1 $$\alpha, \beta, \Gamma, \Delta, \theta, \Omega$$
α , β , Γ , Δ , θ , Ω \alpha, \beta, \Gamma, \Delta, \theta, \Omega α , β , Γ , Δ , θ , Ω
1 $$\epsilon, \varepsilon, \phi, \varphi$$
ϵ , ε , ϕ , φ \epsilon, \varepsilon, \phi, \varphi ϵ , ε , ϕ , φ
1 $$x_i, x^2, x^{y^z}, x_{i,j}, e^{-\alpha t}$$
x i , x 2 , x y z , x i , j , e − α t x_i, x^2, x^{y^z}, x_{i,j}, e^{-\alpha t} x i , x 2 , x y z , x i , j , e − α t
a b \frac{a}{b} b a
1 $$\dfrac{1+\frac{a}{b}}{1+\frac{b}{a}}$4
1 + a b 1 + b a \dfrac{1+\frac{a}{b}}{1+\frac{b}{a}} 1 + a b 1 + b a
1 $$\sqrt{x}, \sqrt[n]{x}$$
x , x n \sqrt{x}, \sqrt[n]{x} x , n x
1 2 3 4 $$\sum_{i=1}^n a_i$$, $$\int_a^b f(x) \, dx$$, $$\iint_D dA$$, $$\oint_C \mathbf{F} \cdot d\mathbf{r}$$
∑ i = 1 n a i \sum_{i=1}^n a_i i = 1 ∑ n a i
∫ a b f ( x ) d x \int_a^b f(x) \, dx ∫ a b f ( x ) d x
∬ D d A \iint_D dA ∬ D d A
∮ C F ⋅ d r \oint_C \mathbf{F} \cdot d\mathbf{r} ∮ C F ⋅ d r
1 2 $$\lim_{x \to 0} \frac{\sin x}{x} = 1$$ $$f'(x), \frac{df}{dx}, \frac{\partial^2 u}{\partial x^2}$$
lim x → 0 sin x x = 1 \lim_{x \to 0} \frac{\sin x}{x} = 1 x → 0 lim x sin x = 1
f ′ ( x ) , d f d x , ∂ 2 u ∂ x 2 f'(x), \frac{df}{dx}, \frac{\partial^2 u}{\partial x^2} f ′ ( x ) , d x d f , ∂ x 2 ∂ 2 u
1 2 3 4 5 6 7 8 9 10 11 12 13 14 $$ \begin{pmatrix} a & b \\ c & d \\ \end{pmatrix}, \quad \begin{bmatrix} 0 & \cdots & 1 \\ \vdots & \ddots & \vdots \\ \end{bmatrix}, \quad \begin{vmatrix} x & y \\ z & w \\ \end{vmatrix} $$
( a b c d ) , [ 0 ⋯ 1 ⋮ ⋱ ⋮ ] , ∣ x y z w ∣ \begin{pmatrix} a & b \\ c & d \\ \end{pmatrix}, \quad \begin{bmatrix} 0 & \cdots & 1 \\ \vdots & \ddots & \vdots \\ \end{bmatrix}, \quad \begin{vmatrix} x & y \\ z & w \\ \end{vmatrix} ( a c b d ) , [ 0 ⋮ ⋯ ⋱ 1 ⋮ ] , ∣ ∣ ∣ ∣ ∣ x z y w ∣ ∣ ∣ ∣ ∣
1 2 3 4 5 6 7 $$ f(n) = \begin{cases} n/2 & \text{if } n \text{ even} \\ 3n+1 & \text{if } n \text{ odd} \end{cases} $$
f ( n ) = { n / 2 if n even 3 n + 1 if n odd f(n) = \begin{cases} n/2 & \text{if } n \text{ even} \\ 3n+1 & \text{if } n \text{ odd} \end{cases} f ( n ) = { n / 2 3 n + 1 if n even if n odd
1 2 3 $\sin \theta, \cos \pi, \tan \phi$, $\log_2 x, \ln e, e^x$, $\nabla \cdot \mathbf{F}, \Delta u$
sin θ , cos π , tan ϕ \sin \theta, \cos \pi, \tan \phi sin θ , cos π , tan ϕ
log 2 x , ln e , e x \log_2 x, \ln e, e^x log 2 x , ln e , e x
∇ ⋅ F , Δ u \nabla \cdot \mathbf{F}, \Delta u ∇ ⋅ F , Δ u
1 2 $$\forall x \in \mathbb{R}, \exists y \notin A$$, $$A \cup B, A \cap B, A \subseteq B$$
∀ x ∈ R , ∃ y ∉ A \forall x \in \mathbb{R}, \exists y \notin A ∀ x ∈ R , ∃ y ∈ / A
A ∪ B , A ∩ B , A ⊆ B A \cup B, A \cap B, A \subseteq B A ∪ B , A ∩ B , A ⊆ B
1 $$a \neq b, x \geq y, \approx, \equiv \mod n$$
