latex数学公式总结

数学公式小结

请运行以下程序：

documentclass[11pt]{article}

usepackage{CJK}

usepackage{indentfirst}

usepackage{latexsym}

usepackage{bm}

usepackage{amsmath,amssymb,amsfonts}

usepackage{wasysym}

usepackage{xcolor}

usepackage{cases}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% 重定义字体、字号命令 %

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

newcommand{song}{CJKfamily{song}} % 宋体 (Windows自带

newcommand{fs}{CJKfamily{fs}} % 仿宋体 (Windows自带

newcommand{kai}{CJKfamily{kai}} % 楷体 (Windows自带

newcommand{hei}{CJKfamily{hei}} % 黑体 (Windows自带

newcommand{li}{CJKfamily{li}} % 隶书 (Windows自带

newcommand{you}{CJKfamily{you}} % 幼圆 (Windows自带

newcommand{chuhao}{fontsize{42pt}{baselineskip}selectfont} % 字号设置

newcommand{xiaochuhao}{fontsize{36pt}{baselineskip}selectfont} % 字号设置

newcommand{yichu}{fontsize{32pt}{baselineskip}selectfont} % 字号设置

newcommand{yihao}{fontsize{28pt}{baselineskip}selectfont} % 字号设置

newcommand{erhao}{fontsize{21pt}{baselineskip}selectfont} % 字号设置

newcommand{xiaoerhao}{fontsize{18pt}{baselineskip}selectfont} % 字号设置

newcommand{sanhao}{fontsize{}{baselineskip}selectfont} % 字号设置

newcommand{xiaosanhao}{fontsize{15pt}{baselineskip}selectfont} % 字号设置

newcommand{sihao}{fontsize{14pt}{baselineskip}selectfont} % 字号设置

newcommand{xiaosihao}{fontsize{12pt}{baselineskip}selectfont} % 字号设置

newcommand{wuhao}{fontsize{}{baselineskip}selectfont} % 字号设置

newcommand{xiaowuhao}{fontsize{9pt}{baselineskip}selectfont} % 字号设置

newcommand{liuhao}{fontsize{}{baselineskip}selectfont} % 字号设置

newcommand{qihao}{fontsize{}{baselineskip}selectfont} % 字号设置

%%%%%%%%% END %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

renewcommand{baselinestretch}{}

begin{document}

begin{CJK*}{GBK}{song}

CJKtildeCJKindent

{heisanhao 数学公式举例:}

bigskip

section{概述}

数学模式中的普通文本必须放入一个~LR 盒子里. 如:

$ x^2+sin(x)=0 is a nonlinear equation$.

$ x^2+sin(x)=0 mbox{ is a nonlinear equation} $.

$ x^2+sin(x)=0 mbox{ 是一个非线性方程}$.

section{行内公式}

勾股定理~begin{math}a^2+b^2=c^2end{math}~也称商高定理.

勾股定理~(a^2+b^2=c^2)~也称商高定理.

勾股定理~$a^2+b^2=c^2$~也称商高定理.

section{行间公式}

subsection{单行公式}

begin{displaymath}

a^2+b^2=c^2.

end{displaymath}

[

a^2+b^2 = c^2.

]

begin{equation}

a^2+b^2=c^2.

end{equation}

$$

a^2+b^2=c^2. eqno (*)

$$

$$

a^2+b^2=c^2. eqno (4a)

$$

begin{equation}label{eq:square}

x^2+y^2=R^2.

end{equation}

公式~ref{eq:square}~表示的是一个圆的标准方程.

setcounter{equation}{5}

begin{equation}label{lap}

-triangle u(x,y) = f(x,y),quad (x,y)inOmega .

end{equation}

方程~eqref{lap}~则是一个椭圆型的偏微分方程.

subsection{多行公式}

begin{eqnarray*}

x^2 + y^2 = R^2

2x + 3y = b

end{eqnarray*}

begin{eqnarray}

x^2 + y^2 & = & R^2

2x + 3y & = & b

end{eqnarray}

setlength{arraycolsep}{}

setcounter{equation}{1}

begin{eqnarray}

d(uv) & = & (uv)' dx

& = & (u'v+uv') dx

& = & v(u'dx)+u(v'dx) nonumber

setcounter{equation}{5}

& = & v du+u dv label{leibniz}

end{eqnarray}

这样就得到了公式~(ref{leibniz}).

section{角标: 上标与下标}

注意: 这里的角标命令必须在数学模式下使用!!

$$

x_1, quad

x_{11}, quad

x_{11}^{22}, quad

x_{m}^{(k)},quad

{}^* x ^*, quad

x^{m^n}, quad

{x^x}^{x^x}

$$

中文角标:qquad

$ x^{mbox{scriptsize 平方}},quad x^{y^{mbox{tiny 平方}}} $

导数符号:qquad

$ f^{prime} quadmbox{或者}quad f' $

section{分式}

出现在行内的分式: $ (x+y)/2 $ 和~$ frac{x+y}{2} $, 第二个分式用的是一级角标字体.

