- Partial Differential Equations -generally, elliptic and parabolic pdes
(typified by the Laplace and heat equations). More specifically, overdetermined
boundary value problems ( too much data puts constraints on the geometry
of the region for existence of a solutiion), maximum principles (where the
maximun can be attained and consequences thereof such as bounds for the solution
and/or its gradient), temporal and spatial decay results (use differential
inequalities or maximum principles to determine the exponential decay of solutions),
Liouville theorems (conditions for elliptic systems or fourth order equations
to have entire solutions which are constant), radial solutions ( explicit
solutions of nonlinear higher ordered elliptic equations). These results are
for linear and nonlinear equations.
- See list of publications in vita
Spring 2002 -- Math 300 (Introduction to Abstract Mathematics)
and Math 141 (Calculus I).
See above link for detailed information.
I was born in Baltimore, Maryland and raised in Toledo,
Ohio. After graduating from John Carroll University with BS and MS degrees
and serving in the military, I recieved the Ph.D degree from the University of
Maryland. Before coming to the University of Tennessee, I spent three years at
the University of South Florida.
Research leaves have been spent at Universitat Karlsruhe
(Germany) in 1985 and Cornell University in 1988 and 1992. In addition, I have
participated in conferences recently in Glasgow, Scotland in 1990, Zurich, Switzerland
in 1994, Athens, Greece in 1996, and Catania, Sicily in 2000.
As a faculty member at UTK, I have served on numerous
department, college, and university committees and taught classes mostly in
analysis, i.e., calculus, advanced calculus, analytical applied mathematics,
ordinary and partial differential equations at the undergraduate and graduate
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Last update: January, 2002