Students will build and analyze a model of the fraction of people who are married (for the first time) by a certain age. This model comes from a paper by Hernes and, in this project, is compared to another model used by Coale.
These models are first-order ordinary differential equations (which are also separable and autonomous). Students are asked to set up and solve these differential equations. They are then expected to analyze the behavior of these models, both mathematically (for example, by analyzing the stability of equilibrium points) and physically (determining whether the solution makes sense or not). Reasonable initial conditions are discussed. Finally, an alternatively scaled model is presented, and students are asked to relate this solution to the previous one.
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