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 A∪BA \cup B A ∩ B A \cap B A∩BA \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+cosz0sinzforforfor∣z∣<33≤∣z∣≤5∣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
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*} 2x−5y3x+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*} x2x−4+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} kλλ⋮λλkλ⋮λλλk⋮λ⋯⋯⋯⋯λλλ⋮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}
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} h→0limhf(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} ∂x∂f ∂ 2 f ∂ x 2 \frac{\partial^2 f}{\partial x^2} ∂x2∂2f
$\sum\limits_{j=1}^k A_{\alpha_j}$
∫ \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 ∫f−1(x−xa)dx
( n k ) = n ! k ! ( n − k ) ! \binom{n}{k} = \frac{n!}{k!(n-k)!} (kn)=k!(n−k)!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+cos2tdt=[2t−3cos3t]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