分式中的分式: $frac{frac{x}{x+y}}{x+y+z}$, 字体会更小, 但最小为二级角标字体.

行间公式

$$

frac{x+y}{2},qquad frac{frac{x}{x+y}}{x+y+z}

$$

section{根式}

$ sqrt{x},quad sqrt{1+sqrt{2}} $

$ surd{x},quad surd{1+sqrt{2}} $

当被开方式字符高度不同时, 根号线会在不同水平线上, 如:

$sqrt{a}, sqrt{b}$.

解决办法: 加入{hei数学支柱}~

textbackslash{}mathstrutfootnote{宽度为~0,高度与圆括号相同}, 例:

$sqrt{a}, sqrt{b},quad sqrt{amathstrut}, sqrt{bmathstrut}$.

section{求和与积分}

newcommand{dx}{mathrm{d},x}

$$

int_a^b f(x)mathrm{d}x,quad

oint_a^b f(x)mathrm{d}x,quad

$$

$$

intlimits_a^b f(x)mathrm{d}x,quad

ointlimits_a^b f(x)mathrm{d}x,quad

$$

直立的积分号:

$$

varint_a^b f(x)dx, quad

iint_a^b f(x)dx, quad

iiint_a^b f(x)dx,quad

varoint_a^b f(x)dx,quad

oiint_a^b f(x)dx,quad

$$

$$

varintnolimits_a^b f(x)dx, quad

iintnolimits_a^b f(x)dx, quad

iiintnolimits_a^b f(x)dx,quad

varointnolimits_a^b f(x)dx,quad

oiintnolimits_a^b f(x)dx,quad

$$

section{数学重音符号}

newcommand{ml}[1]{texttt{textcolor{blue}{char` #1}}}

renewcommand{arraystretch}{}

setlength{tabcolsep}{6pt}

begin{tabular}{|p{textwidth}|p{textwidth}|}hline

ml{hat}{a}~$to hat{a}$ & ml{bar}{a}~$to bar{a}$

ml{dot}{a}~$to dot{a}$ & ml{ddot}{a}~$to ddot{a}$

ml{tilde}{a}~$to tilde{a}$ & ml{vec}{a}~$to vec{a}$

ml{breve}{a}~$to breve{a}$ & ml{check}{a}~$to check{a}$

ml{acute}{a}~$to acute{a}$ & ml{grave}{a}~$to grave{a}$

ml{mathring}{a}~$to mathring{a}$ &

hline

end{tabular}

bigskip

加宽的帽子和波浪号: $widehat{hello},quad widetilde{good}$

section{上划线、下划线及类似符号}

$$ overline{overline{a}^2 + underline{ab} + bar{b}^2} $$

bigskip

$$ underbrace{a+overbrace{b+dots+b}^{mmbox{scriptsize个}}+ c}_

{20mbox{scriptsize个}}

$$

section{堆积符号}

$$

vec{x} stackrel{mathrm{def}}{=} (x_1,ldots,x_n)

$$

section{可以变大的定界符}

略

section{阵列}

一个简单的阵列(行内):

$

begin{array}{ccc}

11 & 12 & 13

21 & 22 & 23

end{array}

$

阵列(行间)

$$

left(

begin{array}{ccc}

11 & 12

21 & 22 & 23

end{array}

right)

$$

一个较复杂的例子

$$

left{

begin{array}{ccccccccc}

a_{11}x_1 &+& a_{12}x_2 &+& cdots &+& a_{1n}x_n &=& b_1

a_{21}x_1 &+& a_{22}x 2 &+& cdots &+& a_{2n}x_n &=& b_2

multicolumn{9}{c}{dotfill}

a_{n1}x_1 &+& a_{n2}x_2 &+& cdots &+& a_{nn}x_n &=& b_n

end{array}

right.

$$

另一个较复杂的例子

begin{equation}

f(x)=left{

begin{array}{ll}

x & mbox{当~$xge 0$~时;}

-x & mbox{其它情形}

end{array}

right.

end{equation}

section{添加宏包 quad $backslash mbox{usepackage{cases}}$}

subsection{cases 环境}

begin{numcases}{|x|=}

x, & for $xgeq0$

-x, & for $x<0$

end{numcases}

begin{subnumcases}{|x|=}

x, & for $xgeq0$

-x, & for $x<0$

end{subnumcases}

begin{subnumcases}{ }

x, & for $xgeq0$

-x, & for $x<0$

end{subnumcases}

begin{equation}

f(x)=begin{cases}

1 & -1

end{cases}

end{equation}

subsection{subequations~环境}

begin{subequations}

begin{align}

(a+b)^2 & =a^2+b^2

a+b+c)^2 & =a^2+b^2+c^2+2ab+2ac+2bc

end{align}

begin{equation}

(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3

end{equation}

end{subequations}

begin{equation}

(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3

end{equation}

end{CJK*}

end{document}