两条直线的交点公式latex数学公式总结

2020年10月1日发(作者：秦道夫)
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
newc ommand{xiaochuhao}{fontsize{36pt}{baselineskip}sel ectfont} % 字号设置
newcommand{yichu}{fontsize{32p t}{baselineskip}selectfont} % 字号设置
newcom mand{yihao}{fontsize{28pt}{baselineskip}selectfont } % 字号设置
newcommand{erhao}{fontsize{21pt} {baselineskip}selectfont} % 字号设置
newcomma nd{xiaoerhao}{fontsize{18pt}{baselineskip}selectfo nt} % 字号设置
newcommand{sanhao}{fontsize{}{base lineskip}selectfont} % 字号设置
newcommand{xiaosa nhao}{fontsize{15pt}{baselineskip}selectfont} % 字号设置
newcommand{sihao}{fontsize{14pt}{baseline skip}selectfont} % 字号设置
newcommand{xiaosi hao}{fontsize{12pt}{baselineskip}selectfont} % 字号设置
newcommand{wuhao}{fontsize{}{baselineskip }selectfont} % 字号设置
newcommand{xiaowuhao}{f ontsize{9pt}{baselineskip}selectfont} % 字号设置
newcommand{liuhao}{fontsize{}{baselineskip}select font} % 字号设置
newcommand{qihao}{fontsize{}{bas elineskip}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



$$$$ u nderbrace{a+overbrace{b+dots+b}^{mmbox{scriptsize个 }}+ c}_
{20mbox{scriptsize个}}
$$$$


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 & -1end{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}