[LaTeX Tutorial] 04. LaTeX inserts mathematical formulas and symbols

[LaTeX Tutorial] 04. LaTeX carets and mathematical formulas

LaTeX official

I will grasp the format of the mathematical formulas used in the recent articles for your reference.
First,
the simplest mathematical model

$xxx$   %一个$符号，中间的内容是行内模式
$$xxx$$ %两个$符号，中间的内容是行间模式(行间模式会单独占一行)

A step further is the pattern with the formula number

\begin{
    
    eqnarray}
		%输入公式，此模式公式为行间模式，并带有公式编号
\end{
    
    eqnarray}

or

\begin{
    
    equation}
		x^2+y^2=1
\end{
    
    equation}

Insert the formula in curly brackets,
typically the LJ potential commonly used in molecular dynamics simulations

    \begin{
    
    eqnarray}
    	U_\mathrm{
    
    LJ}(r)=\left\{
    
    
    	\begin{
    
    array}{
    
    rcl}
    		4\epsilon_\mathrm{
    
    LJ}\lbrack(\frac{
    
    \sigma}{
    
    r})^{
    
    12}-(\frac{
    
    \sigma}{
    
    r})^6\rbrack & & {
    
    r\leq r_c}\\
    		0                                                  &     & {
    
    r   >      r_c}\\
    	\end{
    
    array} \right.
    \end{
    
    eqnarray}

Superscript vs Subscript in LaTeX

subscript

Use " _ " to achieve, for example: a ₀

Superscript

Use " ^ " to achieve, such as: a ⁰

special superscript

Adding directions to letters represents vectors: $\vec{a}$ $\vec{a}$
Overline letters: $\overline{a}$ $\overline{a}$
Add a hat on the letter to indicate (linear regression, straight line equation) y point: $\hat{a}$ $\hat{a}$
Curved hats on letters:$\hat{a}$ $\widehat{a}$
Overline letters: $\overline{a}$ $\overline{a}$
Add small tildes to letters: $\tilde{a}$ $\tilde{a}$
Increase the tilde on the letter:$\tilde{a}$ $\widetilde{a}$
Add a dot to a letter: $\stackrel{\dot{}Add}{a}$ $\dot{a}$
two dots to a letter:$\stackrel{¨Add}{a}$ $\ddot{a}$
a tone to a letter:
$\grave{a}$ $\grave{a}$
$\check{a}$ $\check{a}$
$\acute{a}$ $\acute{a}$
$\breve{a}$ $\breve{a}$

vertical subscript

For example:

example	LaTeX says
$\sum _{i=1}^n$	$\sum\limits_{i=1}^{n}$
$\underset{i=1}{\overset{n}{\mathrm{Pi}}}$	$\mathop{\Pi}\limits_{i=1}^{n}$

pay attention

Many subscripts in mathematical formulas do not need italics,
such as k _B Boltzmann constant, and the lower B does not need italics ,
so you can use $k_\mathrm{B}to achieve
the same. Subscripts that have no physical meaning can use regular fonts,
such as
U _Coul , the Coulomb potential Coul only represents the meaning of Coulomb, and there is also the Fene potential U _FENE , and the "c" under the LJ potential U _LJ
r _{c represents the meaning of cutoff, which has no physical meaning and does not need italics. The same is true for} ε _r x

Operation symbols in LaTeX

Dot product: a $\cdot$ b$\cdot$
cross product: a$\times$ b$\times$
divided by: a$÷$ b$\div$
math function
$\sin$ $\sin$
$\cos$ $\cos$
$\ln$ $\ln$
$\log$ $\log$
${\sin }^{2}x+{\cos }^{2}x=1$ $\sin^{2}x + \cos^2x = 1$
$\sqrt[4]{x}$%radical $\sqrt[4]{x}$
$\frac{3}{4}$%Fraction $\frac{3}{4}$

