ACMS Seminar (fwd)
---------- Forwarded message ----------
Date: Wed, 26 Feb 2003 14:07:10 -0800 (PST)
From: Jim Burke <burke@math.washington.edu>
Reply-To: acmsinfo@u.washington.edu
To: ACMS Seminar <acmseminar@u.washington.edu>, acmsinfo@u.washington.edu,
acmsmajors@u.washington.edu
Subject: ACMS Seminar
Applied and Computational Mathematical Sciences
Undergraduate Seminar
Title: The Gauss-Lucas Theorem and Stability Theory
Speaker: Jim Burke, Mathematics
Time: 3:30--4:30pm, Friday, February 28, 2003
Place: Thomson 134
Abstract:
Rolles's Theorem says that between any two points where a differentiable
function takes a common value there must be a point at which the
derivative is zero. Consequently, if a polynomial has only distinct real
roots, then its derivative also has only distinct real roots and these roots
must interlace the the roots of the polynomial. This observation is easily
generalized to the case where the roots are real but not distinct. But
what about the case where some or all of the roots are complex? Gauss
answered this question with a beautiful and elementary result sometime
between 1830 and 1835. This results has been re-discovered by many
researchers since. The most important of these being Lucas who fine tuned
the result in the multiple zero case. I will present the proof of this
theorem, and if time permits show how it can be used to yield an
elementary proof of some recent results in the stability theory of
dynamical system.
http://www.ms.washington.edu/acms/seminars/W03/schedule.html
*****************************************************************
* James V. Burke * ACMS Program Director *
* University of Washington * e-mail: burke@math.washington.edu *
* Mathematics Department * Phone : 206-543-6183 *
* Box 354350 * FAX : 206-543-0397 *
* Seattle, WA 98195-4350 * *
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