Analysis Chapter 1
Analysis Chapter 1 and Neorged everything for Analysis
This commit is contained in:
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\chapter{Fourier Analysis}
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\chapter{Komplexe Zahlen}
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\chapter{Komplexwertige Funktionen}
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\chapter{Laplace-Transformation}
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178
fs25/mathematische_methoden/letterfonts.tex
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178
fs25/mathematische_methoden/letterfonts.tex
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% Things Lie
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\newcommand{\kb}{\mathfrak b}
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\newcommand{\kg}{\mathfrak g}
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\newcommand{\kh}{\mathfrak h}
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\newcommand{\kn}{\mathfrak n}
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\newcommand{\ku}{\mathfrak u}
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\newcommand{\kz}{\mathfrak z}
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\DeclareMathOperator{\Ext}{Ext} % Ext functor
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\DeclareMathOperator{\Tor}{Tor} % Tor functor
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\newcommand{\gl}{\opname{\mathfrak{gl}}} % frak gl group
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\renewcommand{\sl}{\opname{\mathfrak{sl}}} % frak sl group chktex 6
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% More script letters etc.
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\newcommand{\SA}{\mathcal A}
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\newcommand{\SB}{\mathcal B}
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\newcommand{\SC}{\mathcal C}
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\newcommand{\SF}{\mathcal F}
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\newcommand{\SG}{\mathcal G}
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\newcommand{\SH}{\mathcal H}
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\newcommand{\OO}{\mathcal O}
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\newcommand{\SCA}{\mathscr A}
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\newcommand{\SCB}{\mathscr B}
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\newcommand{\SCC}{\mathscr C}
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\newcommand{\SCD}{\mathscr D}
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\newcommand{\SCE}{\mathscr E}
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\newcommand{\SCF}{\mathscr F}
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\newcommand{\SCG}{\mathscr G}
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\newcommand{\SCH}{\mathscr H}
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% Mathfrak primes
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\newcommand{\km}{\mathfrak m}
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\newcommand{\kp}{\mathfrak p}
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\newcommand{\kq}{\mathfrak q}
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% number sets
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\newcommand{\RR}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{R}}{\mathbb{R}^{#1}}}}
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\newcommand{\NN}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{N}}{\mathbb{N}^{#1}}}}
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\newcommand{\ZZ}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{Z}}{\mathbb{Z}^{#1}}}}
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\newcommand{\QQ}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{Q}}{\mathbb{Q}^{#1}}}}
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\newcommand{\CC}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{C}}{\mathbb{C}^{#1}}}}
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\newcommand{\PP}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{P}}{\mathbb{P}^{#1}}}}
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\newcommand{\HH}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{H}}{\mathbb{H}^{#1}}}}
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\newcommand{\FF}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{F}}{\mathbb{F}^{#1}}}}
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% expected value
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\newcommand{\EE}{\ensuremath{\mathbb{E}}}
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\newcommand{\charin}{\text{ char }}
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\DeclareMathOperator{\sign}{sign}
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\DeclareMathOperator{\Aut}{Aut}
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\DeclareMathOperator{\Inn}{Inn}
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\DeclareMathOperator{\Syl}{Syl}
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\DeclareMathOperator{\Gal}{Gal}
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\DeclareMathOperator{\GL}{GL} % General linear group
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\DeclareMathOperator{\SL}{SL} % Special linear group
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%---------------------------------------
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% BlackBoard Math Fonts :-
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%---------------------------------------
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%Captital Letters
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\newcommand{\bbA}{\mathbb{A}} \newcommand{\bbB}{\mathbb{B}}
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\newcommand{\bbC}{\mathbb{C}} \newcommand{\bbD}{\mathbb{D}}
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\newcommand{\bbE}{\mathbb{E}} \newcommand{\bbF}{\mathbb{F}}
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\newcommand{\bbG}{\mathbb{G}} \newcommand{\bbH}{\mathbb{H}}
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\newcommand{\bbI}{\mathbb{I}} \newcommand{\bbJ}{\mathbb{J}}
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\newcommand{\bbK}{\mathbb{K}} \newcommand{\bbL}{\mathbb{L}}
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\newcommand{\bbM}{\mathbb{M}} \newcommand{\bbN}{\mathbb{N}}
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\newcommand{\bbO}{\mathbb{O}} \newcommand{\bbP}{\mathbb{P}}
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\newcommand{\bbQ}{\mathbb{Q}} \newcommand{\bbR}{\mathbb{R}}
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\newcommand{\bbS}{\mathbb{S}} \newcommand{\bbT}{\mathbb{T}}
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\newcommand{\bbU}{\mathbb{U}} \newcommand{\bbV}{\mathbb{V}}
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\newcommand{\bbW}{\mathbb{W}} \newcommand{\bbX}{\mathbb{X}}
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\newcommand{\bbY}{\mathbb{Y}} \newcommand{\bbZ}{\mathbb{Z}}
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%---------------------------------------
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% MathCal Fonts :-
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%---------------------------------------
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%Captital Letters
