Math examples

This is an inline \(a^*=x-b^*\) equation. This is an inline $a^*=x-b^*$ equation.

These are block equations:

\[a^*=x-b^*\]\[ a^*=x-b^* \]\[ a^*=x-b^* \]

These are also block equations:

$$a^*=x-b^*$$$$ a^*=x-b^* $$$$ a^*=x-b^* $$$$ C_p[\ce{H2O(l)}] = \pu{75.3 J // mol K} $$\[ \begin{aligned} KL(\hat{y} || y) &= \sum_{c=1}^{M}\hat{y}_c \log{\frac{\hat{y}_c}{y_c}} \\ JS(\hat{y} || y) &= \frac{1}{2}(KL(y||\frac{y+\hat{y}}{2}) + KL(\hat{y}||\frac{y+\hat{y}}{2})) \end{aligned} \]$$ \int_0^\infty \frac{x^3}{e^x-1}\,dx = \frac{\pi^4}{15} $$

\begin{gather*} a_1=b_1+c_1\ a_2=b_2+c_2-d_2+e_2 \end{gather*}

\begin{align} a_{11}& =b_{11}& a_{12}& =b_{12}\ a_{21}& =b_{21}& a_{22}& =b_{22}+c_{22} \end{align}

Euler’s formula is remarkable: $e^{i\pi} + 1 = 0$.

$$ \frac{\partial \rho}{\partial t} + \nabla \cdot \vec{j} = 0 \,. \label{eq:continuity} $$$$ \int_{\partial\Omega} \omega = \int_{\Omega} \mathrm{d}\omega \,. \label{eq:stokes} $$