a ≠ b , x ≥ y , ≈ , ≡ m o d n a \neq b, x \geq y, \approx, \equiv \mod n a = b , x ≥ y , ≈ , ≡ m o d n
1 2 $$A \rightarrow B, \leftrightarrow$$, $$\Rightarrow, \Leftrightarrow, \neg P \lor Q$$
A → B , ↔ A \rightarrow B, \leftrightarrow A → B , ↔
⇒ , ⇔ , ¬ P ∨ Q \Rightarrow, \Leftrightarrow, \neg P \lor Q ⇒ , ⇔ , ¬ P ∨ Q
1 2 3 4 5 6 7 $$ \begin{aligned} E &= mc^2 \\ F &= ma \\ \nabla \times \mathbf{B} &= \mu_0 \mathbf{J} + \epsilon_0 \frac{\partial E}{\partial t} \end{aligned} $$
E = m c 2 F = m a ∇ × B = μ 0 J + ϵ 0 ∂ E ∂ t \begin{aligned} E &= mc^2 \\ F &= ma \\ \nabla \times \mathbf{B} &= \mu_0 \mathbf{J} + \epsilon_0 \frac{\partial E}{\partial t} \end{aligned} E F ∇ × B = m c 2 = m a = μ 0 J + ϵ 0 ∂ t ∂ E
1 2 3 4 5 6 $$ \begin{split} \cos(a + b) = \cos a \cos b - \sin a \sin b \\ \sin(a + b) = \sin a \cos b + \cos a \sin b \end{split} $$
1 2 $\mathbb{R}, \mathcal{ABC}, \mathfrak{g}, \mathbf{v}$ $\left( \frac{a}{b} \right), \bigg[ \bigg]$
R , A B C , g , v \mathbb{R}, \mathcal{ABC}, \mathfrak{g}, \mathbf{v} R , A B C , g , v
( a b ) , [ 1 ] \left( \frac{a}{b} \right), \bigg[ 1\bigg] ( b a ) , [ 1 ]
1 2 3 $$ f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(a)}{n!} (x-a)^n $$
f ( x ) = ∑ n = 0 ∞ f ( n ) ( a ) n ! ( x − a ) n f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(a)}{n!} (x-a)^n f ( x ) = n = 0 ∑ ∞ n ! f ( n ) ( a ) ( x − a ) n
1 2 3 4 5 6 7 8 9 10 11 12 13 $$ \mathbf{AB} = \begin{pmatrix} \mathbf{A}_{11} & \cdots & \mathbf{A}_{1n} \\ \vdots & \ddots & \vdots \\ \mathbf{A}_{m1} & \cdots & \mathbf{A}_{mn} \end{pmatrix} \begin{pmatrix} \mathbf{B}_{11} & \cdots & \mathbf{B}_{1p} \\ \vdots & \ddots & \vdots \\ \mathbf{B}_{n1} & \cdots & \mathbf{B}_{np} \end{pmatrix} $$
A B = ( A 11 ⋯ A 1 n ⋮ ⋱ ⋮ A m 1 ⋯ A m n ) ( B 11 ⋯ B 1 p ⋮ ⋱ ⋮ B n 1 ⋯ B n p ) \mathbf{AB} = \begin{pmatrix} \mathbf{A}_{11} & \cdots & \mathbf{A}_{1n} \\ \vdots & \ddots & \vdots \\ \mathbf{A}_{m1} & \cdots & \mathbf{A}_{mn} \end{pmatrix} \begin{pmatrix} \mathbf{B}_{11} & \cdots & \mathbf{B}_{1p} \\ \vdots & \ddots & \vdots \\ \mathbf{B}_{n1} & \cdots & \mathbf{B}_{np} \end{pmatrix} A B = ⎝ ⎜ ⎜ ⎛ A 1 1 ⋮ A m 1 ⋯ ⋱ ⋯ A 1 n ⋮ A m n ⎠ ⎟ ⎟ ⎞ ⎝ ⎜ ⎜ ⎛ B 1 1 ⋮ B n 1 ⋯ ⋱ ⋯ B 1 p ⋮ B n p ⎠ ⎟ ⎟ ⎞
1 2 3 $$ \mathcal{F}\{f(x)\} = \int_{-\infty}^{\infty} f(x) e^{-i2\pi\xi x} dx $$
F { f ( x ) } = ∫ − ∞ ∞ f ( x ) e − i 2 π ξ x d x \mathcal{F}\{f(x)\} = \int_{-\infty}^{\infty} f(x) e^{-i2\pi\xi x} dx F { f ( x ) } = ∫ − ∞ ∞ f ( x ) e − i 2 π ξ x d x
环境与语法 ：
块级公式用 $$ ... $$ 或 \[ ... \]，行内公式用 \( ... \)。 矩阵用 pmatrix, bmatrix, cases 等环境。 对齐用 align, aligned, split 等。 特殊符号 ：
希腊字母需小写/大写前缀（如 \alpha, \Gamma）。 特殊符号需用反斜杠（如 \infty, \partial, \nabla）。 排版细节 ：
空格不影响公式，但 \,、\quad 可调整间距。 使用 \text{} 在公式中插入文本。 更多细节请参考 MathJax 官方文档 。