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\newcommand{\mcA}{\mathcal{A}} \newcommand{\mcB}{\mathcal{B}}
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\newcommand{\mcC}{\mathcal{C}} \newcommand{\mcD}{\mathcal{D}}
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\newcommand{\mcE}{\mathcal{E}} \newcommand{\mcF}{\mathcal{F}}
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\newcommand{\mcG}{\mathcal{G}} \newcommand{\mcH}{\mathcal{H}}
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\newcommand{\mcI}{\mathcal{I}} \newcommand{\mcJ}{\mathcal{J}}
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\newcommand{\mcK}{\mathcal{K}} \newcommand{\mcL}{\mathcal{L}}
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\newcommand{\mcM}{\mathcal{M}} \newcommand{\mcN}{\mathcal{N}}
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\newcommand{\mcO}{\mathcal{O}} \newcommand{\mcP}{\mathcal{P}}
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\newcommand{\mcQ}{\mathcal{Q}} \newcommand{\mcR}{\mathcal{R}}
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\newcommand{\mcS}{\mathcal{S}} \newcommand{\mcT}{\mathcal{T}}
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\newcommand{\mcU}{\mathcal{U}} \newcommand{\mcV}{\mathcal{V}}
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\newcommand{\mcW}{\mathcal{W}} \newcommand{\mcX}{\mathcal{X}}
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\newcommand{\mcY}{\mathcal{Y}} \newcommand{\mcZ}{\mathcal{Z}}
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%---------------------------------------
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% Bold Math Fonts :-
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%---------------------------------------
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%Captital Letters
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\newcommand{\bmA}{\boldsymbol{A}} \newcommand{\bmB}{\boldsymbol{B}}
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\newcommand{\bmC}{\boldsymbol{C}} \newcommand{\bmD}{\boldsymbol{D}}
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\newcommand{\bmE}{\boldsymbol{E}} \newcommand{\bmF}{\boldsymbol{F}}
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\newcommand{\bmG}{\boldsymbol{G}} \newcommand{\bmH}{\boldsymbol{H}}
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\newcommand{\bmI}{\boldsymbol{I}} \newcommand{\bmJ}{\boldsymbol{J}}
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\newcommand{\bmK}{\boldsymbol{K}} \newcommand{\bmL}{\boldsymbol{L}}
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\newcommand{\bmM}{\boldsymbol{M}} \newcommand{\bmN}{\boldsymbol{N}}
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\newcommand{\bmO}{\boldsymbol{O}} \newcommand{\bmP}{\boldsymbol{P}}
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\newcommand{\bmQ}{\boldsymbol{Q}} \newcommand{\bmR}{\boldsymbol{R}}
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\newcommand{\bmS}{\boldsymbol{S}} \newcommand{\bmT}{\boldsymbol{T}}
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\newcommand{\bmU}{\boldsymbol{U}} \newcommand{\bmV}{\boldsymbol{V}}
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\newcommand{\bmW}{\boldsymbol{W}} \newcommand{\bmX}{\boldsymbol{X}}
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\newcommand{\bmY}{\boldsymbol{Y}} \newcommand{\bmZ}{\boldsymbol{Z}}
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%Small Letters
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\newcommand{\bma}{\boldsymbol{a}} \newcommand{\bmb}{\boldsymbol{b}}
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\newcommand{\bmc}{\boldsymbol{c}} \newcommand{\bmd}{\boldsymbol{d}}
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\newcommand{\bme}{\boldsymbol{e}} \newcommand{\bmf}{\boldsymbol{f}}
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\newcommand{\bmg}{\boldsymbol{g}} \newcommand{\bmh}{\boldsymbol{h}}
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\newcommand{\bmi}{\boldsymbol{i}} \newcommand{\bmj}{\boldsymbol{j}}
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\newcommand{\bmk}{\boldsymbol{k}} \newcommand{\bml}{\boldsymbol{l}}
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\newcommand{\bmm}{\boldsymbol{m}} \newcommand{\bmn}{\boldsymbol{n}}
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\newcommand{\bmo}{\boldsymbol{o}} \newcommand{\bmp}{\boldsymbol{p}}
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\newcommand{\bmq}{\boldsymbol{q}} \newcommand{\bmr}{\boldsymbol{r}}
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\newcommand{\bms}{\boldsymbol{s}} \newcommand{\bmt}{\boldsymbol{t}}
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\newcommand{\bmu}{\boldsymbol{u}} \newcommand{\bmv}{\boldsymbol{v}}
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\newcommand{\bmw}{\boldsymbol{w}} \newcommand{\bmx}{\boldsymbol{x}}
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\newcommand{\bmy}{\boldsymbol{y}} \newcommand{\bmz}{\boldsymbol{z}}
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%---------------------------------------
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% Scr Math Fonts :-
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%---------------------------------------
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\newcommand{\sA}{{\mathscr{A}}} \newcommand{\sB}{{\mathscr{B}}}
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\newcommand{\sC}{{\mathscr{C}}} \newcommand{\sD}{{\mathscr{D}}}
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\newcommand{\sE}{{\mathscr{E}}} \newcommand{\sF}{{\mathscr{F}}}
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\newcommand{\sG}{{\mathscr{G}}} \newcommand{\sH}{{\mathscr{H}}}
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\newcommand{\sI}{{\mathscr{I}}} \newcommand{\sJ}{{\mathscr{J}}}
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\newcommand{\sK}{{\mathscr{K}}} \newcommand{\sL}{{\mathscr{L}}}
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\newcommand{\sM}{{\mathscr{M}}} \newcommand{\sN}{{\mathscr{N}}}
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\newcommand{\sO}{{\mathscr{O}}} \newcommand{\sP}{{\mathscr{P}}}
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\newcommand{\sQ}{{\mathscr{Q}}} \newcommand{\sR}{{\mathscr{R}}}
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\newcommand{\sS}{{\mathscr{S}}} \newcommand{\sT}{{\mathscr{T}}}
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\newcommand{\sU}{{\mathscr{U}}} \newcommand{\sV}{{\mathscr{V}}}
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\newcommand{\sW}{{\mathscr{W}}} \newcommand{\sX}{{\mathscr{X}}}
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\newcommand{\sY}{{\mathscr{Y}}} \newcommand{\sZ}{{\mathscr{Z}}}
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%---------------------------------------
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% Math Fraktur Font
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%---------------------------------------
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%Captital Letters
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\newcommand{\mfA}{\mathfrak{A}} \newcommand{\mfB}{\mathfrak{B}}
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\newcommand{\mfC}{\mathfrak{C}} \newcommand{\mfD}{\mathfrak{D}}
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\newcommand{\mfE}{\mathfrak{E}} \newcommand{\mfF}{\mathfrak{F}}
