Front Matter

\(\DeclareMathOperator{\RE}{Re} \DeclareMathOperator{\IM}{Im} \DeclareMathOperator{\ess}{ess} \DeclareMathOperator{\intr}{int} \DeclareMathOperator{\dist}{dist} \DeclareMathOperator{\dom}{dom} \DeclareMathOperator{\diag}{diag} \DeclareMathOperator\re{\mathrm {Re~}} \DeclareMathOperator\im{\mathrm {Im~}} \newcommand\dd{\mathrm d} \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{\M}{\mathcal{M}} \newcommand{\F}{\mathbb{F}} \newcommand{\N}{\mathcal{N}} \newcommand{\T}{\mathbb{T}} \newcommand{\W}{\mathcal{W}} \newcommand{\X}{\mathcal{X}} \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]{\left\vert#1\right\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\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{\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{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \)

Differential Equations

Phanuel Mariano

Union College

Ryan Tully-Doyle

California Polytechnic State University, San Luis Obispo

March 10, 2021

This set of lecture notes covers topics typical of an introductory course in differential equations. The notes draw extensively from Phanuel Mariano's “Lecture notes in differential equations”.

This is the Second Edition.