Mathematics
and Computer Science Speaker Series
California State University, Stanislaus
Date: Friday, September 23,
2011
Time: 4:00 - 5:00 p.m
Room: P-164
Speakers: Jason
Barnett and William Bishop
Title: George Green: His Theorem and Its Applications
Abstract: Greens Theorem
is regarded as the counterpart of the Fundamental Theorem of Calculus
for double integrals and is an example from a family of theorems which
connect line integrals, and their higher dimensional analogues, with
definite integrals. Considered to be a special case of Stokes Theorem,
Greens Theorem contributed directly to the work of James Clerk Maxwell,
the father of classical electromagnetism. In this talk we provide some
background to Greens Theorem, as well as its proof. We then follow some
of its development by the Cambridge Natural Philosophers. We show how
the theorem is used to solve a textbook problem, as well as how a
numerical application can apply the theorem in computer programs.
Finally, we present a mechanical device which embodies Greens Theorem
in its operation.