  We demonstrate how to derive Maxwell's equations, including Faraday's law and
Maxwell's correction to Amp\`ere's law, by generalizing the description of
static electromagnetism to dynamical situations. Thereby, Faraday's law is
introduced as a consequence of the relativity principle rather than an
experimental fact, in contrast to the historical course and common textbook
presentations. As a by-product, this procedure yields explicit expressions for
the infinitesimal Lorentz and, upon integration, the finite Lorentz
transformation. The proposed approach helps to elucidate the relation between
Galilei and Lorentz transformations and provides an alternative derivation of
the Lorentz transformation without explicitly referring to the speed of light.
