\documentclass{oxmathexam}
\usepackage{standardmacros}





\school{Exam Part}
%Please put the name of the examination in the brackets above, e.g. Honour Moderations, Final Honour School of Mathematics Part B, etc.
\title{Course Title\\
Lecturer\\
Checked by:}
%Please put your course title, your name and the name of your checker in the brackets above.
\date{dd/mm/yyyy}
%Please be sure to mark each draft submitted with the correct date.

\begin{document}

\makecoverpage

\begin{questions}

\question

%\begin{equation}
%\spd{u}{x}=\spd{u}{t}+\pd{u}{t} .
%\label{pde}
%\tag{PDE}
%\end{equation*}


There are built-in commands for roman (\texttt{parts}) and arabic
(\texttt{subparts}) enumeration, whose use is demonstrated below.
\textbf{Please make sure that you make use of these commands for
numbering within questions.} 

 On the rare occasions  a third level of
numbering is needed, employ  a standard LaTeX enumeration environment
with an appropriate form of labelling, for example \texttt{item[($\alpha$)]},
\ldots . 
 


\question 
\begin{parts}
\part
When asking for a definition, please emphasise the thing to be defined
as shown below.

Define the \emph{vorticity} and \emph{helicity} of a fluid flow.

What is meant by the \emph{adjoint} of a linear differential operator?

State and prove the \emph{Maximum Principle} for Poisson's Equation.
\part
Hints are italicised and put in upright square brackets either in
the text [\textit{like this}] or on a separate line as shown
below. Please try to make it clear to which part of the question the
hint refers.

[\textit{Cauchy's Theorem may be used without proof provided it is
  clearly stated.}]
\part
Named theorems, lemmas, hypotheses and so forth are usually
capitalised, as in Jordan's Lemma,
the Generalised Continuum Hypothesis or Hamilton's Principle.
If something is named after several people, we
use long hyphens between the names, as in the Navier--Stokes Equation
or the Prandtl--Batchelor Theorem.
\end{parts} 
\question 

%I've defined some 
We advise the  use of the macros in \texttt{standardmacros.sty}  
for typesetting the following common
constructions nicely.
\begin{parts}
\part
The usual symbols for the integers ($\Z$),
naturals ($\N$),
rationals ($\Q$),
reals ($\R$)
and complex numbers ($\C$) may be obtained like this.

You can use other mathematical fonts as follows:

italic $\mathit{ABCDabcd0123}$,

roman $\mathrm{ABCDabcd0123}$,

bold $\mathbf{ABCDabcd0123}$,

typewriter $\mathtt{ABCDabcd0123}$,

sans serif $\mathsf{ABCDabcd0123}$,

gothic $\mathfrak{ABCDabcd0123}$,

calligraphic (capitals only) $\mathcal{ABCD}$,

blackboard bold (capitals only) $\mathbb{ABCD}$.
\part
%I've created 
There are macros for Euler's exponential constant $\ee$ and
$\ii=\sqrt{-1}$, which are denoted with roman letters, as in
$\ee^{\ii x}=\cos x+\ii\sin x$.
\part
Differentials are denoted using roman ``d'', as in
$\diff{s}^2=\diff{x}^2+\diff{y}^2$.

Integrals should have a small space before the final ``$\d{x}$'',
which may be achieved as follows:
\[
I_1=\int_a^b f(x)\d{x}.
\]
\part
%I've defined
There are  
handy macros for
\begin{subparts}
\subpart
first and second ordinary derivatives, in which we use roman ``d'':
\[
\dd{v}{t}=\sdd{x}{t};
\]
\subpart
first, second and mixed partial derivatives:
\[
\pd{u}{x}=\spd{\phi}{x}=\mpd{\psi}{x}{y}.
\]
\end{subparts}
\part
In applied options, vectors are often typeset as roman bold letters;
for example, let $\ve{u}$ be a vector in $\R^3$.
Note this macro also works on Greek letters and symbols
(unlike, say, \texttt{mathbf}): let
$\ve{\beta}=(\beta_1,\beta_2,\beta_3)^T$.
\end{parts}



