\documentclass[minion]{homework}
\newcommand{\Reals}{\mathbb{R}}

\doclabel{Math F651: Homework 9}
%\docauthor{Your name here.}
\docdate{Due: April 4, 2018}
\begin{document}
\begin{aproblems}


\hproblem 5.24

\hproblem 5.25

\hproblem 5.26

\hproblem 5.29 (There's a hint in the back.)

\hproblem 5.30 (There's a hint in the back.)

\hproblem 6.3

\hproblem 6.5

\hproblem Let $\Omega$ be the unit sphere in three dimensions.
Let $X$ be the space of smooth vector-valued functions on $\Omega$
that vanish
on the boundary of the sphere.  We put an inner product on $\Omega$ by
\[
\left<g,g\right> = \int_{\Omega} |g|^2.
\]
Let $Y$ be the space of smooth functions
on $\Omega$ with the $L^2$ norm.  Let $T:X\rightarrow Y$ be defined by $T g = \mathrm{div}\; g$.
Compute $T^*$.

\end{aproblems}
\end{document}