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\newcommand{\mfG}{\mathfrak{G}} \newcommand{\mfH}{\mathfrak{H}}
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\newcommand{\mfI}{\mathfrak{I}} \newcommand{\mfJ}{\mathfrak{J}}
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\newcommand{\mfK}{\mathfrak{K}} \newcommand{\mfL}{\mathfrak{L}}
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\newcommand{\mfM}{\mathfrak{M}} \newcommand{\mfN}{\mathfrak{N}}
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\newcommand{\mfO}{\mathfrak{O}} \newcommand{\mfP}{\mathfrak{P}}
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\newcommand{\mfQ}{\mathfrak{Q}} \newcommand{\mfR}{\mathfrak{R}}
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\newcommand{\mfS}{\mathfrak{S}} \newcommand{\mfT}{\mathfrak{T}}
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\newcommand{\mfU}{\mathfrak{U}} \newcommand{\mfV}{\mathfrak{V}}
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\newcommand{\mfW}{\mathfrak{W}} \newcommand{\mfX}{\mathfrak{X}}
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\newcommand{\mfY}{\mathfrak{Y}} \newcommand{\mfZ}{\mathfrak{Z}}
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%Small Letters
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\newcommand{\mfa}{\mathfrak{a}} \newcommand{\mfb}{\mathfrak{b}}
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\newcommand{\mfc}{\mathfrak{c}} \newcommand{\mfd}{\mathfrak{d}}
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\newcommand{\mfe}{\mathfrak{e}} \newcommand{\mff}{\mathfrak{f}}
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\newcommand{\mfg}{\mathfrak{g}} \newcommand{\mfh}{\mathfrak{h}}
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\newcommand{\mfi}{\mathfrak{i}} \newcommand{\mfj}{\mathfrak{j}}
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\newcommand{\mfk}{\mathfrak{k}} \newcommand{\mfl}{\mathfrak{l}}
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\newcommand{\mfm}{\mathfrak{m}} \newcommand{\mfn}{\mathfrak{n}}
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\newcommand{\mfo}{\mathfrak{o}} \newcommand{\mfp}{\mathfrak{p}}
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\newcommand{\mfq}{\mathfrak{q}} \newcommand{\mfr}{\mathfrak{r}}
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\newcommand{\mfs}{\mathfrak{s}} \newcommand{\mft}{\mathfrak{t}}
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\newcommand{\mfu}{\mathfrak{u}} \newcommand{\mfv}{\mathfrak{v}}
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\newcommand{\mfw}{\mathfrak{w}} \newcommand{\mfx}{\mathfrak{x}}
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\newcommand{\mfy}{\mathfrak{y}} \newcommand{\mfz}{\mathfrak{z}}
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88
fs25/mathematische_methoden/macros.tex
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88
fs25/mathematische_methoden/macros.tex
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%From M275 "Topology" at SJSU
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\newcommand{\id}{\mathrm{id}}
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\newcommand{\taking}[1]{\xrightarrow{#1}}
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\newcommand{\inv}{^{-1}}
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%From M170 "Introduction to Graph Theory" at SJSU
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\DeclareMathOperator{\diam}{diam}
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\DeclareMathOperator{\ord}{ord}
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\newcommand{\defeq}{\overset{\mathrm{def}}{=}}
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%From the USAMO .tex files
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\newcommand{\ts}{\textsuperscript}
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\newcommand{\dg}{^\circ}
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\newcommand{\ii}{\item}
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% % From Math 55 and Math 145 at Harvard
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% \newenvironment{subproof}[1][Proof]{%
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% \begin{proof}[#1] \renewcommand{\qedsymbol}{$\blacksquare$}}%
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% {\end{proof}}
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\newcommand{\liff}{\leftrightarrow}
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\newcommand{\lthen}{\rightarrow}
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\newcommand{\opname}{\operatorname}
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\newcommand{\surjto}{\twoheadrightarrow}
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\newcommand{\injto}{\hookrightarrow}
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\newcommand{\On}{\mathrm{On}} % ordinals
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\DeclareMathOperator{\img}{im} % Image
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\DeclareMathOperator{\Img}{Im} % Image
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\DeclareMathOperator{\coker}{coker} % Cokernel
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\DeclareMathOperator{\Coker}{Coker} % Cokernel
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\DeclareMathOperator{\Ker}{Ker} % Kernel
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\DeclareMathOperator{\rank}{rank}
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\DeclareMathOperator{\Spec}{Spec} % spectrum
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\DeclareMathOperator{\Tr}{Tr} % trace
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\DeclareMathOperator{\pr}{pr} % projection
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\DeclareMathOperator{\ext}{ext} % extension
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\DeclareMathOperator{\pred}{pred} % predecessor
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\DeclareMathOperator{\dom}{dom} % domain
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\DeclareMathOperator{\ran}{ran} % range
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\DeclareMathOperator{\Hom}{Hom} % homomorphism
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\DeclareMathOperator{\Mor}{Mor} % morphisms
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\DeclareMathOperator{\End}{End} % endomorphism
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\newcommand{\eps}{\epsilon}
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\newcommand{\veps}{\varepsilon}
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\newcommand{\ol}{\overline}
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\newcommand{\ul}{\underline}
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\newcommand{\wt}{\widetilde}
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\newcommand{\wh}{\widehat}
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\newcommand{\vocab}[1]{\textbf{\color{blue} #1}}
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\providecommand{\half}{\frac{1}{2}}
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\newcommand{\dang}{\measuredangle} %% Directed angle
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\newcommand{\ray}[1]{\overrightarrow{#1}}
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\newcommand{\seg}[1]{\overline{#1}}
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\newcommand{\arc}[1]{\wideparen{#1}}
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\DeclareMathOperator{\cis}{cis}
