  A minimalist approach to the linear stability problem in fluid dynamics is
developed that ensures efficiency by utilizing only the essential elements
required to find the eigenvalues for given boundary conditions. It is shown
that the problem is equivalent to a single first-order ordinary differential
equation, and that studying the argument of the unknown complex function in the
eigenvalue space is sufficient to find the dispersion relation. The method is
applied to a model for relativistic magnetized astrophysical jets.
