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