175 lines
5.1 KiB
TeX
175 lines
5.1 KiB
TeX
\documentclass[11pt]{report}
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\usepackage{amsmath, amssymb, amstext, physics}
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\usepackage{amsthm, stackrel, xifthen, mathtools, graphicx}
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\usepackage[makeroom]{cancel}
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\usepackage{hyperref, cleveref}
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\usepackage{enumerate, subcaption}
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\usepackage[shortlabels]{enumitem}
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\usepackage{multicol}
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\usepackage{tikz, pgfplots}
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\usepackage{kbordermatrix}
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\usepackage{fancyhdr}
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\usepackage{pdfpages}
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\usetikzlibrary{calc,trees,positioning,arrows,fit,shapes,angles,patterns}
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\graphicspath{assets}
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\usepackage{color}
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\usepackage{hyperref}
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\hypersetup{
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colorlinks,
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citecolor=black,
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filecolor=black,
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linkcolor=black,
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urlcolor=black
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}
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\usepackage[
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type={CC},
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modifier={by-sa},
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version={4.0},
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]{doclicense}
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\usepackage{subfiles}
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\DeclareMathOperator{\spn}{span}
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%\DeclareMathOperator{\dim}{dim}
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\DeclareMathOperator{\sgn}{sgn}
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\newcommand{\natn}{\mathbb{N}}
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\newcommand{\intn}{\mathbb{Z}}
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\newcommand{\ratn}{\mathbb{Q}}
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\newcommand{\realn}{\mathbb{R}}
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\newcommand{\cmpln}{\mathbb{C}}
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\newcommand{\field}{\mathbb{K}}
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\newcommand{\rec}[1]{\frac{1}{#1}}
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\newcommand{\idf}{\text{id}}
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\newcommand{\inv}[1]{{#1}^{-1}}
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\newcommand{\eqlbl}[1]{\stackrel{\text{#1}}{=}}
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\newcommand{\implbl}[1]{\overset{\text{#1}}{\implies}}
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\newcommand{\imag}{\imaginary}
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\newcommand{\limes}[2]{\lim_{#1 \rightarrow #2}}
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\newcommand{\limn}{\lim_{n \rightarrow \infty}}
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\newcommand{\limk}{\lim_{k \rightarrow \infty}}
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\newcommand{\limz}{\lim_{n \rightarrow 0}}
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\newcommand{\limsupn}{\limsup_{n \rightarrow \infty}}
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\newcommand{\liminfn}{\liminf_{n \rightarrow \infty}}
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\newcommand{\seq}[1]{\left(#1_n\right)}
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\newcommand{\nseqdef}[1]{\seq{#1} \subset \natn}
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\newcommand{\rseqdef}[1]{\seq{#1} \subset \realn}
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\newcommand{\cseqdef}[1]{\seq{#1} \subset \cmpln}
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\newcommand{\rcseqdef}[1]{\seq{#1} \subset \realn \text{ (or } \cmpln \text{)}}
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\newcommand{\anyseqdef}[2][x]{\seq{#1} \subset #2}
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\newcommand{\series}[2][\infty]{\sum_{#2 = 1}^{#1}}
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\newcommand{\finite}{\text{ finite}}
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\newcommand{\conj}[1]{\overline{#1}}
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\newcommand{\must}[1][=]{\stackrel{!}{#1}}
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\newcommand{\metric}[1][X]{(#1, d)}
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\newcommand{\dnorm}{\norm{\cdot}}
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\newcommand{\normed}[1][V]{(#1, \dnorm)}
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\newcommand{\supnorm}[1]{\norm{#1}_{\infty}}
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\newcommand{\cnorm}[2][1]{\norm{#2}_{C_{#1}}}
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\newcommand{\oball}[1][\epsilon]{B_{#1}}
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\newcommand{\cball}[1][\epsilon]{K_{#1}}
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\newcommand{\Oball}{\oball[r]}
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\newcommand{\Cball}{\cball[r]}
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\newcommand{\oline}[1][{x,y}]{S_{#1}}
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\renewcommand{\cline}[1][{x,y}]{\overline{S_{#1}}}
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\newcommand{\interior}[1]{\mathring{#1}}
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\newcommand{\boundary}[1]{\partial #1}
