A PDF viewer for your terminal that reloads on every build.

1\documentclass[11pt]{article}
2\usepackage[margin=1in]{geometry}
3\usepackage{amsmath}
4
5\title{Heat Flow in a Thin Rod}
6\author{A.~Student}
7\date{\today}
8
9\begin{document}
10\maketitle
11
12\begin{abstract}
13We derive the one-dimensional heat equation
14for a thin, insulated rod and solve it by
15separation of variables. The solution is a
16sum of decaying Fourier modes.
17\end{abstract}
18
19\section{The heat equation}
20Let $u(x,t)$ be the temperature of a rod of
21length $L$ with diffusivity $\alpha > 0$.
22Conservation of energy and Fourier's law give
23\begin{equation}
24  \frac{\partial u}{\partial t}
25    = \alpha \, \frac{\partial^2 u}{\partial x^2},
26  \qquad 0 < x < L.
27  \label{eq:heat}
28\end{equation} 
29With the ends held at zero, \eqref{eq:heat} has