## Variational Equation

The variational equation is a fundamental tool in engineering. It is the description of the sensitivity with respect to the initial conditions. A remarkable fact, often presented only in $\mathbf{R}^n$, is that this is in fact the solution of another differential equation, sometimes called the variational equation. I would like to show that this is valid in general manifolds.

## Backward Error Analysis and Equivariance

A little JavaScript application to demonstrate two ideas:

• Equivariance

• Modified vector field

## Modern LaTeX typesetting

LaTeX has undergone incredible changes during the last decade. Unfortunately, many LaTeX users still use it as if we were still in the 90's! Here are some tips to use LaTeX to its maximum.