  We present a method to over-approximate reachable tubes over compact
time-intervals, for linear continuous-time, time-varying control systems whose
initial states and inputs are subject to compact convex uncertainty. The method
uses numerical approximations of transition matrices, is convergent of first
order, and assumes the ability to compute with compact convex sets in finite
dimension. We also present a variant that applies to the case of zonotopic
uncertainties, uses only linear algebraic operations, and yields zonotopic
over-approximations. The performance of the latter variant is demonstrated on
an example.