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\newcommand{\closure}[1]{\bar{#1}}
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\newcommand{\conv}[1]{\xrightarrow{\makebox[2em][c]{$\scriptstyle#1$}}}
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\newcommand{\convinf}{\conv{n \rightarrow \infty}}
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\renewcommand{\kbldelim}{(}
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\renewcommand{\kbrdelim}{)}
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\newcommand{\reader}{Left as an exercise for the reader.}
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\newcommand{\noproof}{Without proof.}
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\newcommand{\setvert}{\,\vert\,}
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\newcommand{\set}[2][]{%
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\left\{%
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#2%
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\ifthenelse{\isempty{#1}}%
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{}%
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{\,\middle|\, #1}%
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\right\}%
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}
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\renewcommand{\innerproduct}[2]{\langle#1,#2\rangle}
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\newcommand{\equalexpl}[1]{%
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\underset{\substack{\big\uparrow\\\mathrlap{\text{\hspace{-1.5em}#1}}}}{=}}
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\newcommand{\leexpl}[1]{%
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\underset{\substack{\big\uparrow\\\mathrlap{\text{\hspace{-1.5em}#1}}}}{\le}}
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\newsavebox{\mathbox}\newsavebox{\mathquote}
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\makeatletter
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\newcommand{\mathquotes}[1]{% \mathquotes{<stuff>}
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\savebox{\mathquote}{\text{``}}% Save quotes
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\savebox{\mathbox}{$\displaystyle #1$}% Save <stuff>
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\raisebox{\dimexpr\ht\mathbox-\ht\mathquote\relax}{``}#1\raisebox{\dimexpr\ht\mathbox-\ht\mathquote\relax}{''}
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}
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\makeatother
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\theoremstyle{definition}
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\newtheorem{defi}{Definition}[chapter]
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\theoremstyle{remark}
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\newtheorem{eg}[defi]{Example}
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\newtheorem{rem}[defi]{Remark}
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\theoremstyle{plain}
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\newtheorem{thm}[defi]{Theorem}
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\newtheorem{lem}[defi]{Lemma}
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\newtheorem{cor}[defi]{Corollary}
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\newenvironment{hproof}{%
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\renewcommand{\proofname}{Heuristic Proof}\proof}{\endproof}
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\Crefname{defi}{Definition}{Definitions}
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\crefname{defi}{Def.}{Defs.}
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\Crefname{rem}{Remark}{Remarks}
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\crefname{rem}{Rem.}{Rems.}
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\Crefname{thm}{Theorem}{Theorems}
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\crefname{thm}{Thm.}{Thms.}
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\Crefname{lem}{Lemma}{Lemmas}
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\crefname{lem}{Lem.}{Lems.}
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\Crefname{cor}{Corollary}{Corollaries}
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\crefname{cor}{Cor.}{Cors.}
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\pgfplotsset{compat=1.17}
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\newcommand{\drawge}{-- (rel axis cs:1,0) -- (rel axis cs:1,1) -- (rel axis cs:0,1) \closedcycle}
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\newcommand{\drawle}{-- (rel axis cs:1,1) -- (rel axis cs:1,0) -- (rel axis cs:0,0) \closedcycle}
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\begin{document}
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\begin{titlepage}
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\begin{center}
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\vspace*{5cm}
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\Huge{Mathematics for Physicists}\\[1cm]
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\Large{\href{https://www.github.com/Lauchmelder23/Mathematics}{https://www.github.com/Lauchmelder23/Mathematics}}\\
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\Large{Alma Mater Lipsiensis}\\[0,5cm]
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\normalsize{\today} \\[7,5cm]
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\end{center}
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\doclicenseThis
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\end{titlepage}
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\tableofcontents
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\pagestyle{headings}
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\subfile{chapters/FaN.tex}
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\subfile{chapters/real_analysis_1.tex}
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\subfile{chapters/linear_algebra.tex}
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\subfile{chapters/real_analysis_2.tex}
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\subfile{chapters/topo_of_metr_spaces.tex}
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\subfile{chapters/multivar_calc.tex}
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\end{document}
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