The 2023 exam

$\newcommand{\Q}{\mathbb{Q}} \newcommand{\R}{\mathbb{R}} \newcommand{\C}{\mathbb{C}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\N}{\mathbb{N}} \newcommand\maps\colon \newcommand\by\times \newcommand{\anda}{\text{ and }} \newcommand{\ifa}{\text{ if }} \newcommand{\st}{\text{ s.t. }} \newcommand{\asa}{\text{ as }} \newcommand{\ina}{\text{ in }} \newcommand{\ona}{\text{ on }} \newcommand{\ata}{\text{ at }} \newcommand{\wherea}{\text{ where }} \newcommand{\witha}{\text{ with }} \newcommand{\fora}{\text{ for }} \newcommand{\ora}{\text{ or }} \newcommand{\abs}[2][]{#1\lvert #2 #1\rvert} \newcommand{\n}[2][]{#1\lVert #2 #1\rVert} \newcommand{\supp}{\operatorname{supp}} \newcommand{\dist}{\operatorname{dist}} \newcommand{\trace}{\operatorname{trace}} \newcommand{\without}{\setminus} \newcommand{\dashint}{\hbox{\(-$}\mspace{-19.25mu}\int} \newcommand{\tdashint}{\raise 0.3ex \hbox{$\scriptstyle-$}\mspace{-14mu}\int} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \definecolor{fillinmathshade}{gray}{0.9} \newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}} \)

Section G.4 The 2023 exam

Links on the Library website.

This is a closed-book exam written by me, and is a very good model for this year’s exam. Of course no single exam can cover all of what we did during the unit, and so you should not expect this year’s exam to involve precisely the same topics.

There is a typo in the solution to Question 2(a)(ii): the conditions satisfied by $h$ should be

\begin{equation*} \left\{ \begin{alignedat}{2} \Delta h \amp= 0 \amp\quad\amp \ina B, \\ h \amp \ge u \amp\quad\amp \ona \partial B, \end{alignedat} \right. \end{equation*}

with $B$ and $\partial B$ rather than $\Omega$ and $\partial\Omega\text{.}$ Compare with Definition 4.12.

Prev Top Next