Not offered 2007-2008
MATH 433 Mathematical Modeling and Control Theory (Q)
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 real-world behavior can be interpreted in terms of mathematical
shapes. The models we investigate include feedback phenomena, phase locked oscillators,
multiple population dynamics, reaction-diffusion equations, shock waves, morphogenesis,
and the spread of pollution, forest fires, and diseases. Often the natural phenomenon has
some aspect we can control-such as how much pollution, electric charge, or
chemotherapeutic agent we put into a river, circuit, or cancer patient. We will investigate
how to operate such controls in order to achieve a specific goal or optimize some
interpretation of performance. We will employ tools from the fields of differential equations
and dynamical systems. 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.
Format: lecture. Evaluation will be based primarily on performance of problem sets and
exams.
Prerequisites: Mathematics 209 or Physics 210 and Mathematics 301 or 305 or permission
of instructor. No enrollment limit (expected: 12).
S. JOHNSON