math.tex

$$
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
$$

$$
f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}
$$

$$
\int_{a}^{b} f(x) \, dx = F(b) - F(a)
$$

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

$$
e^{i\pi} + 1 = 0
$$

$$
i\hbar \frac{\partial}{\partial t} \Psi(\mathbf{r},t) = \left[ -\frac{\hbar^2}{2m}\nabla^2 + V(\mathbf{r},t) \right] \Psi(\mathbf{r},t)
$$

$$
\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}
$$

$$
ds^2 = g_{\mu\nu} dx^\mu dx^\nu
$$

$$
\hat{f}(\xi) = \int_{-\infty}^{\infty} f(x) e^{-2\pi i x \xi} \, dx
$$