Following an overview of mathematical methods of analyzing air pollution, detailed developments of inputs, techniques, and validations are presented for photochemical smog modeling. Finite difference formulations are employed to compute concentration histories. The chemical kinetics are expressed as lumped parameter reaction mechanisms derived from laboratory data in the literature. Turbulent diffusion coefficients, which depend on height and time, come from atmospheric measurements. Inputs consist of source inventories for the Los Angeles basin and solar irradiation curves for the appropriate days. Predicted time histories of reactive hydrocarbons, oxides of nitrogen, and ozone are consistent with the variations observed at air monitoring stations. With refined descriptions of advection, the mathematical model will serve as a tool in planning legislation and guiding urban planning in the future. (Author)