Latex语法速查

字母

希腊字母表

小写大写变体
α \alpha α \alpha A \Alpha A \Alpha
β \beta β\beta B \Beta B\Beta
χ \chi χ\chi X \Chi X\Chi
δ \delta δ\delta Δ \Delta Δ\Delta
ϵ \epsilon ϵ\epsilon E \Epsilon E\Epsilon ε \varepsilon ε \varepsilon
η \eta η\eta H \Eta H\Eta
γ \gamma γ\gamma Γ \Gamma Γ\Bamma
ι \iota ι\iota I \Iota I\Iota
κ \kappa κ\kappa K \Kappa K\Kappa ϰ \varkappa ϰ\varkappa
λ \lambda λ\lambda Λ \Lambda Λ\Lambda
μ \mu μ\mu M \Mu M\Mu
ν \nu ν\nu N \Nu N\Nu
o o oo O O OO
ω \omega ω\omega Ω \Omega Ω\Omega
ϕ \phi ϕ\phi Φ \Phi Φ\Phi φ \varphi φ\varphi
π \pi π\pi Π \Pi Π\Pi ϖ \varpi ϖ\varpi
ψ \psi ψ\psi Ψ \Psi Ψ\Psi
ρ \rho ρ\rho P \Rho P\Rho ϱ \varrho ϱ\varrho
σ \sigma σ\sigma Σ \Sigma Σ\sigma ς \varsigma ς\varsigma
τ \tau τ\tau T \Tau T\tau
θ \theta θ\theta Θ \Theta Θ\Theta ϑ \vartheta ϑ\vartheta
υ \upsilon υ\upsilon Υ \Upsilon Υ\Upsilon
ξ \xi ξ\xi Ξ \Xi Ξ\Xi
ζ \zeta ζ\zeta Z \Zeta Z\Zeta

数学常用字体

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z \mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ} ABCDEFGHIJKLMNOPQRSTUVWXYZ

 \mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ}

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z \mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ} ABCDEFGHIJKLMNOPQRSTUVWXYZ

 \mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z \mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ} ABCDEFGHIJKLMNOPQRSTUVWXYZ

\mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ}

算数

运算符号

名称

四则运算:\times × \times × \div ÷ \div ÷

正负:\pm ± \pm ± \mp ∓ \mp

点积: ⋅ \cdot \cdot

相等: = = = = ≠ \ne = \ne ≈ \approx \approx ∼ \sim \sim ≡ \equiv \equiv

大小: ≥ \geq \geq ≤ \leq \geq

集合

集合符号:\in ∈ \in \subset ⊂ \subset \subseteq ⊆ \subseteq \nsubseteq ⊈ \nsubseteq

∅ \emptyset \emptyset

A ∪ B A \cup B ABA \cup B A ∩ B A \cap B ABA \cap B

逻辑符号

∀ \forall \forall ∃ \exists \exists ∄ \nexists \nexists

函数

分段函数

f ( z ) = { z 2 + cos ⁡ z for ∣ z ∣ < 3 0 for 3 ≤ ∣ z ∣ ≤ 5 sin ⁡ z for ∣ z ∣ > 5 f(z) = \left\{ \begin{array}{rcl} z^2+\cos z & \text{for} & |z|<3 \\ 0 & \text{for} & 3\leq|z|\leq5 \\ \sin z & \text{for} & |z|>5 \end{array}\right. f(z)= z2+cosz0sinzforforforz<33z5z>5

f(z) = \left\{ \begin{array}{rcl}
         z^2+\cos z
           & \text{for} & |z|<3 \\ 
         0  
           & \text{for} & 3\leq|z|\leq5 \\
         \sin z
           & \text{for} & |z|>5
\end{array}\right

矢量代数

A B → \overrightarrow{AB} AB \overrightarrow{AB}

⟨ A B → , C D → ⟩ \langle \overrightarrow{AB} , \overrightarrow{CD} \rangle AB ,CD \langle \overrightarrow{AB} , \overrightarrow{CD} \rangle

