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\usepackage{amsmath}
\usepackage{CJK}
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\begin{document}
\begin{CJK*}{Bg5}{kai}

\title{撑腑计}
\author{89013900 ㏄}

\maketitle

璝\,$f(x)$\,秅戳\,$2\pi$\,ぇ\,{\it pointwise smooth function}玥
\begin{align*}
f(x) &
= \frac{1}{2} A_{0} + \sum_{n = 1}^{\infty}\bigl( A_{n} \cos(nx) + B_{n} \sin(nx)\bigr)\\
\end{align*}
ㄤい\,$A_{0}, A_{n}, B_{n}$\,だ
\begin{align*}
A_{0} &
= \frac{1}{\pi} \int^{\pi}_{-\pi} f(x) dx\\
A_{n} &
= \frac{1}{\pi} \int^{\pi}_{-\pi} f(x) \cos(nx) dx\quad\text{for $n = 1, 2, 3, \cdots$}\\
B_{n} &
= \frac{1}{\pi} \int^{\pi}_{-\pi} f(x) \sin(nx) dx\quad\text{for $n = 1, 2, 3, \cdots$}
\end{align*}

\section{材肈}
\begin{align*}
f(x)
& = x \\
A_{0}
& = \frac{1}{\pi} \int_{-\pi}^{\pi} x dx\\
& = 0\quad\text{\,$x$\,ㄧ计}\\
\\
A_{n}
& = \frac{1}{\pi} \int_{-\pi}^{\pi} x \cos(nx) dx\\
& = 0\quad\text{\,$x \cos(nx)$\,ㄧ计}\\
\\
B_{n}
& = \frac{1}{\pi} \int_{-\pi}^{\pi} x \sin(nx) dx \\
& = \frac{2}{\pi} \int_{0}^{\pi} x \sin(nx) dx\quad\text{\,$x \sin(nx)$\,案ㄧ计}\\
& = \frac{2}{\pi} \Bigl( \bigl( -\frac{x}{n}\cos(nx) \bigr)|_{0}^{\pi} -\bigl( \int_{0}^{\pi} -\frac{1}{n}\cos(nx) dx\bigr) \Bigr)\quad\text{だ场縩だ}\\
& = \frac{2}{\pi} \Bigl( \bigr( -\frac{\pi}{n}\cos(n\pi) \bigr) + \frac{1}{n^{2}}\sin(n\pi) \Bigr)\\
& = \frac{2}{\pi} \bigr( -\frac{\pi\cos(n\pi)}{n} \bigr)\quad\text{\,$sin$\,场\,$0$}\\
& = \frac{-2\cos(n\pi)}{n}\\
\\
f(x)
& = \sum_{n = 1}^{\infty}\frac{-2\cos(n\pi)}{n}\sin(nx)\\
\end{align*}

\section{材肈}
\begin{align*}
f(x)
& = \lvert x \rvert\\
\\
A_{0}
& = \frac{1}{\pi} \int_{-\pi}^{\pi} \lvert x \rvert dx\\
& = \frac{2}{\pi} \int_{0}^{\pi} \lvert x \rvert dx\quad\text{\,$\lvert x \rvert$\,案ㄧ计}\\
& = \frac{2}{\pi} \int_{0}^{\pi} x dx\quad\text{絛瞅\,$[0, \pi]$}\\
& = \frac{2}{\pi} \bigr( \frac{1}{2}\pi^{2} \bigl)\\
& = \pi\\
\\
A_{n}
& = \frac{1}{\pi} \int_{-\pi}^{\pi} \lvert x \rvert \cos(nx) dx \\
& = \frac{2}{\pi} \int_{0}^{\pi} \lvert x \rvert \cos(nx) dx\quad\text{\,$\lvert x \rvert \cos(nx)$\,案ㄧ计}\\
& = \frac{2}{\pi} \int_{0}^{\pi} x \cos(nx) dx\quad\text{絛瞅\,$[0, \pi]$}\\
& = \frac{2}{\pi} \Bigl( \bigl( \frac{x}{n}\sin(nx) \bigr)|_{0}^{\pi} - \int_{0}^{\pi} \frac{1}{n}\sin(nx) dx \Bigr)\quad\text{だ场縩だ}\\
& = \frac{2}{\pi} \Bigl( \bigr( \frac{\pi}{n}\sin(n\pi) \bigr) - \bigr( -\frac{\cos(n\pi) + 1}{n^{2}} \bigl) \Bigr)\\
& = \frac{2}{\pi} \bigr( \frac{\cos(n\pi) - 1}{n^{2}} \bigr)\quad\text{\,$\sin$\,场だ\,$0$}\\
& = \frac{2\cos(n\pi) - 2}{n^{2}\pi}\\
\\
B_{n}
& = \frac{1}{\pi} \int_{-\pi}^{\pi} \lvert x \rvert \sin(nx) dx\\
& = 0\quad\text{\,$\lvert x \rvert \sin(nx)$\,ㄧ计}\\
\\
f(x)
& = \frac{\pi}{2} + \sum_{n = 1}^{\infty}\frac{2\cos(n\pi) - 2}{n^{2}\pi}\cos(nx)\\
\end{align*}

