This paper derives closed-form expressions for modeling a magnetic recording channel with transition noise. The closed-form expressions assume matched filtering, a Lorentzian transition response, and a first-order position jitter and width variation model. The result is a model that is straightforward and easy to use for simulation and analytical purposes. From the model, equations are derived for partial response targets of constrained length that minimize mean squared error in the presence of transition noise. Simulation results for the resulting targets in various transition noise environments are also included, along with a discussion of the results.