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\DeclareMathOperator*{\lcm}{lcm}
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\DeclareMathOperator*{\argmin}{arg min}
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\DeclareMathOperator*{\argmax}{arg max}
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\newcommand{\cycsum}{\sum_{\mathrm{cyc}}}
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\newcommand{\symsum}{\sum_{\mathrm{sym}}}
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\newcommand{\cycprod}{\prod_{\mathrm{cyc}}}
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\newcommand{\symprod}{\prod_{\mathrm{sym}}}
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\newcommand{\Qed}{\begin{flushright}\qed\end{flushright}}
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\newcommand{\parinn}{\setlength{\parindent}{1cm}}
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\newcommand{\parinf}{\setlength{\parindent}{0cm}}
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% \newcommand{\norm}{\|\cdot\|}
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\newcommand{\inorm}{\norm_{\infty}}
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\newcommand{\opensets}{\{V_{\alpha}\}_{\alpha\in I}}
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\newcommand{\oset}{V_{\alpha}}
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\newcommand{\opset}[1]{V_{\alpha_{#1}}}
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\newcommand{\lub}{\text{lub}}
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\newcommand{\del}[2]{\frac{\partial #1}{\partial #2}}
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\newcommand{\Del}[3]{\frac{\partial^{#1} #2}{\partial^{#1} #3}}
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\newcommand{\deld}[2]{\dfrac{\partial #1}{\partial #2}}
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\newcommand{\Deld}[3]{\dfrac{\partial^{#1} #2}{\partial^{#1} #3}}
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\newcommand{\lm}{\lambda}
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\newcommand{\uin}{\mathbin{\rotatebox[origin=c]{90}{$\in$}}}
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\newcommand{\usubset}{\mathbin{\rotatebox[origin=c]{90}{$\subset$}}}
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\newcommand{\lt}{\left}
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\newcommand{\rt}{\right}
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\newcommand{\bs}[1]{\boldsymbol{#1}}
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\newcommand{\exs}{\exists}
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\newcommand{\st}{\strut}
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\newcommand{\dps}[1]{\displaystyle{#1}}
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\newcommand{\sol}{\setlength{\parindent}{0cm}\textbf{\textit{Solution:}}\setlength{\parindent}{1cm} }
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\newcommand{\solve}[1]{\setlength{\parindent}{0cm}\textbf{\textit{Solution: }}\setlength{\parindent}{1cm}#1 \Qed}
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52
fs25/mathematische_methoden/notizen_koma_ruh_jirayu.aux
Normal file
52
fs25/mathematische_methoden/notizen_koma_ruh_jirayu.aux
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\relax
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\providecommand{\transparent@use}[1]{}
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\providecommand \babel@aux [2]{\global \let \babel@toc \@gobbletwo }
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\@nameuse{bbl@beforestart}
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\catcode `"\active
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\providecommand\hyper@newdestlabel[2]{}
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\providecommand\HyField@AuxAddToFields[1]{}
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\providecommand\HyField@AuxAddToCoFields[2]{}
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\providecommand\BKM@entry[2]{}
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\providecommand \oddpage@label [2]{}
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\babel@aux{ngerman}{}
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\BKM@entry{id=1,open,dest={746F632E73656374696F6E},srcline={29}}{5C3337365C3337375C303030495C3030306E5C303030685C303030615C3030306C5C303030745C303030735C303030765C303030655C303030725C3030307A5C303030655C303030695C303030635C303030685C3030306E5C303030695C30303073}
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\pgfsyspdfmark {pgfid1}{4025872}{43485761}
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\@writefile{toc}{\contentsline {chapter}{\numberline {1}Komplexe Zahlen}{2}{chapter.1}\protected@file@percent }
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\@writefile{lof}{\addvspace {10\p@ }}
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\@writefile{lot}{\addvspace {10\p@ }}
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\@writefile{loa}{\addvspace {10\p@ }}
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\@writefile{lot}{\addvspace {10\p@ }}
|
||||
\@writefile{loa}{\addvspace {10\p@ }}
|
||||
\@input{taylor_laurentreihen/reihen_entwicklung.aux}
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||||
\BKM@entry{id=5,open,dest={73656374696F6E2E332E31},srcline={1}}{5C3337365C3337375C303030335C3030302E5C303030315C3030305C3034305C303030525C303030655C303030695C303030685C303030655C3030306E5C3030302D5C303030455C3030306E5C303030745C303030775C303030695C303030635C303030685C3030306C5C303030755C3030306E5C30303067}
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265
fs25/mathematische_methoden/notizen_koma_ruh_jirayu.fdb_latexmk
Normal file
265
fs25/mathematische_methoden/notizen_koma_ruh_jirayu.fdb_latexmk
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INPUT ./notizen_koma_ruh_jirayu.toc
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INPUT taylor_laurentreihen/taylor_laurentreihen.tex
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INPUT taylor_laurentreihen/reihen_entwicklung.tex
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INPUT taylor_laurentreihen/reihen_entwicklung.tex
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INPUT ./fourier_analysis/fourier_analysis.tex
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INPUT fourier_analysis/fourier_analysis.tex
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INPUT ./fourier_analysis/fourier_analysis.tex
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INPUT fourier_analysis/fourier_analysis.tex
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INPUT ./laplace_transformation/laplace_transformation.tex
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INPUT laplace_transformation/laplace_transformation.tex
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fs25/mathematische_methoden/notizen_koma_ruh_jirayu.pdf
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fs25/mathematische_methoden/notizen_koma_ruh_jirayu.tex
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|
||||
\documentclass{report}
|
||||
|
||||
\def\papertitle{Notizen zu Mathematische Methoden (frühere Name: Komplexe Analysis)}
|
||||
|
||||
\def\theorytitle{Theorie}
|
||||
\def\corollarytitle{Korollar}
|
||||
\def\proposaltitle{Vorschlag}
|
||||
\def\claimtitle{Behauptung}
|
||||
\def\exercisetitle{Aufgabe}
|
||||
\def\exampletitle{Beispiel}