Distribution symbols in LaTeX

$\sim$ use$\sim$

Sum symbol in LaTeX

symbol position	example	LaTeX format
symbol on top right	${\sum }^n$	$\sum^n$
symbol placed directly above	$\sum ^n$	$\sum\limits^n$
symbol on the bottom right	${\sum }_{k=1}$	$\sum_{k=1}$
symbol placed directly below	$\sum _{k=1}$	$\sum\limits_{k=1}$

Vector expression in LaTeX

1. The vector is not bold with arrow
$\vec{v}$
$\vec{E}$
$\overrightarrow{E_{\mathrm{p}}}$

$\vec{
    
    v}$ 
$\vec{
    
    E}$
$\vec{
    
    E_\mathrm{
    
    p}}$

2. Vector bold without arrow
$v$

$\boldsymbol{
    
    v}$

Attached below are the special characters that can be basically used

greek letter case

Greek lowercase, uppercase	LaTeX format	Greek lowercase, uppercase	LaTeX format
$a$ $A$	$\alpha$ $A$	$m$ $N$	$\mu$ $N$
$b$ $B$	$\beta$ $B$	$\xi$ $X$	$\xi$ $\Xi$
$c$ $C$	$\gamma$ $\Gamma$	$the$ $O$	$o$ $O$
$d$ $D$	$\delta$ $\Delta$	$\pi$ $Pi$	$\pi$ $\Pi$
$ϵ$ $e$ $E$	$\epsilon$ $\varepsilon$ $E$	$\rho$ $X$	$\rho$ $\xi$
$\zeta$ $Z$	$\zeta$ $Z$	$\sigma$ $S$	$\sigma$ $\Sigma$
$\eta$ $H$	$\eta$ $H$	$t$ $T$	$\tau$ $T$
$\theta$ $\vartheta$ $Th$	$\theta$ $\vartheta$ $\Theta$	$y$ $Y$	$\upsilon$ $\Upsilon$
$\iota$ $I$	$\iota$ $I$	$\varphi$ $\phi$ $Phi$	$\phi$ $\varphi$ $\Phi$
$Mr.$ $K$	$\kappa$ $K$	$\chi$ $X$	$\chi$ $X$
$\lambda$ $L$	$\lambda$ $\Lambda$	$\psi$ $Ps$	$\psi$ $\Psi$
$\mu$ $M$	$\mu$ $M$	$oh$ $Oh$	$\omega$ $\Omega$

math mode accent

math mode accent	LaTeX format	math mode accent	LaTeX format
$\hat{a}$	$\hat{a}$	$\check{a}$	$\check{a}$
$\tilde{a}$	$\tilde{a}$	$\acute{a}$	$\acute{a}$
$\grave{a}$	$\grave{a}$	$\dot{a}$	$\dot{a}$
$\ddot{a}$	$\ddot{a}$	$\breve{a}$	$\breve{a}$
$\bar{a}$	$\bar{a}$	$\vec{a}$	$\vec{a}$
$\hat{a}$	$\widehat{a}$	$\tilde{a}$	$\widetilde{a}$

binary relational symbol

binary relational symbol	LaTeX format	binary relational symbol	LaTeX format	binary relational symbol	LaTeX format
<	<	>	>	=	=
$\le$	$\le$ or $\leq$	$\ge$	$\ge$or$\geq$	$\equiv$	$\equiv$
$\ll$	$\ll$	$\gg$	$\gg$	$\doteq$	$\doteq$
$\prec$	$\prec$	$\succ$	$\succ$	$\sim$	$\sim$
$⪯$	$\preceq$	$⪰$	$\succeq$	$\simeq$	$\simeq$
$\subset$	$\subset$	$\supset$	$\supset$	$\approx$	$\approx$
$\subseteq$	$\subseteq$	$\supseteq$	$\supseteq$	$\cong$	$\cong$
$⊏$	$\sqsubset$	$⊐$	$\sqsubset$	$\bowtie$	$\Join$
$⊑$	$\sqsubseteq$	$⊒$	$\sqsupseteq$	$\bowtie$	$\bowtie$
$\in$	$\in$	$\ni$	$\ni$ or $\owns$	$\propto$	$\propto$
$⊢$	$\vdash$	$⊣$	$\dashv$	$\models$	$\models$
$\mid$	$\mid$	$\parallel$	$\parallel$	$\perp$	$\perp$
$⌣$	$\smile$	$⌢$	$\frown$	$\asymp$	$\asymp$
:	:	$\notin$	$\notin$	$\ne$	$\neq$ or $\ne$

