Mathematical Modeling

(4 Credits)

Often, the most difficult task of the applied mathematician is the formulation of an analyzable model in the face of a perplexing phenomenon or data set. This course gives students an introduction to all aspects of this process. The basic tools of modeling, including dimensional analysis, asymptotic approximations, qualitative analysis of differential equations, elementary probability, are presented. They are then used, sometimes in combination with very simple numerical simulations, to give a mathematical formulation of and to analyze several self-contained examples, taken mostly from the natural sciences. Students will also be asked to develop or analyze a model of their own choice, in a field of their interest.