Andrej Cherkaev cherk@math.utah.edu, 1-6822, JWB 225

MATH 5740/MATH 6870 Math. Modeling (Course Outline)

Goals This course deals with principles and examples of mathematical modeling. We discuss modeling of evolution, dynamics, transition, uncertainties, and optimization, working out a number of examples.

Course work consists of reports and presentations.

Preliminary Syllabus

1. Introduction. Types of Models.

2. Great Models: Copernicus, Newton, Einstein. Black holes. Fractals.

3. Population dynamics. Simple models and their combinations

4. Epidemics: disease spread

5. Dimensionality analysis

6. Discrete and continuum waves: domino train and traffic wave

7. Optimal design of a friction stopper

8. Thresholds: model of damage propagation

9. Stochastic Modeling for uncertainties

10. Game theory: Modeling for the worse case scenario