A new coordinate expansion based on a Taylor series is used to derive the one-dimensional approximation to unsteady isothermal jet flows. The expansion procedure is carried out for an isothermal, Newtonian jet with no surface tension and air drag, and it can be used to derive a higher order approximation to the flow field. Two new formulations have been derived for the eigenvalue problem for fiber spinning stability for negligible inertia and gravity. (C) 2004 Wiley Periodicals, Inc.