注意：可以在上述命令前面加上 \not 来得到否定形式

二元运算符

二元运算符	LaTeX形式	二元运算符	LaTeX形式	二元运算符	LaTeX形式
+	+	-	-
$\pm$	$\pm$	$\mp$	$\mp$	$◃$	$\triangleleft$
$\cdot$	$\cdot$	$÷$	$\div$	$▹$	$\triangleright$
$\times$	$\times$	$\setminus$	$\setminus$	$\star$	$\star$
$\cup$	$\cup$	$\cap$	$\cap$	$\ast$	$\ast$
$\bigsqcup$	$\sqcup$	$\sqcap$	$\sqcap$	$\circ$	$\circ$
$\vee$	$\vee$	$\wedge$	$\wedge$	$\bullet$	$\bullet$
$\oplus$	$\oplus$	$\ominus$	$\ominus$	$\diamond$	$\diamond$
$\odot$	$\odot$	$\oslash$	$\oslash$	$\uplus$	$\uplus$
$\otimes$	$\otimes$	$◯$	$\bigcirc$	$⨿$	$\amalg$
$△$	$\bigtriangleup$	$▽$	$\bigtriangledown$	$†$	$\dagger$
$⊲$	$\lhd$	$⊳$	$\rhd$	$‡$	$\ddagger$
$⊴$	$\unlhd$	$⊵$	$\unrhd$	$\wr$	$\wr$

大尺寸运算符

大尺寸运算符	LaTeX形式	大尺寸运算符	LaTeX形式	大尺寸运算符	LaTeX形式	大尺寸运算符	LaTeX形式
$\sum$	$\sum$	$\bigcup$	$\bigcup$	$\bigvee$	$\bigvee$	$⨁$	$\bigoplus
$\prod$	$\prod$	$\bigcap$	$\bigcap$	$\bigwedge$	$\bigwedge$	$⨂$	$\bigotimes$
$\coprod$	$\coprod$	$⨆$	$\bigsqcup$	$⨀$	$\bigodot$
$\int$	$\int$	$\oint$	$\oint$	$⨄$	$\biguplus$

箭头

箭头	LaTeX形式	箭头	LaTeX形式	箭头	LaTeX形式
$\leftarrow$	$\leftarrow$	$⟵$	$\longleftarrow$	$\uparrow$	$\uparrow$
$\to$	$\rightarrow$ or $\to$	$⟶$	$\longrightarrow$	$\downarrow$	$\downarrow$
$\leftrightarrow$	$\leftrightarrow$	$⟷$	$\longleftrightarrow$	$\updownarrow$	$\updownarrow$
$\Leftarrow$	$\Leftarrow$	$⟸$	$\Longleftarrow$	$\Uparrow$	$\Uparrow$
$\Rightarrow$	$\Rightarrow$ or $\to$	$⟹$	$\Longrightarrow$	$\Downarrow$	$\Downarrow$
$\iff$	$\Leftrightarrow$	$⟺$	$\Longleftrightarrow$	$\Updownarrow$	$\Updownarrow$
$\mapsto$	$\mapsto$	$⟼$	$\longmapsto$	$\nearrow$	$\nearrow$
$\hookleftarrow$	$\hookleftarrow$	$\hookrightarrow$	$\hookrightarrow$	$\searrow$	$\searrow$
$\leftharpoonup$	$\leftharpoonup$	$\rightharpoonup$	$\rightharpoonup$	$\swarrow$	$\swarrow$
$\leftharpoondown$	$\leftharpoondown$	$\rightharpoondown$	$\rightharpoondown$	$\nwarrow$	$\nwarrow$
$\rightleftharpoons$	$\rightleftharpoons$	$⟺$	$\iff$	$⇝$	$\leadsto$

