% Homework for Physical Mathematics I
% Ewan Stewart
% KAIST
% 2011/10/4

\documentclass[a4paper,12pt]{article}

\usepackage{pm1}

\setcounter{homework}{4}

\begin{document}

\begin{homework}
[Answers should be submitted, as both a tex file and a pdf file, to both me and the teaching assistants. You may use this file as a template.]

\question{contour}

Calculate
\begin{equation}
\int_0^\infty \frac{\sin(px)}{x} \d{x}
\end{equation}
for $p \in \R$.

Use PGF to draw a diagram illustrating your answer.


\question{integrals}

Calculate
\begin{equation} \label{int}
\int_0^1 \frac{\d{a}}{z-a}
\end{equation}
Compare the holomorphic structure of \eq{int} with that of your answer.

Calculate
\begin{equation}
\int_C \d{z} \int_0^1 \frac{\d{a}}{z-a}
\end{equation}
where $C$ is an anticlockwise loop around $0$ and $1$.
Check your answer by reversing the order of integration.

Use PGF to draw a diagram illustrating your answer.

\end{homework}

\end{document}

