数学公式¶
MkDocs Material 支持通过 MathJax 渲染 LaTeX 数学公式。
行内公式¶
使用单个 $ 包裹行内公式：
勾股定理：\(a^2 + b^2 = c^2\)
二次方程求根公式：\(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)
欧拉公式：\(e^{i\pi} + 1 = 0\)
块级公式¶
使用两个 $$ 包裹块级公式：
二次方程求根公式¶
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
定积分¶
\[
\int_{a}^{b} f(x) \, dx = F(b) - F(a)
\]
泰勒级数展开¶
\[
e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!} = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \cdots
\]
傅里叶变换¶
\[
F(\omega) = \int_{-\infty}^{\infty} f(t) e^{-i\omega t} \, dt
\]
麦克斯韦方程组¶
\[
\begin{aligned}
\nabla \cdot \mathbf{E} &= \frac{\rho}{\varepsilon_0} \\
\nabla \cdot \mathbf{B} &= 0 \\
\nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}}{\partial t} \\
\nabla \times \mathbf{B} &= \mu_0 \mathbf{J} + \mu_0 \varepsilon_0 \frac{\partial \mathbf{E}}{\partial t}
\end{aligned}
\]
常用符号¶
希腊字母¶
| 小写 | 大写 | 名称 |
|---|---|---|
| \(\alpha\) | \(A\) | alpha |
| \(\beta\) | \(B\) | beta |
| \(\gamma\) | \(\Gamma\) | gamma |
| \(\delta\) | \(\Delta\) | delta |
| \(\epsilon\) | \(E\) | epsilon |
| \(\theta\) | \(\Theta\) | theta |
| \(\lambda\) | \(\Lambda\) | lambda |
| \(\mu\) | \(M\) | mu |
| \(\pi\) | \(\Pi\) | pi |
| \(\sigma\) | \(\Sigma\) | sigma |
| \(\phi\) | \(\Phi\) | phi |
| \(\omega\) | \(\Omega\) | omega |
运算符¶
\[
\pm \quad \times \quad \div \quad \cdot \quad \leq \quad \geq \quad \neq \quad \approx \quad \equiv \quad \infty \quad \partial \quad \nabla \quad \int \quad \oint \quad \sum \quad \prod
\]
箭头¶
\[
\leftarrow \quad \rightarrow \quad \Leftarrow \quad \Rightarrow \quad \leftrightarrow \quad \Leftrightarrow \quad \uparrow \quad \downarrow \quad \Uparrow \quad \Downarrow \quad \mapsto \quad \longrightarrow
\]
矩阵¶
基础矩阵¶
\[
\mathbf{A} = \begin{bmatrix}
a_{11} & a_{12} & a_{13} \\
a_{21} & a_{22} & a_{23} \\
a_{31} & a_{32} & a_{33}
\end{bmatrix}
\]
行列式¶
\[
\det(\mathbf{A}) = \begin{vmatrix}
a & b & c \\
d & e & f \\
g & h & i
\end{vmatrix} = a(ei - fh) - b(di - fg) + c(dh - eg)
\]
单位矩阵¶
\[
\mathbf{I}_3 = \begin{bmatrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{bmatrix}
\]
概率统计¶
正态分布¶
\[
f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{(x-\mu)^2}{2\sigma^2}}
\]
期望值¶
\[
E[X] = \sum_{i=1}^{n} x_i p(x_i) \quad \text{或} \quad E[X] = \int_{-\infty}^{\infty} x f(x) \, dx
\]
方差¶
\[
\text{Var}(X) = E[(X - \mu)^2] = E[X^2] - (E[X])^2
\]
贝叶斯定理¶
\[
P(A|B) = \frac{P(B|A) \cdot P(A)}{P(B)}
\]
微积分¶
导数定义¶
\[
f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}
\]
链式法则¶
\[
\frac{d}{dx}[f(g(x))] = f'(g(x)) \cdot g'(x)
\]
分部积分¶
\[
\int u \, dv = uv - \int v \, du
\]
格林定理¶
\[
\oint_C (P \, dx + Q \, dy) = \iint_D \left(\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y}\right) \, dA
\]
线性代数¶
向量点积¶
\[
\mathbf{a} \cdot \mathbf{b} = \sum_{i=1}^{n} a_i b_i = |\mathbf{a}| |\mathbf{b}| \cos\theta
\]
向量叉积¶
\[
\mathbf{a} \times \mathbf{b} = \begin{vmatrix}
\mathbf{i} & \mathbf{j} & \mathbf{k} \\
a_1 & a_2 & a_3 \\
b_1 & b_2 & b_3
\end{vmatrix}
\]
特征值方程¶
\[
\mathbf{A}\mathbf{v} = \lambda\mathbf{v}
\]
奇异值分解¶
\[
\mathbf{A} = \mathbf{U}\mathbf{\Sigma}\mathbf{V}^T
\]
物理学公式¶
牛顿第二定律¶
\[
\mathbf{F} = m\mathbf{a}
\]
动能公式¶
\[
E_k = \frac{1}{2}mv^2
\]
万有引力定律¶
\[
F = G\frac{m_1 m_2}{r^2}
\]
薛定谔方程¶
\[
i\hbar\frac{\partial}{\partial t}\Psi(\mathbf{r}, t) = \hat{H}\Psi(\mathbf{r}, t)
\]
爱因斯坦质能方程¶
\[
E = mc^2
\]
化学公式¶
理想气体状态方程¶
\[
PV = nRT
\]
阿伦尼乌斯方程¶
\[
k = A e^{-\frac{E_a}{RT}}
\]
能斯特方程¶
\[
E = E^\circ - \frac{RT}{nF} \ln Q
\]