MATH 433 - Mathematical Modeling and Control Theory

Institution:

Williams College

Subject:

Mathematics

Description:

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.

Credits:

3.00

Credit Hours:

Prerequisites:

Mathematics 209 or Physics 210 and Mathematics 301 or 305 or permission of instructor

Corequisites:

Exclusions:

Level:

Instructional Type:

Lecture

Notes:

Additional Information:

Historical Version(s):

Institution Website:

www.williams.edu

Phone Number:

(413) 597-3131

Regional Accreditation:

New England Association of Schools and Colleges

Calendar System:

Four-one-four plan

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