Math contents sample

\documentclass{jarticle} \begin{document} \title{Math contents sample} \author{(Authour's name)} \address{(Address)} \date{} \maketitle \begin{abstract} This is a sample file to create math contents. \end{abstract} \section{Mathematical Discription.} \subsection{Maxwell's equations} For example, this is a representation of Maxwell's equations. \begin{align} \nabla \circ \mathrm{E} & = \frac{\rho}{\epsilon_0}, \\ \nabla \circ \mathrm{B} & = 0, \\ \nabla \times \mathrm{E} & = - \frac{\partial \mathrm{B}}{\partial t}, \\ \nabla \times \mathrm{B} & = \mu_0 \mathrm{J} + \mu_0 \epsilon_0 \frac{\partial \mathrm{E}}{\partial t}. \end{align} \subsection{Complex sequence} It is able to derive these relations for $z:=x+iy$ and $Y:=-\mathrm{sgn}(y)$. \begin{equation} f(z):=\frac{n !}{2 \pi} (i z)^{-n-1} e^{2 i \delta} \Rightarrow \left\{ \begin{array}{rcl} \mathrm{Re} f(z) & = & \displaystyle{ \frac{(Y')^{n+1}}{4 \pi} \int |\xi|^n e^{\xi Y + Y' i \mathrm{sgn}(\xi) 2 \delta - i \xi x} d\xi, }\\ \mathrm{Im} f(z) & = & \displaystyle{ - \frac{(Y')^n}{4 \pi} \int |\xi|^n i \mathrm{sgn}(\xi) e^{\xi Y + Y' i \mathrm{sgn}(\xi) 2 \delta - i \xi x} d\xi. } \end{array} \right. \end{equation} \end{document}