This document includes three units on applications of first-order difference equations to American politics. The first module is designed to help the user: 1) develop flexibility in analyzing difference equations in quadratic format; 2) understand how Choundy and Phillips' Theorem can be used to provide information about the time path of a difference equation in a quadratic format; and 3) understand the process through which national governments adopted family planning policies. The second unit is focused on: 1) introduction of non-linear representation (first order quadratic difference equation) for political mobilization processes; 2) estimation of model parameters and substantive interpretations; and 3) investigating analytic consequences of substantive assumptions. The final module is a continuation of the second, and looks at the analytic properties of the model presented there. The unit investigates mathematical properties of first-order quadratic difference equation equilibria, local stability, and global stability, and shows ways to use these analytic results to better understand political mobilization processes. Each unit contains exercises, with answers given at the conclusion of each module. (MP)