Covert katex math into any kind of images
- by walkerchi
https://walkerchi.github.io/math2pix
\begin{aligned}
\nabla \cdot \boldsymbol E &= \frac{\rho}{\varepsilon_0}
\\
\nabla \cdot \boldsymbol B &= 0
\\
\nabla \times \boldsymbol E &= -\frac{\partial \boldsymbol B}{\partial t}
\\
\nabla \times \boldsymbol B &= \mu_0 (\boldsymbol J + \varepsilon_0\frac{\partial \boldsymbol E}{\partial t})
\end{aligned}-
$\boldsymbol E$ : Electric Field (vector field) -
$\boldsymbol B$ : Magnetic Field (pseudovector field) -
$\boldsymbol J$ : current density -
$\rho$ : charge density -
$\varepsilon_0$ : permittivity of free space -
$\mu_0$ : permeability of free
\begin{aligned}
\frac{\partial \boldsymbol u}{\partial t}+
(\boldsymbol u\cdot \nabla)\boldsymbol u -
\nu \nabla^2 \boldsymbol u =
- \frac{1}{\rho}\nabla p + \boldsymbol g
\end{aligned}-
$\boldsymbol{ u}$ : flow velocity -
$\rho$ : mass density -
$p$ : pressure -
$\boldsymbol{ g}$ : body accerlation on the continuum like gravity
\begin{aligned}
i\hbar\frac{\partial \Psi(x,t)}{\partial t} =
\left[-\frac{\hbar^2\partial^2}{2m\partial x^2} + V(x,t) \right] \Psi(x,t)
\end{aligned}-
$\Psi(x,t)$ : wave function in$\mathbb C$ -
$V(x,t)$ : potential -
$\hbar$ : plank constant -
$i$ : imaginary unit
\begin{aligned}
P(S_t,t) &= N(-d_2)Ke^{-r(T-t)} - N(-d_1)S_T
\\
C(S_t, t) &= N(d_1)S_t - N(d_2)Ke^{-r(T-t)}
\\
d_1 &= \frac{1}{\sigma\sqrt{T-t}}\left[ln\left(\frac{S_t}{K}\right)+\left(r+\frac{\sigma^2}{2}\right)(T-t)\right]
\\
d_2 &= d_1 - \sigma\sqrt{T-t}
\end{aligned}-
$P(S_t,t)$ : price of a European put(sell) option -
$C(S_t,t)$ : price of a European call(buy) option -
$N(x)$ : gaussian cumulative distribution function(cdf) -
$T$ : time of option expiration -
$S_t$ : price of the underlying asset at time$t$ -
$r$ : annualized risk-free interest rate -
$K$ : strike price(fixed price) of the option -
$\sigma$ : standard deviation of the stock's returns
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