MathJax

插入LaTeX公式:用$ $...$ $定義。例如:

$$\sum_{i=0}^N\int_{a}^{b}g(t,i)\text{d}t$$

$$W_G^{mn}=max\{0,W_G.\xi_G(f_G^m,f_G^n)\}$$ $$Δ = b^2 – 4\cdot a\cdot c$$

The Quadratic Formula

\[x = {-b \pm \sqrt{b^2-4ac} \over 2a}\]

Cauchy's Integral Formula

\[f(a) = \frac{1}{2\pi i} \oint\frac{f(z)}{z-a}dz\]

Angle Sum Formula for Cosines

\[ \cos(\theta+\phi)=\cos(\theta)\cos(\phi)−\sin(\theta)\sin(\phi) \]

Gauss' Divergence Theorem

\[ \int_D ({\nabla\cdot} F)dV=\int_{\partial D} F\cdot ndS \]

Curl of a Vector Field

\[ \vec{\nabla} \times \vec{F} = \left( \frac{\partial F_z}{\partial y} - \frac{\partial F_y}{\partial z} \right) \mathbf{i} + \left( \frac{\partial F_x}{\partial z} - \frac{\partial F_z}{\partial x} \right) \mathbf{j} + \left( \frac{\partial F_y}{\partial x} - \frac{\partial F_x}{\partial y} \right) \mathbf{k} \]

Standard Deviation

\[\sigma = \sqrt{ \frac{1}{N} \sum_{i=1}^N (x_i -\mu)^2} \]

Definition of Christoffel Symbols

\[(\nabla_X Y)^k = X^i (\nabla_i Y)^k = X^i \left( \frac{\partial Y^k}{\partial x^i} + \Gamma_{im}^k Y^m \right)\] display-maths-formulas-webpage quadratic-equation-solver
上下標上標 ^
下標 _
C_n^2 $$C_n^2$$
向量\vec a $$\vec a$$\overrightarrow{xy} $$\overrightarrow{xy}$$
印表機字型Typewriter\mathtt{ABCDEF}$$\mathtt{ABCDE..XYZ}$$
黑板粗體字Blackboard Bold\mathbb{ABCDEF}$$\mathbb{ABCDE..XYZ}$$
無襯線字體Sans Serif\mathsf{ABCDEF}$$\mathsf{ABCDE..XYZ}$$
手寫體Script\mathscr{ABCDEF}$$\mathscr{ABCDE..XYZ}$$
羅馬字體Roman\mathrm{ABCDEF}$$\mathrm{ABCDE..XYZ}$$
括弧< >\langle\rangle$$\langle ... \rangle$$
自我調整括弧\left(\right)$$\left( ... \right)$$
\left(\frac{x}{y}\right)$$\left(\frac{x}{y}\right)$$
普通括弧(\frac{x}{y})$$(\frac{x}{y})$$
總和\sum\sum_{i=1}^n{a_i}$$\sum_{i=1}^n{a_i}$$
極限\lim\lim_{x\to 0}$$\lim_{x \to 0}$$
積分\int\int_0^xf(x)dx$$\int_0^xf(x)dx$$
分數\frac\frac{b^2-4ac}{2a}$$\frac{b^2-4ac}{2a}$$
根式\sqrt\sqrt[n]{b^2-4ac}$$\sqrt[n]{b^2-4ac}$$
特殊函數\sin\sin \theta$$\sin \theta$$
\ln\ln\ x$$\ln\ x$$
\max\max(A,B,C)$$\max(A,B,C)$$
空格\ a\ b$$a\ b$$
四個空格\quada\quad b$$a\quad b$$
矩陣\ begin{matrix}
\ end{matrix}
行末標記\\
$$\begin{matrix} 1&0&0\\ 0&1&0\\ 0&0&1\\ \end{matrix}$$ $$\begin{bmatrix} {a_{11}}&{a_{12}}&{\cdots}&{a_{1n}}\\ {a_{21}}&{a_{22}}&{\cdots}&{a_{2n}}\\ {\vdots}&{\vdots}&{\ddots}&{\vdots}\\ {a_{m1}}&{a_{m2}}&{\cdots}&{a_{mn}}\\ \end{bmatrix}$$
公式編號\tag{n}f(x)=x\tag{1}g(x)=x\tag{2}
$$f(x)=x\tag{1}$$ $$g(x)=x\tag{2}$$
$$\begin{cases} a_1x+b_1y+c_1z=d_1\\ a_2x+b_2y+c_2z=d_2\\ a_3x+b_3y+c_3z=d_3\\ \end{cases} $$

呈現為:
矩陣邊框
•	在起始、結束標記處用下列詞替換matrix
o	pmatrix:小括弧邊框
o	bmatrix:中括弧邊框
o	Bmatrix:大括弧邊框
o	vmatrix:單分隔號邊框
o	Vmatrix:雙分隔號邊框
省略元素
o	橫省略號:\cdots
o	豎省略號:\vdots
o	斜省略號:\ddots
o	舉例
$$\begin{bmatrix}
{a_{11}}&{a_{12}}&{\cdots}&{a_{1n}}\\
{a_{21}}&{a_{22}}&{\cdots}&{a_{2n}}\\
{\vdots}&{\vdots}&{\ddots}&{\vdots}\\
{a_{m1}}&{a_{m2}}&{\cdots}&{a_{mn}}\\
\end{bmatrix}$$
呈現為:
方程組
•	需要cases環境:起始、結束處以{cases}聲明
•	舉例
$$\begin{cases}
a_1x+b_1y+c_1z=d_1\\
a_2x+b_2y+c_2z=d_2\\
a_3x+b_3y+c_3z=d_3\\
\end{cases}$$