To make predictive statements about the role and reactions of different species in physicochemically reactive systems, it is necessary to formulate and solve a set of coupled differential equations describing the systems kinetic behavior. A symbolic algebra module, eqParse.m, is described, which parses an input file containing a set of chemical reactions, rate constants, source and sink terms, and initial conditions. From this information a ratelaw equation for each species is generated; the set of these equations may then be solved for the system's time evolution. In this article, the general mathematical framework for the treatment of such chemical-kinetic systems is first outlined. A description of the user interface is then given, with a brief discussion of the limitations inherent in such symbolic and numerical methods. The general usefulness of the proposed protocol is then demonstrated in both symbolic and numerical computations in a variety of investigations in organic reaction mechanism analysis and oscillatory combustion reactions and chaotic behavior in autocatalysis. The computed results are shown to be in good accord with experimental observations, and conclusions are drawn from these.