Course Description

Part of the course will use the textbooks by Mark Meerschaert and Richard Haberman. Both have titles of Mathematical models. Most mathematical models fall into one of three categories: optimization models, dynamical system models, and probability models. The course will be divided into three main parts: Optimization models that will cover topics such as sensitivity analysis, model robustness, model identifiability, multivarible optimization and linear programming. The second part will focus on Dynamical Systems that will cover both the analysis, including bifurcation theory, and computation. Finally, we will spend time covering probability models, both discrete and continuous and stochastic models.

Students will spend time working in a computer lab using matlab to visualize the results that are found via pen and paper. If time permits, we will also cover some topics in Calculus of Variations. There will time set aside for group discussions and modeling projects related to the more interesting and advanced issues concerning topics of interest. Approximately one class period each week will be held in the mathematics computer laboratory where numerical techniques for finding and visualizing solutions of differential and discrete systems will be discussed.

Textbook