\question
You can use standard \texttt{AMSTeX} commands including those listed
below. See the guide at
\texttt{ftp://ftp.ams.org/pub/tex/doc/amsmath/short-math-guide.pdf}
for more details.
\begin{parts}
\part
\texttt{pmatrix} and its variants create vectors and matrices:
\[
\ve{\tau}=\begin{pmatrix}
\tau_{xx} & \tau_{xy} \\ \tau_{xy} & \tau_{yy}
\end{pmatrix} ;
\quad
\lvert\ve{\tau}\rvert=\begin{vmatrix}
\tau_{xx} & \tau_{xy} \\ \tau_{xy} & \tau_{yy}
\end{vmatrix} .
\]
\part
\texttt{cases} is good for functions with piecewise definitions:
\[
f(x)=\begin{cases}
x^4 & x<0, \\
0 & x\geq0 .
\end{cases}
\]
\part
Use these commands for multiple integral signs:
\[
I_2=\iint_A f(x,y)\d{S},
\quad
I_3=\iiint_D f(x,y,z) \d{x}\d{y}\d{z}.
\]
\part
You can label a particular equation in the usual way
\begin{equation}
x^2+y^2=z^2 ,
\label{pythag}
\end{equation}
and then refer to equation  (\ref{pythag})
 like this.
If you really \emph{must} choose your own label, you can do so using
the command \texttt{tag}:
\begin{equation} 
\spd{u}{x}=\spd{u}{t}+\pd{u}{t} .
\label{pde}
\tag{PDE}
\end{equation}
Then refer to equation (\ref{pde})
 like this.
\end{parts}
For unnumbered equations, replace 
\texttt{equation}  by
\texttt{equation*}, and likewise for 
commands such as \texttt{align}, \texttt{alignat}, \texttt{multline}, and so on.  


\question
Here are some stylistic conventions that the examiners prefer to
follow. Many of these are lifted from Knuth's \TeX\ book.
\begin{parts}
\part
Please avoid starting a sentence with a mathematical symbol;
for example, we prefer
\begin{quote}
Let $\ve{u}(\ve{x})$ be the displacement field\ldots
\end{quote}
to
\begin{quote}
$\ve{u}(\ve{x})$ is the displacement field\ldots.
\end{quote}
\part 
Avoid (the possibility of) an isolated symbol starting a new line by including a tie:
\begin{quote}
\ldots  where~$\ell$ is the distance \ldots 
\end{quote}
 


\part
We use slanted ``greater-or-equal'' and ``less-or-equal'' signs, so
I've redefined the usual \texttt{geq} and \texttt{leq} to give
$\geq$ and $\leq$ respectively.
\part
We denote vector products with $\times$, and scalar ``dot'' products
with a \texttt{cdot}, as in
\[
(\ve{u}\cdot\ve{\nabla})\ve{u}=
\ve{\nabla}\left(\frac{1}{2}\lvert\ve{u}\rvert^2\right)-
\ve{u}\times(\ve{\nabla}\times\ve{u}).
\]
\part
It is best to use ``/'' for fractions in the text, as in $k=-3/2$, and
in exponents, for example
\[
y\sim\ee^{-1/x}\text{ as }x\rightarrow0.
\]
Otherwise, it may be possible to avoid fractions and other expressions which are difficult to
read by making appropriate use of \texttt{displaymath} or, 
alternatively,  by 
replacing \texttt{frac} by  \texttt{dfrac} or by employing 
\texttt{\{displaystyle \ldots \}}.

\part 
For functions, the use of \texttt{colon} ($f\colon A \to B$) gives better spacing than \texttt{:}
($f : A \to B$).
\end{parts}

\end{questions}
\end{document}



