1、数学公式的前后要加上 $ 或 \( 和 \)，比如：$f(x) = 3x + 7$ 和 \(f(x) = 3x + 7\) 效果是一样的；
如果用 \[ 和 \]，或者使用 $$ 和 $$，则该公式独占一行；
如果用 \begin{equation} 和 \end{equation}，则公式除了独占一行还会自动被添加序号， 如何公式不想编号则使用 \begin{equation*} 和\end{equation*}.
2、字符
普通字符在数学公式中含义一样，除了
# $ % & ~ _ ^ \ { }
若要在数学环境中表示这些符号# $ % & _ { }，需要分别表示为\# \$ \% \& \_ \{ \}，即在个字符前加上\。
3、上标和下标
用 ^ 来表示上标，用 _ 来表示下标，看一简单例子：
$$\sum_{i=1}^n a_i=0$$
$$f(x)=x^{x^x}$$
效果:
4、希腊字符
5、数学函数
例如sin x， 输入应该为\sin x
6、在公式中插入文本可以通过 \mbox{text} 在公式中添加text，比如：
\usepackage{CJK}
\begin{CJK*}{GBK}{song}
\begin{document}
$$\mbox{对任意的$x>0$}, \mbox{有 }f(x)>0. $$
\end{CJK*}
\end{document}
效果:
7、分数及开方
\frac{numerator}{denominator} \sqrt{expr
\sqrt[n]{expr
8、省略号（3个点）
\ldots 表示跟文本底线对齐的省略号；\cdots 表示跟文本中线对齐的省略号，
比如：
表示为 $$f(x_1,x_x,\ldots,x_n) = x_1^2 + x_2^2 + \cdots + x_n^2 $$
9、括号和分隔符
() 和 [ ] 和 ｜ 对应于自己；
{} 对应于 \{ \}；
|| 对应于 \|。
当要显示大号的括号或分隔符时，要对应用 \left 和 \right，如：
\[f(x,y,z) = 3y^2 z \left( 3 + \frac{7x+5}{1 + y^2} \right).\]对应于
\left. 和 \right. 只用与匹配，本身是不显示的，比如，要输出：
则用 $$\left. \frac{du}{dx} \right|_{x=0}.$$
10、多行的数学公式
可以表示为：
\begin{eqnarray*}
\cos 2\theta & = & \cos^2 \theta - \sin^2 \theta \\
& = & 2 \cos^2 \theta - 1.
\end{eqnarray*}
其中&是对其点，表示在此对齐。
*使latex不自动显示序号，如果想让latex自动标上序号，则把*去掉
11、矩阵
表示为：
The \emph{characteristic polynomial} $\chi(\lambda)$ of the
$3 \times 3$~matrix
\[ \left( \begin{array}{ccc}
a & b & c \\
d & e & f \\
g & h & i \end{array} \right)\]
is given by the formula
\[ \chi(\lambda) = \left| \begin{array}{ccc}
\lambda - a & -b & -c \\
-d & \lambda - e & -f \\
-g & -h & \lambda - i \end{array} \right|.\]
c表示向中对齐，l表示向左对齐，r表示向右对齐。
12、导数、极限、求和、积分(Derivatives, Limits, Sums and Integrals)
The expr
are obtained in LaTeX by typing
\frac{du}{dt} and \frac{d^2 u}{dx^2}
respectively. The mathematical symbol 
is produced using \partial. Thus the Heat Equation
is obtained in LaTeX by typing
\[ \frac{\partial u}{\partial t}
= h^2 \left( \frac{\partial^2 u}{\partial x^2}
+ \frac{\partial^2 u}{\partial y^2}
+ \frac{\partial^2 u}{\partial z^2}\right)\]
To obtain mathematical expr
in displayed equations we type \lim_{x \to +\infty}, \inf_{x > s} and\sup_K respectively. Thus to obtain
(in LaTeX) we type
\[ \lim_{x \to 0} \frac{3x^2 +7x^3}{x^2 +5x^4} = 3.\]
Added by Goldman2000@126:-------------------------
To compulsively display "u \to \infty" under the limit,
we type in LaTeX
\frac{1}{\lim_{u \rightarrow \infty}}, \frac{1}{\lim\limits_{u \rightarrow \infty}} or
\frac{1}{ \displaystyle \lim_{u \rightarrow \infty}} respectively.
Ended by Goldman2000@126: -------------------------
To obtain a summation sign such as
we type \sum_{i=1}^{2n}. Thus
is obtained by typing
\[ \sum_{k=1}^n k^2 = \frac{1}{2} n (n+1).\]
We now discuss how to obtain integrals in mathematical documents. A typical integral is the following:
This is typeset using
\[ \int_a^b f(x)\,dx.\]
The integral sign is typeset using the control sequence \int, and the limits of integration (in this case a and b are treated as a subscript and a superscript on the integral sign.
Most integrals occurring in mathematical documents begin with an integral sign and contain on
and
are obtained by typing
\[ \int_0^{+\infty} x^n e^{-x} \,dx = n!.\]
\[ \int \cos \theta \,d\theta = \sin \theta.\]
\[ \int_{x^2 + y^2 \leq R^2} f(x,y)\,dx\,dy
= \int_{\theta=0}^{2\pi} \int_{r=0}^R
f(r\cos\theta,r\sin\theta) r\,dr\,d\theta.\]
and
\[ \int_0^R \frac{2x\,dx}{1+x^2} = \log(1+R^2).\]
respectively.
In some multiple integrals (i.e., integrals containing more than on
is obtained by typing
\[ \int_0^1 \! \int_0^1 x^2 y^2\,dx\,dy.\]
Had we typed
\[ \int_0^1 \int_0^1 x^2 y^2\,dx\,dy.\]
we would have obtained
A particularly noteworthy example comes when we are typesetting a multiple integral such as
Here we use \! three times to obtain suitable spacing between the integral signs. We typeset this integral using
\[ \int \!\!\! \int_D f(x,y)\,dx\,dy.\]
Had we typed
\[ \int \int_D f(x,y)\,dx\,dy.\]
we would have obtained
The following (reasonably complicated) passage exhibits a number of the features which we have been discussing:
On
$\psi(\mathbf{r},t)$ of a particle satisfies the
\emph{Schr\"{o}dinger Wave Equation}
\[ i\hbar\frac{\partial \psi}{\partial t}
= \frac{-\hbar^2}{2m} \left(
\frac{\partial^2}{\partial x^2}
+ \frac{\partial^2}{\partial y^2}
+ \frac{\partial^2}{\partial z^2}
\right) \psi + V \psi.\]
It is customary to normalize the wave equation by
demanding that
\[ \int \!\!\! \int \!\!\! \int_{\textbf{R}^3}
\left| \psi(\mathbf{r},0) \right|^2\,dx\,dy\,dz = 1.\]
A simple calculation using the Schr\"{o}dinger wave
equation shows that
\[ \frac{d}{dt} \int \!\!\! \int \!\!\! \int_{\textbf{R}^3}
\left| \psi(\mathbf{r},t) \right|^2\,dx\,dy\,dz = 0,\]
and hence
\[ \int \!\!\! \int \!\!\! \int_{\textbf{R}^3}
\left| \psi(\mathbf{r},t) \right|^2\,dx\,dy\,dz = 1\]
for all times~$t$. If we normalize the wave function in this
way then, for any (measurable) subset~$V$ of $\textbf{R}^3$
and time~$t$,
\[ \int \!\!\! \int \!\!\! \int_V
\left| \psi(\mathbf{r},t) \right|^2\,dx\,dy\,dz\]
represents the probability that the particle is to be found
within the region~$V$ at time~$t$.