A small rant about the usefulness of the exponential function to express proportional changes.

Blackbody radiation as an application of the foundation of thermodynamics

The fundamental mathematical ideas behind thermodynamics

Some notes on the elementary properties of the exponential families

A proof of the divergence of the harmonic series with the Coq proof assistant.

A companion matrix is a matrix with a prescribed characteristic polynomial. I would like to show them from a broader perspective: companion matrices are the matrix version of a shift operator.

My goal is to derive Maxwell's equations of electromagnetism with almost no effort at all. As often in mathematics, things look simpler when there is less structure. Here, as in mechanics, we do not assume any prior metric, so the geometry of the space at hand is very simple.

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.