Gaussian Integrals & LaTeX

This is a demonstration of how LaTeX renders in this blog.

Inline Math

The famous identity is eiπ+1=0e^{i\pi} + 1 = 0. You can write inline equations easily.

Block Math

Here is the Gaussian integral:

∫−∞∞e−x2dx=π\int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}

Matrices

[123abc]\begin{bmatrix} 1 & 2 & 3 \\ a & b & c \end{bmatrix}

Maxwell’s Equations

∇⋅E=ρε0∇⋅B=0∇×E=−∂B∂t∇×B=μ0J+μ0ε0∂E∂t\begin{aligned} \nabla \cdot \mathbf{E} &= \frac{\rho}{\varepsilon_0} \\ \nabla \cdot \mathbf{B} &= 0 \\ \nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}}{\partial t} \\ \nabla \times \mathbf{B} &= \mu_0\mathbf{J} + \mu_0\varepsilon_0\frac{\partial \mathbf{E}}{\partial t} \end{aligned}