|
||||
\def\questiontitle{Frage}
|
||||
\def\wrongctitle{Falscher Konzept}
|
||||
\def\pagetitle{Seite}
|
||||
\def\pagetitle{Kapitel}
|
||||
|
||||
\input{preamble}
|
||||
\input{macros}
|
||||
\input{letterfonts}
|
||||
|
||||
\title{\huge{\papertitle}}
|
||||
\author{\huge{Jirayu Ruh}}
|
||||
\date{}
|
||||
|
||||
\begin{document}
|
||||
|
||||
\maketitle
|
||||
\newpage% or \cleardoublepage
|
||||
% \pdfbookmark[<level>]{<title>}{<dest>}
|
||||
\pdfbookmark[section]{\contentsname}{toc}
|
||||
\tableofcontents
|
||||
\pagebreak
|
||||
|
||||
\import{komplexe_zahlen}{komplexe_zahlen.tex}
|
||||
\import{komplexwertige_funktionen}{komplexwertige_funktionen.tex}
|
||||
\import{taylor_laurentreihen}{taylor_laurentreihen.tex}
|
||||
\import{fourier_analysis}{fourier_analysis.tex}
|
||||
\import{laplace_transformation}{laplace_transformation.tex}
|
||||
|
||||
\end{document}
|
||||
8
fs25/mathematische_methoden/notizen_koma_ruh_jirayu.toc
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8
fs25/mathematische_methoden/notizen_koma_ruh_jirayu.toc
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|
||||
\babel@toc {ngerman}{}\relax
|
||||
\contentsline {chapter}{\numberline {1}Komplexe Zahlen}{2}{chapter.1}%
|
||||
\contentsline {chapter}{\numberline {2}Komplexwertige Funktionen}{3}{chapter.2}%
|
||||
\contentsline {chapter}{\numberline {3}Taylor- und Laurentreihen}{4}{chapter.3}%
|
||||
\contentsline {section}{\numberline {3.1}Reihen-Entwichlung}{5}{section.3.1}%
|
||||
\contentsline {chapter}{\numberline {4}Fourier Analysis}{6}{chapter.4}%
|
||||
\contentsline {chapter}{\numberline {5}Laplace-Transformation}{7}{chapter.5}%
|
||||
\contentsfinish
|
||||
741
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|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% PACKAGE IMPORTS
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
|
||||
% TODO: Uncomment if the paper is in German
|
||||
\usepackage[ngerman]{babel}
|
||||
\usepackage[tmargin=2cm,rmargin=1in,lmargin=1in,margin=0.85in,bmargin=2cm,footskip=.2in]{geometry}
|
||||
\usepackage{amsmath,amsfonts,amsthm,amssymb,mathtools}
|
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\usepackage[varbb]{newpxmath}
|
||||
\usepackage{xfrac}
|
||||
\usepackage[makeroom]{cancel}
|
||||
\usepackage{mathtools}
|
||||
\usepackage{bookmark}
|
||||
\usepackage{enumitem}
|
||||
\usepackage{hyperref,theoremref}
|
||||
\hypersetup{
|
||||
pdftitle={Assignment},
|
||||
colorlinks=true, linkcolor=doc!90,
|
||||
bookmarksnumbered=true,
|
||||
bookmarksopen=true
|
||||
}
|
||||
\usepackage[most,many,breakable]{tcolorbox}
|
||||
\usepackage{xcolor}
|
||||
\usepackage{varwidth}
|
||||
\usepackage{varwidth}
|
||||
\usepackage{etoolbox}
|
||||
%\usepackage{authblk}
|
||||
\usepackage{nameref}
|
||||
\usepackage{multicol,array}
|
||||
\usepackage{tikz-cd}
|
||||
\usepackage[ruled,vlined,linesnumbered]{algorithm2e}
|
||||
\usepackage{comment} % enables the use of multi-line comments (\ifx \fi)
|
||||
\usepackage{import}
|
||||
\usepackage{xifthen}
|
||||
\usepackage{pdfpages}
|
||||
\usepackage{transparent}
|
||||
|
||||
\newcommand\mycommfont[1]{\footnotesize\ttfamily\textcolor{blue}{#1}}
|
||||
\SetCommentSty{mycommfont}
|
||||
\newcommand{\incfig}[1]{%
|
||||
\def\svgwidth{\columnwidth}
|
||||
\import{./figures/}{#1.pdf_tex}
|
||||
}
|
||||
|
||||
\usepackage{tikzsymbols}
|
||||
\renewcommand\qedsymbol{$\Laughey$}
|
||||
|
||||
|
||||
%\usepackage{import}
|
||||
%\usepackage{xifthen}
|
||||
%\usepackage{pdfpages}
|
||||
%\usepackage{transparent}
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% SELF MADE COLORS
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
|
||||
\definecolor{myg}{RGB}{56, 140, 70}
|
||||
\definecolor{myb}{RGB}{45, 111, 177}
|
||||
\definecolor{myr}{RGB}{199, 68, 64}
|
||||
\definecolor{mytheorembg}{HTML}{F2F2F9}
|
||||
\definecolor{mytheoremfr}{HTML}{00007B}
|
||||
\definecolor{mylenmabg}{HTML}{FFFAF8}
|
||||
\definecolor{mylenmafr}{HTML}{983b0f}
|
||||
\definecolor{mypropbg}{HTML}{f2fbfc}
|
||||
\definecolor{mypropfr}{HTML}{191971}
|
||||
\definecolor{myexamplebg}{HTML}{F2FBF8}
|
||||
\definecolor{myexamplefr}{HTML}{88D6D1}
|
||||
\definecolor{myexampleti}{HTML}{2A7F7F}
|
||||
\definecolor{mydefinitbg}{HTML}{E5E5FF}
|
||||
\definecolor{mydefinitfr}{HTML}{3F3FA3}
|
||||
\definecolor{notesgreen}{RGB}{0,162,0}
|
||||
\definecolor{myp}{RGB}{197, 92, 212}
|
||||
\definecolor{mygr}{HTML}{2C3338}
|
||||
\definecolor{myred}{RGB}{127,0,0}
|
||||
\definecolor{myyellow}{RGB}{169,121,69}
|
||||
\definecolor{myexercisebg}{HTML}{F2FBF8}
|
||||
\definecolor{myexercisefg}{HTML}{88D6D1}
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% TCOLORBOX SETUPS
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
|
||||
\setlength{\parindent}{0cm}
|
||||
|
||||
%================================
|
||||
% THEOREM BOX
|
||||
%================================
|
||||
|
||||
\tcbuselibrary{theorems,skins,hooks}
|
||||
\newtcbtheorem[number within=section]{Theorem}{\theorytitle}
|
||||
{%
|
||||
enhanced,
|
||||
breakable,
|
||||
colback = mytheorembg,
|
||||
frame hidden,
|
||||
boxrule = 0sp,
|
||||
borderline west = {2pt}{0pt}{mytheoremfr},
|
||||
sharp corners,
|
||||
detach title,
|
||||
before upper = \tcbtitle\par\smallskip,
|
||||
coltitle = mytheoremfr,
|
||||
fonttitle = \bfseries\sffamily,
|
||||
description font = \mdseries,
|
||||
separator sign none,
|
||||
segmentation style={solid, mytheoremfr},
|
||||
}
|
||||
{th}
|
||||
|
||||
\tcbuselibrary{theorems,skins,hooks}
|
||||
\newtcbtheorem[number within=chapter]{theorem}{\theorytitle}
|
||||
{%
|
||||
enhanced,
|
||||
breakable,
|
||||
colback = mytheorembg,
|
||||
frame hidden,
|
||||
boxrule = 0sp,
|
||||
borderline west = {2pt}{0pt}{mytheoremfr},
|
||||
sharp corners,
|
||||
detach title,
|
||||
before upper = \tcbtitle\par\smallskip,
|
||||
coltitle = mytheoremfr,
|
||||
fonttitle = \bfseries\sffamily,
|
||||
description font = \mdseries,
|
||||
separator sign none,
|
||||
segmentation style={solid, mytheoremfr},
|
||||
}
|
||||
{th}
|
||||
|
||||
|
||||
\tcbuselibrary{theorems,skins,hooks}
|
||||
\newtcolorbox{Theoremcon}
|
||||
{%
|
||||
enhanced
|
||||
,breakable
|
||||
,colback = mytheorembg
|
||||
,frame hidden
|
||||
,boxrule = 0sp
|
||||
,borderline west = {2pt}{0pt}{mytheoremfr}
|
||||
,sharp corners
|
||||
,description font = \mdseries
|
||||
,separator sign none
|
||||
}
|
||||
|
||||
|
||||
%================================
|
||||
% Corollery
|
||||
%================================
|
||||
|
||||
\tcbuselibrary{theorems,skins,hooks}
|
||||
\newtcbtheorem[number within=section]{Corollary}{\corollarytitle}
|
||||
{%
|
||||
enhanced
|
||||
,breakable
|
||||
,colback = myp!10
|
||||
,frame hidden
|
||||
,boxrule = 0sp
|
||||
,borderline west = {2pt}{0pt}{myp!85!black}
|
||||
,sharp corners
|
||||
,detach title
|
||||
,before upper = \tcbtitle\par\smallskip
|
||||
,coltitle = myp!85!black
|
||||
,fonttitle = \bfseries\sffamily
|
||||
,description font = \mdseries
|
||||
,separator sign none
|
||||
,segmentation style={solid, myp!85!black}
|
||||
}
|
||||
{th}
|
||||
\tcbuselibrary{theorems,skins,hooks}
|
||||
\newtcbtheorem[number within=chapter]{corollary}{\corollarytitle}
|
||||
{%
|
||||
enhanced
|
||||
,breakable
|
||||
,colback = myp!10
|
||||
,frame hidden
|
||||
,boxrule = 0sp
|
||||
,borderline west = {2pt}{0pt}{myp!85!black}
|
||||
,sharp corners
|
||||
,detach title
|
||||
,before upper = \tcbtitle\par\smallskip
|
||||
,coltitle = myp!85!black
|
||||
