  We present an approximate and heuristic scheme for the derivation of
continuum kinetic equations from microscopic dynamics for stochastic,
interacting systems. The method consists of a mean-field type, decoupled
approximation of the master equation followed by the `naive' continuum limit.
The Ising model and driven diffusive systems are used as illustrations. The
equations derived are in agreement with other approaches, and consequences of
the microscopic dependences of coarse-grained parameters compare favorably with
exact or high-temperature expansions. The method is valuable when more
systematic and rigorous approaches fail, and when microscopic inputs in the
continuum theory are desirable.
