A linear-systems matrix-based mathematical formulation for predicting continuous particulate air monitor (CPAM) responses when monitoring a system of compartments served by an HVAC system is developed. The CPAM responses, for both fixed- and moving-filter monitors, are found using a "quasi-numerical" approach, combining numerical eigenvector/eigenvalues with closed-form analytical solutions, for sources with exponential time-dependence. This formulation is general and can handle complex or simple systems with no changes to the mathematics. Parent-progeny (decay chain) nuclides, with branching, are handled directly. The monitor responses are found via several alternative methods. The computations are readily mechanized, providing a valuable analytical tool for the efficient analysis of many CPAM applications. Two example cases are presented: 1) a multicompartment, multisource system, for a single nuclide; 2) a two-compartment, 88Kr-88Rb decay chain system, as found in an actual PWR containment building.