diff --git a/Software/Development/Language/LaTex/LaTex_数学公式.md b/Software/Development/Language/LaTex/LaTex_数学公式.md new file mode 100644 index 0000000..842c0be --- /dev/null +++ b/Software/Development/Language/LaTex/LaTex_数学公式.md @@ -0,0 +1,192 @@ +# LaTex 数学公式 + +- [LaTex 数学公式](#latex-数学公式) + - [1. 行内公式与行间公式](#1-行内公式与行间公式) + - [2. 角标](#2-角标) + - [3. 运算符](#3-运算符) + - [4. 希腊字母](#4-希腊字母) + - [5. 带标字母](#5-带标字母) + - [6. 常用数集](#6-常用数集) + - [7. 组合](#7-组合) + +## 1. 行内公式与行间公式 + +行内公式使用“\$”进行包含,行间公式使用“$$” 进行包含: + +- 行内公式:$a+b$ +- 行间公式: + +$$a+b$$ + +## 2. 角标 + +- 下标:$a_0$ +- 上标:$a^n$ + +## 3. 运算符 + +| Operator | LaTex | +|----------|-------| +| + - | + - | +| × · | \times \cdot | +| ÷ / | \div \frac{a}{b} | +| ± ∓ | \pm \mp | +| () [] {} | () [] \{\} | +| ⌊ ⌋ | \lfloor \rfloor | +| ⌈ ⌉ | \lceil \rceil | +| ∑ ∏ ∐ | \sum \prod \coprod | +| ∫ ∮ | \int \oint | +| ⊕, ⊗ ⊙ ⊎ | \oplus \otimes \odot \uplus | +| ⨁, ⨂ ⨀ ⨄ | \bigoplus \bigotimes \bigodot \biguplus | +| > < | > < | +| ≥ ≤ | \geq \leq | +| ≧ ≦ | \gegg \leqq | +| ≫ ≪ | \gg \ll | +| = | = | +| $\neq$ | \neq | +| ≡ | \equiv | +| ≈ | \approx | +| ∼ | \sim | +| ∝ | \propto | +| $\widehat{=}$ | \widehat{=} | +| : | \colon | +| ∣ | \mid \| \vert | +| ⊆ | \subset | +| ⊂ ⊊ | \subset \subsetneq | +| ⊇ | \supseteq | +| ⊃ ⊋ | \supset \supsetneq | +| $\in \ni$ | \in \ni | +| $\notin \not\ni$ | \notin \not\ni | +| ∪ | \cup | +| ∩ | \cap | +| \ | \backslash | +| △ | \triangle | +| ∪ | \dot\cup +| ⊔ | \sqcup | +| C | ^{\mathrm{C}} | +| $\mathcal{P}$ | \mathcal{P} | +| $\sqcup {P}$ | \sqcup{P} | +| $\vee{P}$ | \vee{P} | +| $\wedge {P}$ | \wedge{P} | +| $\land p$ | \land p | +| $\wedge p$ | \wedge p | +| $\bigwedge p$ | \bigwedge p | +| $\to p$ | \to p | +| $\lor p$ | \lor p | +| $\vee p$ | \vee p | +| $\bigvee p$ | \bigvee p | +| $\lnot p$ | \lnot p | +| $\neg p$ | \neg p | +| $\setminus p$ | \setminus p | +| $\smallsetminus p$ | \smallsetminus p | + +## 4. 希腊字母 + +| Greek | LaTex | +|-------|-------| +| αA | \alpha A | +| βB | \beta B | +| γΓ | \gamma \Gamma | +| δΔ | \delta \ Delta | +| ϵεE | \epsilon \varepsilon E | +| ζZ | \zeta Z | +| ηH | \eta H | +| θϑΘ | \theta \vartheta \Theta | +| ιI | \iota I | +| κK | \kappa K | +| λΛ | \lambda \Lambda | +| μM | \mu M | +| ξΞ | \xi \Xi | +| oO | o O | +| πΠ | \pi \Pi | +| ρϱP | \rho \varrho P | +| σΣ | \sigma \Sigma | +| τT | \tau T | +| υΥ | \upsilon \Upsilon | +| ϕφΦ | \phi \varphi \Phi | +| χX | \chi X | +| ψΨ | \psi \Psi | +| ωΩ | \omega \Omega | +| $\int_{a}^{b} x^2 dx$ | \int_{a}^{b} x^2 dx | +| $\iint_V \mu(u,v) \,du\,dv$ | \iint_V \mu(u,v) \,du\,dv | +| $\iiint_V \mu(u,v,w) \,du\,dv\,dw$ | \iiint_V \mu(u,v,w) \,du\,dv\,dw | +| $\sum_{n=-\infty}^{+\infty}$ | \sum_{n=-\infty}^{+\infty} | +| $\prod_{i=a}^{b}$ | \prod_{i=a}^{b} | +| $\lim_{x\to\infty} f(x)$ | \lim_{x\to\infty} f(x) | + +## 5. 带标字母 + +| Letter | LaTex | +|--------|-------| +| $\bar{x}$ | \bar{x} | +| $\acute{x}$ | \acute{x} | +| $\check{x}$ | \check{x} | +| $\grave{x}$ | \grave{x} | +| $\breve{x}$ | \breve{x} | +| $\ddot{x}$ | \ddot{x} | +| $\dot{x}$ | \dot{x} | +| $\hat{x}$ | \hat{x} | +| $\tilde{x}$ | \tilde{x} | + +## 6. 常用数集 + +| Operator | LaTex | +|----------|-------| +| $\mathbb{N}$ | \mathbb{N} | +| $\mathbb{Z}$ | \mathbb{Z} | +| $\mathbb{Q}$ | \mathbb{Q} | +| $\mathbb{R}$ | \mathbb{R} | +| $\mathbb{A}$ | \mathbb{A} | +| $\mathbb{C}$ | \mathbb{C} | + +## 7. 组合 + +等式: + +$$\begin{equation} + f=a+b \\ +\end{equation}$$ + +带序号的公式: + +$$\begin{gather} + a+b=b+a\\ + ab=ba +\end{gather}$$ + +无序号的公式: + +$$\begin{gather*} + a+b=b+a\\ + ab=ba +\end{gather*}$$ + +利用“\notag”阻止编号: + +$$\begin{gather} + a+b=b+a \notag\\ + ab=ba +\end{gather}$$ + +将公式对齐: + +$$\begin{align*} + 2a+b=a+2b \\ + a=b +\end{align*}$$ + +分段函数排版: + +$$\begin{equation*} + D(x)=\begin{cases} + 1,&\text{如果} x \in \mathbb{Q};\\ + 0,&\text{如果} x \in \mathbb{R} \setminus \mathbb{Q}. + \end{cases} +\end{equation*}$$ + +一个公式多行排版: + +$$\begin{split} + F_s(s)=\int_{0}^{\infty}[\sum_{n=0}^{\infty}f(nT)\delta(t-nT)]e^{-st}dt \\ + =\sum_{n=0}^{\infty}f(nT)e^{-snT} \\ +\end{split}$$