\section{材肈}
\begin{align*}
f(x)
& = \left\{\begin{array}{ll}
1 & x > 0\\
-1 & x < 0
\end{array}\right.\\
\\
A_{0}
& = \frac{1}{\pi} \int_{-\pi}^{\pi} f(x) dx\\
& = 0\quad\text{\,$f(x)$\,ㄧ计}\\
\\
A_{n}
& = \frac{1}{\pi} \int_{-\pi}^{\pi} f(x) cos(nx) dx\\
& = 0\quad\text{\,$f(x) cos(nx)$\,ㄧ计}\\
\\
B_{n}
& = \frac{1}{\pi} \int_{-\pi}^{\pi} f(x) sin(nx) dx\\
& = \frac{2}{\pi} \int_{0}^{\pi} f(x) sin(nx) dx\quad\text{\,$f(x) sin(nx)$\,案ㄧ计}\\
& = \frac{2}{\pi} \int_{0}^{\pi} sin(nx) dx\quad\text{絛瞅\,$[0, \pi]$}\\
& = \frac{2}{\pi} \bigr( -\frac{\cos(n\pi) - 1}{n} \bigl)\\
& = \frac{2 - 2\cos(n\pi)}{n\pi}\\
\\
f(x)
& = \sum_{1}^{\infty}\frac{2 - 2\cos(n\pi)}{n\pi}sin(nx)\\
\end{align*}

\section{材肈}

\begin{figure}
\includegraphics[angle=-90, scale=0.5]{pic.1.1.ps}
\end{figure}
\begin{figure}
\includegraphics[angle=-90, scale=0.5]{pic.1.2.ps}
\end{figure}
\begin{figure}
\includegraphics[angle=-90, scale=0.5]{pic.1.3.ps}
\end{figure}
\begin{figure}
\includegraphics[angle=-90, scale=0.5]{pic.1.4.ps}
\end{figure}
\begin{figure}
\includegraphics[angle=-90, scale=0.5]{pic.1.5.ps}
\end{figure}
\begin{figure}
\includegraphics[angle=-90, scale=0.5]{pic.1.100.ps}
\end{figure}
\begin{figure}
\includegraphics[angle=-90, scale=0.5]{pic.2.1.ps}
\end{figure}
\begin{figure}
\includegraphics[angle=-90, scale=0.5]{pic.2.2.ps}
\end{figure}
\begin{figure}
\includegraphics[angle=-90, scale=0.5]{pic.2.3.ps}
\end{figure}
\begin{figure}
\includegraphics[angle=-90, scale=0.5]{pic.2.4.ps}
\end{figure}
\begin{figure}
\includegraphics[angle=-90, scale=0.5]{pic.2.5.ps}
\end{figure}
\begin{figure}
\includegraphics[angle=-90, scale=0.5]{pic.2.100.ps}
\end{figure}
\begin{figure}
\includegraphics[angle=-90, scale=0.5]{pic.3.1.ps}
\end{figure}
\begin{figure}
\includegraphics[angle=-90, scale=0.5]{pic.3.2.ps}
\end{figure}
\begin{figure}
\includegraphics[angle=-90, scale=0.5]{pic.3.3.ps}
\end{figure}
\begin{figure}
\includegraphics[angle=-90, scale=0.5]{pic.3.4.ps}
\end{figure}
\begin{figure}
\includegraphics[angle=-90, scale=0.5]{pic.3.5.ps}
\end{figure}
\begin{figure}
\includegraphics[angle=-90, scale=0.5]{pic.3.100.ps}
\end{figure}
\clearpage

\section{把σ戈}
\begin{itemize}
\item James S. Walker, Fourier Analysis 
\item Michael Downes, Short Math Guide for \LaTeX
\end{itemize}

\section{ㄏノㄣ}
\begin{itemize}
\item FreeBSD, http://www.freebsd.org/
\item \TeX, http://www.tug.org/
\item \LaTeX, http://www.latex-project.org/
\item CJK, amsmath, graphicx, figure packages
\item C Programming Language
\item Gnuplot, http://www.gnuplot.info/
\item Dvips, http://www.radicaleye.com/dvips.html
\item Ghostscript, http://www.gnu.org/software/ghostscript/ghostscript.html
\item Ghostview, http://www.gnu.org/software/ghostview/ghostview.html
\end{itemize}

\end{CJK*}
\end{document}