\documentclass[12pt,letterpaper]{book}

\usepackage{227_preamble}
\usepackage{pdfpages}
\usepackage{url}


\graphicspath{{./figures}}

\begin{document}




%coverpage
\setcounter{page}{0}\includepdf[noautoscale=false]{figures/227-solutions-cover.pdf}




\begin{titlepage}
\begin{center}
\textsc{\LARGE Notes on Multivariable Calculus II
\\[2ex]
Solutions Manual
}\\[2ex]

\vspace{5ex}
\hrule
\vspace{5ex}

\begin{minipage}[t]{0.3\textwidth} \begin{flushleft}
\large Izabella \textsc{{\L}aba}
\end{flushleft} \end{minipage}%
\begin{minipage}[t]{0.3\textwidth} \begin{flushleft}
\large Caleb \textsc{Marshall}
\end{flushleft} \end{minipage}%
\end{center}
\vspace{2ex}
\hrule

\vfill
\textsc{This document was typeset on \today.}
\end{titlepage}




\subsection*{Copyright information}
\begin{itemize}
\item Copyright \copyright\ 2026 Izabella {\L}aba and Caleb Marshall

\item Cover page photo by Izabella {\L}aba

\item Cover page design by Krysten Casumpang


\item This work is licensed under the
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International
License. You can view a copy of the license at \\
\url{https://creativecommons.org/licenses/by-nc-sa/4.0/}.


\begin{center}
\includegraphics{by-nc-sa.pdf}
\end{center}


%\item Links to the source files can be found at the \href{https://www.math.ubc.ca/~CLP/index.html}{text webpage}
\end{itemize}





\frontmatter


\tableofcontents

\mainmatter

%Can change the chapter count if we add an introduction
%\setcounter{chapter}{-1}

\chapter{Parametrized Curves}

\input{solutions/sol11}

\input{solutions/sol12}

\input{solutions/sol13}

\input{solutions/sol14}

\input{solutions/sol15}

\input{solutions/sol16}

\chapter{Vector Fields}

\input{solutions/sol21}

\input{solutions/sol22}

\input{solutions/sol23}

\input{solutions/sol24}

\chapter{Parametric Surfaces and Surface Integration}

\input{solutions/sol31}

\input{solutions/sol32}

\chapter{Main Theorems of Vector Calculus}

\input{solutions/sol41}

\input{solutions/sol42}

\input{solutions/sol43}

\input{solutions/sol44}

\chapter{Differential Forms}

\input{solutions/sol51}

\input{solutions/sol52}

\input{solutions/sol53}

\input{solutions/sol54}


\end{document}