,fonttitle = \bfseries\sffamily
|
||||
,description font = \mdseries
|
||||
,separator sign none
|
||||
,segmentation style={solid, myp!85!black}
|
||||
}
|
||||
{th}
|
||||
|
||||
|
||||
%================================
|
||||
% LENMA
|
||||
%================================
|
||||
|
||||
\tcbuselibrary{theorems,skins,hooks}
|
||||
\newtcbtheorem[number within=section]{Lenma}{Lenma}
|
||||
{%
|
||||
enhanced,
|
||||
breakable,
|
||||
colback = mylenmabg,
|
||||
frame hidden,
|
||||
boxrule = 0sp,
|
||||
borderline west = {2pt}{0pt}{mylenmafr},
|
||||
sharp corners,
|
||||
detach title,
|
||||
before upper = \tcbtitle\par\smallskip,
|
||||
coltitle = mylenmafr,
|
||||
fonttitle = \bfseries\sffamily,
|
||||
description font = \mdseries,
|
||||
separator sign none,
|
||||
segmentation style={solid, mylenmafr},
|
||||
}
|
||||
{th}
|
||||
|
||||
\tcbuselibrary{theorems,skins,hooks}
|
||||
\newtcbtheorem[number within=chapter]{lenma}{Lenma}
|
||||
{%
|
||||
enhanced,
|
||||
breakable,
|
||||
colback = mylenmabg,
|
||||
frame hidden,
|
||||
boxrule = 0sp,
|
||||
borderline west = {2pt}{0pt}{mylenmafr},
|
||||
sharp corners,
|
||||
detach title,
|
||||
before upper = \tcbtitle\par\smallskip,
|
||||
coltitle = mylenmafr,
|
||||
fonttitle = \bfseries\sffamily,
|
||||
description font = \mdseries,
|
||||
separator sign none,
|
||||
segmentation style={solid, mylenmafr},
|
||||
}
|
||||
{th}
|
||||
|
||||
|
||||
%================================
|
||||
% PROPOSITION
|
||||
%================================
|
||||
|
||||
\tcbuselibrary{theorems,skins,hooks}
|
||||
\newtcbtheorem[number within=section]{Prop}{\proposaltitle}
|
||||
{%
|
||||
enhanced,
|
||||
breakable,
|
||||
colback = mypropbg,
|
||||
frame hidden,
|
||||
boxrule = 0sp,
|
||||
borderline west = {2pt}{0pt}{mypropfr},
|
||||
sharp corners,
|
||||
detach title,
|
||||
before upper = \tcbtitle\par\smallskip,
|
||||
coltitle = mypropfr,
|
||||
fonttitle = \bfseries\sffamily,
|
||||
description font = \mdseries,
|
||||
separator sign none,
|
||||
segmentation style={solid, mypropfr},
|
||||
}
|
||||
{th}
|
||||
|
||||
\tcbuselibrary{theorems,skins,hooks}
|
||||
\newtcbtheorem[number within=chapter]{prop}{\proposaltitle}
|
||||
{%
|
||||
enhanced,
|
||||
breakable,
|
||||
colback = mypropbg,
|
||||
frame hidden,
|
||||
boxrule = 0sp,
|
||||
borderline west = {2pt}{0pt}{mypropfr},
|
||||
sharp corners,
|
||||
detach title,
|
||||
before upper = \tcbtitle\par\smallskip,
|
||||
coltitle = mypropfr,
|
||||
fonttitle = \bfseries\sffamily,
|
||||
description font = \mdseries,
|
||||
separator sign none,
|
||||
segmentation style={solid, mypropfr},
|
||||
}
|
||||
{th}
|
||||
|
||||
|
||||
%================================
|
||||
% CLAIM
|
||||
%================================
|
||||
|
||||
\tcbuselibrary{theorems,skins,hooks}
|
||||
\newtcbtheorem[number within=section]{claim}{\claimtitle}
|
||||
{%
|
||||
enhanced
|
||||
,breakable
|
||||
,colback = myg!10
|
||||
,frame hidden
|
||||
,boxrule = 0sp
|
||||
,borderline west = {2pt}{0pt}{myg}
|
||||
,sharp corners
|
||||
,detach title
|
||||
,before upper = \tcbtitle\par\smallskip
|
||||
,coltitle = myg!85!black
|
||||
,fonttitle = \bfseries\sffamily
|
||||
,description font = \mdseries
|
||||
,separator sign none
|
||||
,segmentation style={solid, myg!85!black}
|
||||
}
|
||||
{th}
|
||||
|
||||
|
||||
|
||||
%================================
|
||||
% Exercise
|
||||
%================================
|
||||
|
||||
\tcbuselibrary{theorems,skins,hooks}
|
||||
\newtcbtheorem[number within=section]{Exercise}{\exercisetitle}
|
||||
{%
|
||||
enhanced,
|
||||
breakable,
|
||||
colback = myexercisebg,
|
||||
frame hidden,
|
||||
boxrule = 0sp,
|
||||
borderline west = {2pt}{0pt}{myexercisefg},
|
||||
sharp corners,
|
||||
detach title,
|
||||
before upper = \tcbtitle\par\smallskip,
|
||||
coltitle = myexercisefg,
|
||||
fonttitle = \bfseries\sffamily,
|
||||
description font = \mdseries,
|
||||
separator sign none,
|
||||
segmentation style={solid, myexercisefg},
|
||||
}
|
||||
{th}
|
||||
|
||||
\tcbuselibrary{theorems,skins,hooks}
|
||||
\newtcbtheorem[number within=chapter]{exercise}{\exercisetitle}
|
||||
{%
|
||||
enhanced,
|
||||
breakable,
|
||||
colback = myexercisebg,
|
||||
frame hidden,
|
||||
boxrule = 0sp,
|
||||
borderline west = {2pt}{0pt}{myexercisefg},
|
||||
sharp corners,
|
||||
detach title,
|
||||
before upper = \tcbtitle\par\smallskip,
|
||||
coltitle = myexercisefg,
|
||||
fonttitle = \bfseries\sffamily,
|
||||
description font = \mdseries,
|
||||
separator sign none,
|
||||
segmentation style={solid, myexercisefg},
|
||||
}
|
||||
{th}
|
||||
|
||||
%================================
|
||||
% EXAMPLE BOX
|
||||
%================================
|
||||
|
||||
\newtcbtheorem[number within=section]{Example}{\exampletitle}
|
||||
{%
|
||||
colback = myexamplebg
|
||||
,breakable
|
||||
,colframe = myexamplefr
|
||||
,coltitle = myexampleti
|
||||
,boxrule = 1pt
|
||||
,sharp corners
|
||||
,detach title
|
||||
,before upper=\tcbtitle\par\smallskip
|
||||
,fonttitle = \bfseries
|
||||
,description font = \mdseries
|
||||
,separator sign none
|
||||
,description delimiters parenthesis
|
||||
}
|
||||
{ex}
|
||||
|
||||
\newtcbtheorem[number within=chapter]{example}{\exampletitle}
|
||||
{%
|
||||
colback = myexamplebg
|
||||
,breakable
|
||||
,colframe = myexamplefr
|
||||
,coltitle = myexampleti
|
||||
,boxrule = 1pt
|
||||
,sharp corners
|
||||
,detach title
|
||||
,before upper=\tcbtitle\par\smallskip
|
||||
,fonttitle = \bfseries
|
||||
,description font = \mdseries
|
||||
,separator sign none
|
||||
,description delimiters parenthesis
|
||||
}
|
||||
{ex}
|
||||
|
||||
%================================
|
||||
% DEFINITION BOX
|
||||
%================================
|
||||
|
||||
\newtcbtheorem[number within=section]{Definition}{Definition}{enhanced,
|
||||
before skip=2mm,after skip=2mm, colback=red!5,colframe=red!80!black,boxrule=0.5mm,
|
||||
attach boxed title to top left={xshift=1cm,yshift*=1mm-\tcboxedtitleheight}, varwidth boxed title*=-3cm,
|
||||
boxed title style={frame code={
|
||||
\path[fill=tcbcolback]
|
||||
([yshift=-1mm,xshift=-1mm]frame.north west)
|
||||
arc[start angle=0,end angle=180,radius=1mm]
|
||||
([yshift=-1mm,xshift=1mm]frame.north east)
|
||||
arc[start angle=180,end angle=0,radius=1mm];
|
||||
\path[left color=tcbcolback!60!black,right color=tcbcolback!60!black,
|
||||
middle color=tcbcolback!80!black]
|
||||
([xshift=-2mm]frame.north west) -- ([xshift=2mm]frame.north east)
|
||||
[rounded corners=1mm]-- ([xshift=1mm,yshift=-1mm]frame.north east)
|
||||
-- (frame.south east) -- (frame.south west)
|
||||
-- ([xshift=-1mm,yshift=-1mm]frame.north west)
|
||||
[sharp corners]-- cycle;
|
||||
},interior engine=empty,
|
||||
},
|
||||
fonttitle=\bfseries,
|
||||
title={#2},#1}{def}
|
||||
\newtcbtheorem[number within=chapter]{definition}{Definition}{enhanced,
|
||||
before skip=2mm,after skip=2mm, colback=red!5,colframe=red!80!black,boxrule=0.5mm,
|
||||
attach boxed title to top left={xshift=1cm,yshift*=1mm-\tcboxedtitleheight}, varwidth boxed title*=-3cm,
|
||||
boxed title style={frame code={
|
||||
\path[fill=tcbcolback]
|
||||
([yshift=-1mm,xshift=-1mm]frame.north west)
|
||||
arc[start angle=0,end angle=180,radius=1mm]
|
||||
([yshift=-1mm,xshift=1mm]frame.north east)
|
||||
arc[start angle=180,end angle=0,radius=1mm];
|
||||
\path[left color=tcbcolback!60!black,right color=tcbcolback!60!black,
|
||||
middle color=tcbcolback!80!black]
|
||||
