1.Layout
\evensidemargin -20mm %even page's left margin, 0mm as -40mm
\oddsidemargin -20mm %odd page's left margin, 0mm as -40mm
\topmargin -30mm %top margin, 0mm as -40mm
\textwidth 170mm %width of main text
\textheight 272mm %height of main text
\columnsep 3mm %gap between columns
\headheight 0mm %no head
2.Command
\newcommand{\dx}{\, \mathrm{d}x}
3.Math Mode
$...$ %normal math mode, multi lines will compress in one line
$...$ or \[...\] %math mode with display style(used a whole row, different from "\displaystyle")
$\displaystyle ...$ %deal well with multi-lines' equations, but the linespacing increases
\mathrm{} %font 'Roman' in math mode
\quad or \qquad %a gap like a tab
\begin{cases} %cases expressions, use '&' to connect expressions in a row
0 & \mathrm{if}\, f(-x)=-f(x) \\
1 & \mathrm{if}\, f(-x)=f(x)
\end{cases}
\begin{array}{c} %array, argument is the number of columns and alignment of every column {l(eft), c(enter), r(ight)}, e.g. {cc}{lcr} for multi-column
\displaystyle a_n=\frac{1}{L}\int_{-L}^{L}{f(x)\cos \frac{n\pi x}{L}}\dx\\
\displaystyle b_n=\frac{1}{L}\int_{-L}^{L}{f(x)\sin \frac{n\pi x}{L}}\dx
\end{array}
\left\{ & \right\}
_ or ^ %subscript and superscript, e.g. A_3^2 or \int_0^{\infty}
