Example Post: Math and Images

This is an example blog post showing how LaTeX equations and images work in Quarto.

LaTeX Equations

Inline math: the Kuramoto model describes coupled oscillators as \(\dot{\theta}_i = \omega_i + \frac{K}{N}\sum_{j=1}^N \sin(\theta_j - \theta_i)\).

Display math:

\[ \dot{x} = Ax + Bu, \quad y = Cx \]

The synchronization condition for a network of \(n\) oscillators requires the coupling strength \(K\) to satisfy:

\[ K > K_c = \frac{2}{\pi g(\bar{\omega})} \]

where \(g(\bar{\omega})\) is the probability density at the mean frequency.

Inserting Images

To insert an image, place it next to this .qmd file and use:

![Caption](image.png){fig-align="center" width="80%"}

For example:

My profile photo

Writing Tips

• Create a new folder under blog/posts/ for each post
• Add an index.qmd inside with YAML frontmatter (title, date, categories)
• The blog listing at /blog updates automatically