Sample Markdown with MathJax

This is a simple Markdown file demonstrating inline and display equations.

Inline Equation

The shear modulus is defined as $G = \frac{\sigma}{\gamma}$, where $\sigma$ is shear stress and $\gamma$ is shear strain.

Display Equation

The 1D wave equation is

$$\frac{\partial^2 u}{\partial t^2}=c^2 \frac{\partial^2 u}{\partial x^2}$$

where $c$ is the wave propagation speed.

Another Display Equation

A Gaussian function:

$$ f(x) = \frac{1}{\sqrt{2\pi\sigma^2}} \exp!\left( -\frac{(x-\mu)^2}{2\sigma^2} \right) $$