Skip to main content\(\DeclareMathOperator{\RE}{Re}
\DeclareMathOperator{\IM}{Im}
\DeclareMathOperator{\ess}{ess}
\DeclareMathOperator{\intr}{int}
\DeclareMathOperator{\dist}{dist}
\DeclareMathOperator{\dom}{dom}
\DeclareMathOperator{\diag}{diag}
\DeclareMathOperator{\rank}{rank}
\DeclareMathOperator{\col}{col}
\DeclareMathOperator{\cl}{cl}
\DeclareMathOperator{\row}{row}
\DeclareMathOperator{\proj}{proj}
\DeclareMathOperator{\ball}{ball}
\DeclareMathOperator{\gd}{grad}
\DeclareMathOperator{\Log}{Log}
\DeclareMathOperator{\Arg}{Arg}
\DeclareMathOperator\re{\mathrm {Re~}}
\DeclareMathOperator\im{\mathrm {Im~}}
\newcommand{\eps}{\varepsilon}
\newcommand{\To}{\longrightarrow}
\newcommand{\hilbert}{\mathcal{H}}
\newcommand{\s}{\mathcal{S}_2}
\newcommand{\A}{\mathcal{A}}
\newcommand\h{\mathcal{H}}
\newcommand{\J}{\mathcal{J}}
\newcommand{\F}{\mathbb{F}}
\newcommand{\K}{\mathcal{K}}
\newcommand{\N}{\mathcal{N}}
\newcommand{\T}{\mathbb{T}}
\newcommand{\W}{\mathcal{W}}
\newcommand{\X}{\mathcal{X}}
\newcommand{\Y}{\mathcal{Y}}
\newcommand{\D}{\mathbb{D}}
\newcommand{\C}{\mathbb{C}}
\newcommand{\BOP}{\mathbf{B}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\BH}{\mathbf{B}(\mathcal{H})}
\newcommand{\KH}{\mathcal{K}(\mathcal{H})}
\newcommand{\pick}{\mathcal{P}_2}
\newcommand{\schur}{\mathcal{S}_2}
\newcommand{\R}{\mathbb{R}}
\newcommand{\Complex}{\mathbb{C}}
\newcommand{\Field}{\mathbb{F}}
\newcommand{\RPlus}{\Real^{+}}
\newcommand{\Polar}{\mathcal{P}_{\s}}
\newcommand{\Poly}{\mathcal{P}(E)}
\newcommand{\EssD}{\mathcal{D}}
\newcommand{\Lop}{\mathcal{L}}
\newcommand{\cc}[1]{\overline{#1}}
\newcommand{\abs}[1]{\vert#1\vert}
\newcommand{\set}[1]{\left\{#1\right\}}
\newcommand{\seq}[1]{\left\lt#1\right>}
\newcommand{\norm}[1]{\left\Vert#1\right\Vert}
\newcommand{\essnorm}[1]{\norm{#1}_{\ess}}
\newcommand{\tr}{\operatorname{tr}}
\newcommand{\ran}[1]{\operatorname{ran}#1}
\newcommand{\nt}{\stackrel{\mathrm {nt}}{\to}}
\newcommand{\pnt}{\xrightarrow{pnt}}
\newcommand{\ip}[2]{\left\langle #1, #2 \right\rangle}
\newcommand{\ad}{^\ast}
\newcommand{\inv}{^{-1}}
\newcommand{\adinv}{^{\ast -1}}
\newcommand{\invad}{^{-1 \ast}}
\newcommand\Pick{\mathcal P}
\newcommand\Ha{\mathbb{H}}
\newcommand{\HH}{\Ha\times\Ha}
\newcommand\Htau{\mathbb{H}(\tau)}
\newcommand{\vp}{\varphi}
\newcommand{\ph}{\varphi}
\newcommand{\vtheta}{\vartheta}
\newcommand\al{\alpha}
\newcommand\ga{\gamma}
\newcommand\de{\delta}
\newcommand\ep{\varepsilon}
\newcommand\la{\lambda}
\newcommand\up{\upsilon}
\newcommand\si{\sigma}
\newcommand\beq{\begin{equation}}
\newcommand\ds{\displaystyle}
\newcommand\eeq{\end{equation}}
\newcommand\df{\stackrel{\rm def}{=}}
\newcommand\ii{\mathrm i}
\newcommand\net[1]{\langle #1 \rangle}
\newcommand{\vectwo}[2]
{
\begin{pmatrix} #1 \\ #2 \end{pmatrix}
}
\newcommand{\vecthree}[3]
{
\begin{pmatrix} #1 \\ #2 \\ #3 \end{pmatrix}
}
\newcommand\blue{\color{blue}}
\newcommand\black{\color{black}}
\newcommand\red{\color{red}}
\newcommand\nn{\nonumber}
\newcommand\bbm{\begin{bmatrix}}
\newcommand\ebm{\end{bmatrix}}
\newcommand\bpm{\begin{pmatrix}}
\newcommand\epm{\end{pmatrix}}
\numberwithin{equation}{section}
\newcommand\nin{\noindent}
\newcommand{\nCr}[2]{\,_{#1}C_{#2}}
\newcommand{\ps}{\displaystyle \sum_{n=0}^\infty a_n x^n}
\newcommand{\psg}{\displaystyle \sum_{n=0}^\infty b_n x^n}
\newcommand{\hz}{\,\mathrm{Hz}}
\newcommand{\dd}{^\prime}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\definecolor{fillinmathshade}{gray}{0.9}
\newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}}
\)
Notes on complex analysis
Ryan Tully-Doyle
Cal Poly, SLO
May 30, 2023