([xshift=-2mm]frame.north west) -- ([xshift=2mm]frame.north east)
|
||||
[rounded corners=1mm]-- ([xshift=1mm,yshift=-1mm]frame.north east)
|
||||
-- (frame.south east) -- (frame.south west)
|
||||
-- ([xshift=-1mm,yshift=-1mm]frame.north west)
|
||||
[sharp corners]-- cycle;
|
||||
},interior engine=empty,
|
||||
},
|
||||
fonttitle=\bfseries,
|
||||
title={#2},#1}{def}
|
||||
|
||||
|
||||
|
||||
%================================
|
||||
% Solution BOX
|
||||
%================================
|
||||
|
||||
\makeatletter
|
||||
\newtcbtheorem{question}{\questiontitle}{enhanced,
|
||||
breakable,
|
||||
colback=white,
|
||||
colframe=myb!80!black,
|
||||
attach boxed title to top left={yshift*=-\tcboxedtitleheight},
|
||||
fonttitle=\bfseries,
|
||||
title={#2},
|
||||
boxed title size=title,
|
||||
boxed title style={%
|
||||
sharp corners,
|
||||
rounded corners=northwest,
|
||||
colback=tcbcolframe,
|
||||
boxrule=0pt,
|
||||
},
|
||||
underlay boxed title={%
|
||||
\path[fill=tcbcolframe] (title.south west)--(title.south east)
|
||||
to[out=0, in=180] ([xshift=5mm]title.east)--
|
||||
(title.center-|frame.east)
|
||||
[rounded corners=\kvtcb@arc] |-
|
||||
(frame.north) -| cycle;
|
||||
},
|
||||
#1
|
||||
}{def}
|
||||
\makeatother
|
||||
|
||||
%================================
|
||||
% SOLUTION BOX
|
||||
%================================
|
||||
|
||||
\makeatletter
|
||||
\newtcolorbox{solution}{enhanced,
|
||||
breakable,
|
||||
colback=white,
|
||||
colframe=myg!80!black,
|
||||
attach boxed title to top left={yshift*=-\tcboxedtitleheight},
|
||||
title=Solution,
|
||||
boxed title size=title,
|
||||
boxed title style={%
|
||||
sharp corners,
|
||||
rounded corners=northwest,
|
||||
colback=tcbcolframe,
|
||||
boxrule=0pt,
|
||||
},
|
||||
underlay boxed title={%
|
||||
\path[fill=tcbcolframe] (title.south west)--(title.south east)
|
||||
to[out=0, in=180] ([xshift=5mm]title.east)--
|
||||
(title.center-|frame.east)
|
||||
[rounded corners=\kvtcb@arc] |-
|
||||
(frame.north) -| cycle;
|
||||
},
|
||||
}
|
||||
\makeatother
|
||||
|
||||
%================================
|
||||
% Question BOX
|
||||
%================================
|
||||
|
||||
\makeatletter
|
||||
\newtcbtheorem{qstion}{\questiontitle}{enhanced,
|
||||
breakable,
|
||||
colback=white,
|
||||
colframe=mygr,
|
||||
attach boxed title to top left={yshift*=-\tcboxedtitleheight},
|
||||
fonttitle=\bfseries,
|
||||
title={#2},
|
||||
boxed title size=title,
|
||||
boxed title style={%
|
||||
sharp corners,
|
||||
rounded corners=northwest,
|
||||
colback=tcbcolframe,
|
||||
boxrule=0pt,
|
||||
},
|
||||
underlay boxed title={%
|
||||
\path[fill=tcbcolframe] (title.south west)--(title.south east)
|
||||
to[out=0, in=180] ([xshift=5mm]title.east)--
|
||||
(title.center-|frame.east)
|
||||
[rounded corners=\kvtcb@arc] |-
|
||||
(frame.north) -| cycle;
|
||||
},
|
||||
#1
|
||||
}{def}
|
||||
\makeatother
|
||||
|
||||
\newtcbtheorem[number within=chapter]{wconc}{\wrongctitle}{
|
||||
breakable,
|
||||
enhanced,
|
||||
colback=white,
|
||||
colframe=myr,
|
||||
arc=0pt,
|
||||
outer arc=0pt,
|
||||
fonttitle=\bfseries\sffamily\large,
|
||||
colbacktitle=myr,
|
||||
attach boxed title to top left={},
|
||||
boxed title style={
|
||||
enhanced,
|
||||
skin=enhancedfirst jigsaw,
|
||||
arc=3pt,
|
||||
bottom=0pt,
|
||||
interior style={fill=myr}
|
||||
},
|
||||
#1
|
||||
}{def}
|
||||
|
||||
|
||||
|
||||
%================================
|
||||
% NOTE BOX
|
||||
%================================
|
||||
|
||||
\usetikzlibrary{arrows,calc,shadows.blur}
|
||||
\tcbuselibrary{skins}
|
||||
\newtcolorbox{note}[1][]{%
|
||||
enhanced jigsaw,
|
||||
colback=gray!20!white,%
|
||||
colframe=gray!80!black,
|
||||
size=small,
|
||||
boxrule=1pt,
|
||||
title=\textbf{Bemerkung:-},
|
||||
halign title=flush center,
|
||||
coltitle=black,
|
||||
breakable,
|
||||
drop shadow=black!50!white,
|
||||
attach boxed title to top left={xshift=1cm,yshift=-\tcboxedtitleheight/2,yshifttext=-\tcboxedtitleheight/2},
|
||||
minipage boxed title=2.5cm,
|
||||
boxed title style={%
|
||||
colback=white,
|
||||
size=fbox,
|
||||
boxrule=1pt,
|
||||
boxsep=2pt,
|
||||
underlay={%
|
||||
\coordinate (dotA) at ($(interior.west) + (-0.5pt,0)$);
|
||||
\coordinate (dotB) at ($(interior.east) + (0.5pt,0)$);
|
||||
\begin{scope}
|
||||
\clip (interior.north west) rectangle ([xshift=3ex]interior.east);
|
||||
\filldraw [white, blur shadow={shadow opacity=60, shadow yshift=-.75ex}, rounded corners=2pt] (interior.north west) rectangle (interior.south east);
|
||||
\end{scope}
|
||||
\begin{scope}[gray!80!black]
|
||||
\fill (dotA) circle (2pt);
|
||||
\fill (dotB) circle (2pt);
|
||||
\end{scope}
|
||||
},
|
||||
},
|
||||
#1,
|
||||
}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% SELF MADE COMMANDS
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
|
||||
|
||||
\newcommand{\thm}[2]{\begin{Theorem}{#1}{}#2\end{Theorem}}
|
||||
\newcommand{\cor}[2]{\begin{Corollary}{#1}{}#2\end{Corollary}}
|
||||
\newcommand{\mlenma}[2]{\begin{Lenma}{#1}{}#2\end{Lenma}}
|
||||
\newcommand{\mprop}[2]{\begin{Prop}{#1}{}#2\end{Prop}}
|
||||
\newcommand{\clm}[3]{\begin{claim}{#1}{#2}#3\end{claim}}
|
||||
\newcommand{\wc}[2]{\begin{wconc}{#1}{}\setlength{\parindent}{1cm}#2\end{wconc}}
|
||||
\newcommand{\thmcon}[1]{\begin{Theoremcon}{#1}\end{Theoremcon}}
|
||||
\newcommand{\ex}[2]{\begin{Example}{#1}{}#2\end{Example}}
|
||||
\newcommand{\dfn}[2]{\begin{Definition}[colbacktitle=red!75!black]{#1}{}#2\end{Definition}}
|
||||
\newcommand{\dfnc}[2]{\begin{definition}[colbacktitle=red!75!black]{#1}{}#2\end{definition}}
|
||||
\newcommand{\qs}[2]{\begin{question}{#1}{}#2\end{question}}
|
||||
\newcommand{\pf}[2]{\begin{myproof}[#1]#2\end{myproof}}
|
||||
\newcommand{\nt}[1]{\begin{note}#1\end{note}}
|
||||
|
||||
\newcommand*\circled[1]{\tikz[baseline=(char.base)]{
|
||||
Wrong Concept \node[shape=circle,draw,inner sep=1pt] (char) {#1};}}
|
||||
\newcommand\getcurrentref[1]{%
|
||||
\ifnumequal{\value{#1}}{0}
|
||||
{??}
|
||||
{\the\value{#1}}%
|
||||
}
|
||||
\newcommand{\getCurrentSectionNumber}{\getcurrentref{section}}
|
||||
\newenvironment{myproof}[1][\proofname]{%
|
||||
\proof[\bfseries #1: ]%
|
||||
}{\endproof}
|
||||
|
||||
\newcommand{\mclm}[2]{\begin{myclaim}[#1]#2\end{myclaim}}
|
||||
\newenvironment{myclaim}[1][\claimname]{\proof[\bfseries #1: ]}{}
|
||||
|
||||
\newcounter{mylabelcounter}
|
||||
|
||||
\makeatletter
|
||||
\newcommand{\setword}[2]{%
|
||||
\phantomsection
|
||||
#1\def\@currentlabel{\unexpanded{#1}}\label{#2}%
|
||||
}
|
||||
\makeatother
|
||||
|
||||
|
||||
|
||||
|
||||
\tikzset{
|
||||
symbol/.style={
|
||||
draw=none,
|
||||
every to/.append style={
|
||||
edge node={node [sloped, allow upside down, auto=false]{$#1$}}}
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
% deliminators
|
||||
\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}
|
||||
\DeclarePairedDelimiter{\norm}{\lVert}{\rVert}
|
||||
|
||||
\DeclarePairedDelimiter{\ceil}{\lceil}{\rceil}
|
||||
\DeclarePairedDelimiter{\floor}{\lfloor}{\rfloor}
|
||||
\DeclarePairedDelimiter{\round}{\lfloor}{\rceil}
|
||||
|
||||
\newsavebox\diffdbox
|
||||
\newcommand{\slantedromand}{{\mathpalette\makesl{d}}}
|
||||
\newcommand{\makesl}[2]{%
|
||||
\begingroup
|
||||
\sbox{\diffdbox}{$\mathsurround=0pt#1\mathrm{#2}$}%
|
||||
\pdfsave
|
||||
\pdfsetmatrix{1 0 0.2 1}%
|
||||
\rlap{\usebox{\diffdbox}}%
|
||||
\pdfrestore
|
||||
\hskip\wd\diffdbox
|
||||
\endgroup
|
||||
}
|
||||