定界符

定界符	LaTeX形式	定界符	LaTeX形式	定界符	LaTeX形式	定界符	LaTeX形式
（	（	）	）	$\uparrow$	$\uparrow$	$\Uparrow$	$\Uparrow$
[	[ or $lbrack$	]	] or $rbrack$	$\downarrow$	$\downarrow$	$\Downarrow$	$\Downarrow$
{	{ or $lbrace$	}	} or $rbrace$	$\updownarrow$	$\updownarrow$	$\Updownarrow$	$\Updownarrow$
$⟨$	$\langle$	$⟩$	$\rangle$	$|$	$\vert$	$\Vert$	$\Vert$
$\lfloor$	$\lfloor$	$\rfloor$	$\rfloor$	$\lceil$	$\lceil$	$\rceil$	$\rceil$
/	/	$\backslash$	$\backslash$

大尺寸定界符

定界符	LaTeX形式	定界符	LaTeX形式	定界符	LaTeX形式	定界符	LaTeX形式
$⟮$	$\lgroup$	$⟯$	$\rgroup$	$⎰$	$\lmoustache$	$⎱$	$\rmoustache$
$|$	$\vert$	$\Vert$	$\Vert$

其他符号

符号	LaTeX形式	符号	LaTeX形式	符号	LaTeX形式	符号	LaTeX形式
$\dots$	$\dots$	$\cdots$	$\cdots$	$⋮$	$\vdots$	$\ddots$	$\ddots$
$\hslash$	$\hbar$	$ı$	$\imath$	$ȷ$	$\jmath$	$\ell$	$\ell$
$\Re$	$\Re$	$\Im$	$\Im$	$A$	$\aleph$	$\wp$	$\wp$
$\forall$	$\forall$	$\exists$	$\exists$	$\mho$	$\mho$	$\partial$	$\partial$
’	’	$\prime$	$\prime$	$\varnothing$	$\emptyset$	$\infty$	$\infty$
$\nabla$	$\nabla$	$△$	$\triangle$	$\square$	$\Box$	$\diamond$	$\diamond$
$\perp$	$\bot$	$\top$	$\top$	$\angle$	$\angle$	$\surd$	$\surd$
$♢$	$\diamondsuit$	$♡$	$\heartsuit$	$♣$	$\clubsuit$	$♠$	$\spadesuit$
$\neg$	$\neg$	$♭$	$\flat$	$♮$	$\natural$	$♯$	$\sharp$

non-mathematical symbols

symbol	LaTeX format	symbol	LaTeX format	symbol	LaTeX format
$†$	$\dag$	$\S$	$\S$	$\text{c◯}$	$\copyright$
$‡$	$\ddag$	$\P$	$\P$	$\pounds$	$\pounds$

AMS delimiter

symbol	LaTeX format	symbol	LaTeX format	symbol	LaTeX format	symbol	LaTeX format
$┌$	$\ulcorner$	$┐$	$\urcorner$	$└$	$\llcorner$	$┘$	$\lrcorner$
$|$	$\lvert$	$|$	$\rvert$	$\Vert$	$\lVert$	$\Vert$	$\rVert$
$ϝ$	$\digamma$	$\varkappa$	$\varkappa$	$B$	$\beth$	$\daleth$	$\daleth$
$third$	$\gimel$

For more detailed formula expressions, please see the following blog post:
Original text link: https://blog.csdn.net/NSJim/article/details/109045914