diff --git a/.gitignore b/.gitignore index 694ad33..12a05a2 100644 --- a/.gitignore +++ b/.gitignore @@ -282,3 +282,4 @@ chinesisch/*.pdf eprog/*.pdf wus/*.pdf !wus/include_degrees_circle.pdf +complex-analysis/*.pdf diff --git a/complex-analysis/complex.tex b/complex-analysis/complex.tex new file mode 100644 index 0000000..f623151 --- /dev/null +++ b/complex-analysis/complex.tex @@ -0,0 +1,146 @@ +% Basic stuff +\documentclass[a4paper,10pt]{article} +\usepackage[utf8]{inputenc} +\usepackage[nswissgerman]{babel} +\usepackage{scrextend} +\usepackage{lipsum} +\usepackage{gauss} +\usepackage{amssymb} % to import \leadsto + +% 3 column landscape layout with fewer margins +\usepackage[landscape, left=0.75cm, top=1cm, right=0.75cm, bottom=1.5cm, footskip=15pt]{geometry} +\usepackage{flowfram} +\usepackage{floatrow} +\usepackage{amsmath} +\usepackage[inline]{enumitem} +\usepackage{pst-node} +\usepackage{auto-pst-pdf} +\usepackage{tikz} +\usepackage{tikz-cd} +\usepackage{multicol} + +\usetikzlibrary{calc,matrix} + +\changefontsizes[9pt]{8pt} +\ffvadjustfalse +\setlength{\columnsep}{1cm} +\Ncolumn{3} +\DeclareMathOperator{\Tr}{Tr} +\DeclareMathOperator{\Sign}{sign} +\DeclareMathOperator{\Rank}{Rank} +\DeclareMathOperator{\Image}{Im} +\DeclareMathOperator{\Columnspace}{\mathcal{R}} +\DeclareMathOperator{\Nullspace}{\mathcal{N}} +\DeclareMathOperator{\Kernel}{Ker} +\DeclareMathOperator{\diag}{diag} +\DeclareMathOperator{\Span}{span} + +\newcommand*{\hermconj}{\mathsf{H}} + +% define nice looking boxes +\usepackage[most]{tcolorbox} + +% a base set, that is then customised +\tcbset { + base/.style={ + boxrule=0mm, + leftrule=1mm, + left=1.75mm, + arc=0mm, + fonttitle=\bfseries, + colbacktitle=black!10!white, + coltitle=black, + toptitle=0.75mm, + bottomtitle=0.25mm, + title={#1} + } +} + +\newcommand{\middot}{~\textperiodcentered~} +\newlist{rowlist}{enumerate*}{1} +\setlist[rowlist]{label={\textbf{\roman*}\text{: }}, afterlabel={}, itemjoin=\middot} + +\newlist{vaxioms}{enumerate*}{1} +\setlist[vaxioms]{label={\textbf{V\arabic*}\text{: }}, afterlabel={}, itemjoin=\middot} + +\makeatletter +\renewcommand*\env@matrix[1][*\c@MaxMatrixCols c]{% + \hskip -\arraycolsep + \let\@ifnextchar\new@ifnextchar + \array{#1}} +\makeatother + +\newcommand\undermat[2]{% + \makebox[0pt][l]{$\smash{\underbrace{\phantom{% + \begin{matrix}#2\end{matrix}}}_{\text{$#1$}}}$}#2} + +\newcommand\overmat[2]{% + \makebox[0pt][l]{$\smash{\overbrace{\phantom{% + \begin{matrix}#2\end{matrix}}}^{\text{$#1$}}}$}#2} + +\definecolor{brandblue}{rgb}{0.34, 0.7, 1} +\newtcolorbox{mainbox}[1]{ + colframe=brandblue, + base={#1} +} + +\newtcolorbox{subbox}[1]{ + colframe=black!20!white, + base={#1} +} + +% Mathematical typesetting & symbols +\usepackage{amsthm, mathtools, amssymb} +\usepackage{marvosym, wasysym} +\allowdisplaybreaks + +% Tables +\usepackage{tabularx, multirow} +\usepackage{booktabs} + +% Make enumerations more compact +\usepackage{enumitem} +\setitemize{itemsep=0.5pt} +\setenumerate{itemsep=0.75pt} + +% To include sketches & PDFs +\usepackage{graphicx} + +% For hyperlinks +\usepackage{hyperref} +\hypersetup{ + colorlinks=true +} + +% Metadata +\title{Cheatsheet Komplexe Analysis} +\author{Thomas Gassmann} +\date{Februar 2024} + +% Math helper stuff +\def\limn{\lim_{n\to \infty}} +\def\limxo{\lim_{x\to 0}} +\def\limxi{\lim_{x\to\infty}} +\def\limxn{\lim_{x\to-\infty}} +\def\sumk{\sum_{k=1}^\infty} +\def\sumn{\sum_{n=0}^\infty} +\def\R{\mathbb{R}} +\def\C{\mathbb{C}} +\def\E{\mathbb{E}} +\def\K{\mathbb{K}} +\def\dx{\text{ d}x} + +\newcommand{\overbar}[1]{\mkern 1.5mu\overline{\mkern-1.5mu#1\mkern-1.5mu}\mkern 1.5mu} + +\begin{document} + +\input{../header.tex} + +Credits: \begin{rowlist} + \item \href{https://github.com/XYQuadrat/eth-cheatsheets}{xyquadrat} +\end{rowlist} + +\section{Vorwissen} +\subsection{Komplexe Zahlen} + +\end{document}