MATH 433 Dynamic Mathematical Modeling (Not offered 1998-99)

Mathematical modeling is concerned with translating a natural phenomenon into a mathematical form. In this abstract form the underlying principles of the phenomenon can be carefully examined and experiments that would be difficult or impossible to carry out in a laboratory can be carried out on a computer in a matter of seconds. The abstract process of modeling will be investigated by stepping through established techniques as they are applied to a number of exciting recently developed models. The models we will investigate include simple and coupled oscillators, feedback phenomena, population dynamics, tidal dynamics, the pumping heart, reaction-diffusion, shock waves, morphogenesis, and the spread of pollution, forest fires, and diseases. We will employ tools from the fields of differential equations, dynamical systems, and catastrophe theory. The course is intended for students in the mathematical, physical, and chemical sciences, as well as for students who are seriously interested in the mathematical aspects of physiology, economics, geology, biology, and environmental studies. Evaluation will be based primarily on performance of problem sets, exams, and a computer laboratory. Prerequisites: Mathematics 105 and some background in differential equations, such as Mathematics 210 or 305. Permission of the instructor is required for those students who have not taken Mathematics 210 or 305.

S. JOHNSON