MS&E201

Dynamic System: Provides a solid foundation in understanding and modeling the dynamics of change. Differential equations are used as a mathematical language to facilitate discussions on dynamic phenomena. Develop mathematical tools to analyze the dynamic models, and use such tools to think about and manage the dynamics of change. The course covers the notions of equilibrium, stability, growth and limit cycle of dynamic systems and discussed in terms of examples in product market penetration, business competition, ecology and spread of epidemics. The course gives an introduction to Catastrophe Theory, which provides a mathematical model for certain discontinuous phenomena like the crash of the stock market and the extinction of species. The course concludes with optimal control theory and differential games. Optimal economic growth model and optimal dynamic pricing are used to illustrate how the optimal control theory is applied to economic modeling analysis and business application. A platform competition model is used to illustrate how different games can be used to do dynamic competitive analysis. Required a project in dynamic system modeling. Pre-requisite: calculus and linear algebra