{\blacksquare}\par}
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