\newcommand{\dd}[1][]{\ensuremath{\mathop{}\!\ifstrempty{#1}{%
|
||||
\slantedromand\@ifnextchar^{\hspace{0.2ex}}{\hspace{0.1ex}}}%
|
||||
{\slantedromand\hspace{0.2ex}^{#1}}}}
|
||||
\ProvideDocumentCommand\dv{o m g}{%
|
||||
\ensuremath{%
|
||||
\IfValueTF{#3}{%
|
||||
\IfNoValueTF{#1}{%
|
||||
\frac{\dd #2}{\dd #3}%
|
||||
}{%
|
||||
\frac{\dd^{#1} #2}{\dd #3^{#1}}%
|
||||
}%
|
||||
}{%
|
||||
\IfNoValueTF{#1}{%
|
||||
\frac{\dd}{\dd #2}%
|
||||
}{%
|
||||
\frac{\dd^{#1}}{\dd #2^{#1}}%
|
||||
}%
|
||||
}%
|
||||
}%
|
||||
}
|
||||
\providecommand*{\pdv}[3][]{\frac{\partial^{#1}#2}{\partial#3^{#1}}}
|
||||
% - others
|
||||
\DeclareMathOperator{\Lap}{\mathcal{L}}
|
||||
\DeclareMathOperator{\Var}{Var} % varience
|
||||
\DeclareMathOperator{\Cov}{Cov} % covarience
|
||||
\DeclareMathOperator{\E}{E} % expected
|
||||
|
||||
% Since the amsthm package isn't loaded
|
||||
|
||||
% I prefer the slanted \leq
|
||||
\let\oldleq\leq % save them in case they're every wanted
|
||||
\let\oldgeq\geq
|
||||
\renewcommand{\leq}{\leqslant}
|
||||
\renewcommand{\geq}{\geqslant}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% TABLE OF CONTENTS
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
|
||||
\usepackage{tikz}
|
||||
\definecolor{doc}{RGB}{0,60,110}
|
||||
\usepackage{titletoc}
|
||||
\contentsmargin{0cm}
|
||||
\titlecontents{chapter}[3.7pc]
|
||||
{\addvspace{30pt}%
|
||||
\begin{tikzpicture}[remember picture, overlay]%
|
||||
\draw[fill=doc!60,draw=doc!60] (-7,-.1) rectangle (-0.9,.5);%
|
||||
\pgftext[left,x=-3.5cm,y=0.2cm]{\color{white}\Large\sc\bfseries Kapitel \thecontentslabel};%
|
||||
\end{tikzpicture}\color{doc!60}\large\sc\bfseries}%
|
||||
{}
|
||||
{}
|
||||
{\;\titlerule\;\large\sc\bfseries Seite \thecontentspage
|
||||
\begin{tikzpicture}[remember picture, overlay]
|
||||
\draw[fill=doc!60,draw=doc!60] (2pt,0) rectangle (4,0.1pt);
|
||||
\end{tikzpicture}}%
|
||||
\titlecontents{section}[3.7pc]
|
||||
{\addvspace{2pt}}
|
||||
{\contentslabel[\thecontentslabel]{2pc}}
|
||||
{}
|
||||
{\hfill\small \thecontentspage}
|
||||
[]
|
||||
\titlecontents*{subsection}[3.7pc]
|
||||
{\addvspace{-1pt}\small}
|
||||
{}
|
||||
{}
|
||||
{\ --- \small\thecontentspage}
|
||||
[ \textbullet\ ][]
|
||||
|
||||
\makeatletter
|
||||
\renewcommand{\tableofcontents}{%
|
||||
\chapter*{%
|
||||
\vspace*{-20\p@}%
|
||||
\begin{tikzpicture}[remember picture, overlay]%
|
||||
\pgftext[right,x=15cm,y=0.2cm]{\color{doc!60}\Huge\sc\bfseries \contentsname};%
|
||||
\draw[fill=doc!60,draw=doc!60] (13,-.75) rectangle (20,1);%
|
||||
\clip (13,-.75) rectangle (20,1);
|
||||
\pgftext[right,x=15cm,y=0.2cm]{\color{white}\Huge\sc\bfseries \contentsname};%
|
||||
\end{tikzpicture}}%
|
||||
\@starttoc{toc}}
|
||||
\makeatother
|
||||
61
fs25/mathematische_methoden/reihen_entwicklung.aux
Normal file
61
fs25/mathematische_methoden/reihen_entwicklung.aux
Normal file
@@ -0,0 +1,61 @@
|
||||
\relax
|
||||
\providecommand{\transparent@use}[1]{}
|
||||
\providecommand\hyper@newdestlabel[2]{}
|
||||
\@setckpt{reihen_entwicklung}{
|
||||
\setcounter{page}{5}
|
||||
\setcounter{equation}{0}
|
||||
\setcounter{enumi}{0}
|
||||
\setcounter{enumii}{0}
|
||||
\setcounter{enumiii}{0}
|
||||
\setcounter{enumiv}{0}
|
||||
\setcounter{footnote}{0}
|
||||
\setcounter{mpfootnote}{0}
|
||||
\setcounter{part}{0}
|
||||
\setcounter{chapter}{3}
|
||||
\setcounter{section}{0}
|
||||
\setcounter{subsection}{0}
|
||||
\setcounter{subsubsection}{0}
|
||||
\setcounter{paragraph}{0}
|
||||
\setcounter{subparagraph}{0}
|
||||
\setcounter{figure}{0}
|
||||
\setcounter{table}{0}
|
||||
\setcounter{parentequation}{0}
|
||||
\setcounter{section@level}{0}
|
||||
\setcounter{Item}{0}
|
||||
\setcounter{Hfootnote}{0}
|
||||
\setcounter{bookmark@seq@number}{0}
|
||||
\setcounter{tcbbreakpart}{0}
|
||||
\setcounter{tcblayer}{0}
|
||||
\setcounter{tcolorbox@number}{0}
|
||||
\setcounter{tcbrastercolumn}{1}
|
||||
\setcounter{tcbrasterrow}{1}
|
||||
\setcounter{tcbrasternum}{1}
|
||||
\setcounter{tcbraster}{0}
|
||||
\setcounter{lstnumber}{1}
|
||||
\setcounter{tcblisting}{0}
|
||||
\setcounter{AlgoLine}{0}
|
||||
\setcounter{algocfline}{0}
|
||||
\setcounter{algocfproc}{0}
|
||||
\setcounter{algocf}{0}
|
||||
\setcounter{AM@survey}{0}
|
||||
\setcounter{tcb@cnt@Theorem}{0}
|
||||
\setcounter{tcb@cnt@theorem}{0}
|
||||
\setcounter{tcb@cnt@Corollary}{0}
|
||||
\setcounter{tcb@cnt@corollary}{0}
|
||||
\setcounter{tcb@cnt@Lenma}{0}
|
||||
\setcounter{tcb@cnt@lenma}{0}
|
||||
\setcounter{tcb@cnt@Prop}{0}
|
||||
\setcounter{tcb@cnt@prop}{0}
|
||||
\setcounter{tcb@cnt@claim}{0}
|
||||
\setcounter{tcb@cnt@Exercise}{0}
|
||||
\setcounter{tcb@cnt@exercise}{0}
|
||||
\setcounter{tcb@cnt@Example}{0}
|
||||
\setcounter{tcb@cnt@example}{0}
|
||||
\setcounter{tcb@cnt@Definition}{0}
|
||||
\setcounter{tcb@cnt@definition}{0}
|
||||
\setcounter{tcb@cnt@question}{0}
|
||||
\setcounter{tcb@cnt@qstion}{0}
|
||||
\setcounter{tcb@cnt@wconc}{0}
|
||||
\setcounter{mylabelcounter}{0}
|
||||
\setcounter{lstlisting}{0}
|
||||
}
|
||||
@@ -0,0 +1,62 @@
|
||||
\relax
|
||||
\providecommand{\transparent@use}[1]{}
|
||||
\providecommand\hyper@newdestlabel[2]{}
|
||||
\@writefile{toc}{\contentsline {section}{\numberline {3.1}Reihen-Entwichlung}{5}{section.3.1}\protected@file@percent }
|
||||
\@setckpt{taylor_laurentreihen/reihen_entwicklung}{
|
||||
\setcounter{page}{6}
|
||||
\setcounter{equation}{0}
|
||||
\setcounter{enumi}{0}
|
||||
\setcounter{enumii}{0}
|
||||
\setcounter{enumiii}{0}
|
||||
\setcounter{enumiv}{0}
|
||||
\setcounter{footnote}{0}
|
||||
\setcounter{mpfootnote}{0}
|
||||
\setcounter{part}{0}
|
||||
\setcounter{chapter}{3}
|
||||
\setcounter{section}{1}
|
||||
\setcounter{subsection}{0}
|
||||
\setcounter{subsubsection}{0}
|
||||
\setcounter{paragraph}{0}
|
||||
\setcounter{subparagraph}{0}
|
||||
\setcounter{figure}{0}
|
||||
\setcounter{table}{0}
|
||||
\setcounter{parentequation}{0}
|
||||
\setcounter{section@level}{1}
|
||||
\setcounter{Item}{0}
|
||||
\setcounter{Hfootnote}{0}
|
||||
\setcounter{bookmark@seq@number}{0}
|
||||
\setcounter{tcbbreakpart}{0}
|
||||
\setcounter{tcblayer}{0}
|
||||
\setcounter{tcolorbox@number}{0}
|
||||
\setcounter{tcbrastercolumn}{1}
|
||||
\setcounter{tcbrasterrow}{1}
|
||||
\setcounter{tcbrasternum}{1}
|
||||
\setcounter{tcbraster}{0}
|
||||
\setcounter{lstnumber}{1}
|
||||
\setcounter{tcblisting}{0}
|
||||
\setcounter{AlgoLine}{0}
|
||||
\setcounter{algocfline}{0}
|
||||
\setcounter{algocfproc}{0}
|
||||
\setcounter{algocf}{0}
|
||||
\setcounter{AM@survey}{0}
|
||||
\setcounter{tcb@cnt@Theorem}{0}
|
||||
\setcounter{tcb@cnt@theorem}{0}
|
||||
\setcounter{tcb@cnt@Corollary}{0}
|
||||
\setcounter{tcb@cnt@corollary}{0}
|
||||
\setcounter{tcb@cnt@Lenma}{0}
|
||||
\setcounter{tcb@cnt@lenma}{0}
|
||||
\setcounter{tcb@cnt@Prop}{0}
|
||||
\setcounter{tcb@cnt@prop}{0}
|
||||
\setcounter{tcb@cnt@claim}{0}
|
||||
\setcounter{tcb@cnt@Exercise}{0}
|
||||
\setcounter{tcb@cnt@exercise}{0}
|
||||
\setcounter{tcb@cnt@Example}{0}
|
||||
\setcounter{tcb@cnt@example}{0}
|
||||
\setcounter{tcb@cnt@Definition}{0}
|
||||
\setcounter{tcb@cnt@definition}{0}
|
||||
\setcounter{tcb@cnt@question}{0}
|
||||
\setcounter{tcb@cnt@qstion}{0}
|
||||
\setcounter{tcb@cnt@wconc}{0}
|
||||
\setcounter{mylabelcounter}{0}
|
||||
\setcounter{lstlisting}{0}
|
||||
}
|
||||
@@ -0,0 +1,3 @@
|
||||
\section{Reihen-Entwichlung}
|
||||
|
||||
|
||||
@@ -0,0 +1,3 @@
|
||||
\chapter{Taylor- und Laurentreihen}
|
||||
|
||||
\include{reihen_entwicklung.tex}
|
||||
Reference in New Issue
Block a user