线性代数

方程组

2 x − 5 y = 8 3 x + 9 y = − 12 \begin{align*} 2x - 5y &= 8 \\ 3x + 9y &= -12 \end{align*} 2x5y3x+9y=8=12

\begin{align*} 
2x - 5y &=  8 \\ 
3x + 9y &=  -12
\end{align*}

x = y w = z a = b + c 2 x = − y 3 w = 1 2 z a = b − 4 + 5 x = 2 + y w + 2 = − 1 + w a b = c b \begin{align*} x&=y & w &=z & a&=b+c\\ 2x&=-y & 3w&=\frac{1}{2}z & a&=b\\ -4 + 5x&=2+y & w+2&=-1+w & ab&=cb \end{align*} x2x4+5x=y=y=2+yw3ww+2=z=21z=1+waaab=b+c=b=cb

\begin{align*}
x&=y           &  w &=z              &  a&=b+c\\
2x&=-y         &  3w&=\frac{1}{2}z   &  a&=b\\
-4 + 5x&=2+y   &  w+2&=-1+w          &  ab&=cb
\end{align*}

矩阵

1 2 3 a b c \begin{matrix} 1 & 2 & 3\\ a & b & c \end{matrix} 1a2b3c

\begin{matrix}
1 & 2 & 3\\
a & b & c
\end{matrix}

[ 3 4 5 1 3 9 ] \left[ \begin{array}{cc|r} 3 & 4 & 5 \\ 1 & 3 & 9 \end{array} \right] [314359]

 \left[ \begin{array}{cc|r}
3 & 4 & 5 \\ 
1 & 3 & 9 
\end{array} \right]

∣ k λ λ ⋯ λ λ k λ ⋯ λ λ λ k ⋯ λ ⋮ ⋮ ⋮ ⋮ λ λ λ ⋯ k ∣ \begin{vmatrix} k & \lambda & \lambda& \cdots & \lambda \\ \lambda & k & \lambda & \cdots & \lambda \\ \lambda & \lambda & k & \cdots & \lambda\\ \vdots & \vdots & \vdots & & \vdots \\ \lambda & \lambda & \lambda & \cdots & k\\ \end{vmatrix} kλλλλkλλλλkλλλλk

\begin{vmatrix}
k & \lambda & \lambda&  \cdots & \lambda \\
\lambda & k & \lambda & \cdots & \lambda  \\
\lambda & \lambda & k & \cdots & \lambda\\
\vdots & \vdots & \vdots &  & \vdots  \\
\lambda & \lambda & \lambda & \cdots & k\\
\end{vmatrix}

微积分

极限

lim ⁡ h → 0 f ( x + h ) − f ( x ) h \lim_{h \to 0 } \frac{f(x+h)-f(x)}{h} h0limhf(x+h)f(x)

  \lim_{h \to 0 } \frac{f(x+h)-f(x)}{h}

微分

偏微分

∂ f ∂ x \frac{\partial f}{\partial x} xf ∂ 2 f ∂ x 2 \frac{\partial^2 f}{\partial x^2} x22f

 $\sum\limits_{j=1}^k A_{\alpha_j}$

∫ \int \int ∬ \iint \iint ∭ \iiint \iiint ∮ \oint \oint

$ \int f^{-1}(x-x_a),dx$ \int f^{-1}(x-x_a),dx

∑ \sum \sum ∏ \prod \prod

∯ ∰ \oiint \oiiint

∫ f − 1 ( x − x a )   d x \int f^{-1}(x-x_a)\,dx f1(xxa)dx

( n k ) = n ! k ! ( n − k ) ! \binom{n}{k} = \frac{n!}{k!(n-k)!} (kn)=k!(nk)!n!

积分

∫ C ( 2 + x 2 y )   d s = ∫ 0 π ( 2 + cos ⁡ 2 t sin ⁡ t ) sin ⁡ 2 t + cos ⁡ 2 t   d t = [ 2 t − cos ⁡ 3 t 3 ] 0 π \int_C(2 + x^2y) \, ds = \int_0^\pi (2 + \cos^2 t \sin t)\sqrt{\sin^2 t + \cos^2 t} \, dt \\ =\left[2t - \frac{\cos^3 t}{3} \right]_0^\pi C(2+x2y)ds=0π(2+cos2tsint)sin2t+cos2t dt=[2t3cos3t]0π

\int_C(2 + x^2y) \, ds 
=  \int_0^\pi (2 + \cos^2 t \sin t)\sqrt{\sin^2 t + \cos^2 t} \, dt \\
=\left[2t - \frac{\cos^3 t}{3} \right]_0^\pi 

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