Derivation of Jacobians for the propagation of covariance matrices of track parameters in homogeneous magnetic fields

In this paper, a set of Jacobians to be used for the propagation of track parameter covariance matrices in homogeneous magnetic fields is derived. Most of the presented formulae have been in widespread use in the high-energy physics community for many years, but have previously only existed in unpublished notes. Very precise, purely numerical schemes for calculating the same derivatives are also presented and used as a baseline for evaluating the correctness of the analytical terms.