MATH 433(F) 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).