skip to content
/var/log/little-things
Search any posts

[example] math expression

example

Examples

Inline

Euler's formula: $e^{\mathbb{i}\theta} = \cos{\theta} + \mathbb{i} \sin{\theta}$

Euler’s formula: eiθ=cos⁡θ+isin⁡θe^{\mathbb{i}\theta} = \cos{\theta} + \mathbb{i} \sin{\theta}

Block

Jacobian matrix
 
$$
\begin{aligned}
\frac{\partial \boldsymbol{f}}{\partial \boldsymbol{r}}
=\frac{\partial(f_1, f_2, \cdots, f_m)}{\partial(x_1, x_2, \cdots, x_n)}
=
\left(
 \begin{array}{cccc}
  \frac{\partial f_1}{\partial x_1} &
        \frac{\partial f_1}{\partial x_2} &
        \cdots &
        \frac{\partial f_1}{\partial x_n}\\
  \frac{\partial f_2}{\partial x_1} &
        \frac{\partial f_2}{\partial x_2} &
        \cdots &
        \frac{\partial f_2}{\partial x_n}\\
        \vdots &
        \vdots &
        \ddots &
        \vdots\\
     \frac{\partial f_m}{\partial x_1} &
        \frac{\partial f_m}{\partial x_2} &
        \cdots &
        \frac{\partial f_m}{\partial x_n}
 \end{array}
\right)
\end{aligned}
$$

Jacobian matrix

∂f∂r=∂(f1,f2,⋯ ,fm)∂(x1,x2,⋯ ,xn)=(∂f1∂x1∂f1∂x2⋯∂f1∂xn∂f2∂x1∂f2∂x2⋯∂f2∂xn⋮⋮⋱⋮∂fm∂x1∂fm∂x2⋯∂fm∂xn)\begin{aligned} \frac{\partial \boldsymbol{f}}{\partial \boldsymbol{r}} =\frac{\partial(f_1, f_2, \cdots, f_m)}{\partial(x_1, x_2, \cdots, x_n)} = \left( \begin{array}{cccc} \frac{\partial f_1}{\partial x_1} & \frac{\partial f_1}{\partial x_2} & \cdots & \frac{\partial f_1}{\partial x_n}\\ \frac{\partial f_2}{\partial x_1} & \frac{\partial f_2}{\partial x_2} & \cdots & \frac{\partial f_2}{\partial x_n}\\ \vdots & \vdots & \ddots & \vdots\\ \frac{\partial f_m}{\partial x_1} & \frac{\partial f_m}{\partial x_2} & \cdots & \frac{\partial f_m}{\partial x_n} \end{array} \right) \end{aligned}