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Over the years I have greatly enjoyed the challenges and rewards of
teaching from the beginning undergraduate to
advanced graduate levels. A major project of mine during the years 1992
to 1994 was the introduction of high level computer
graphics into the first year calculus
classroom. When the Web came into being I transferred some of these to
a Graphics for the Calculus Classroom web
page, which is now listed in the list of
the 60 most frequently linked pages in the mathematical sciences. In
spring 1997, I developed some Graphics for
Complex Analysis as well. In 1996 I was also honored to receive the George W.
Atherton Award for Excellence in Teaching, Penn State's
highest level of recognition for undergraduate education.
Course materials
Some of my course materials are available on the web. As a motivator for numerical
analysis students I have collected some examples of
real life disasters resulting from bad
numerics. I have extensive lecture notes on complex analysis and functional analysis at the level
of a first year graduate course.
Other materials can be found off various course home pages:
- Penn State MATH/CSE 455, senior level numerical analysis
- Penn State MATH 502, graduate level analysis
- Penn State MATH 597I, graduate level numerical analysis
In November 1996 and September 1997 I gave a MASS
Colloquium entitled Connecting the Dots:
the Theory and Practice of Interpolation. The talk was highly computerized,
and in response to popular demand I have made the
computer files available.
Ph.D. students
My first Ph.D. student, Raymond Cheng received his
degree from the Universisty of Maryland under my guidance in 1987 with a
thesis entitled
Delta-Trigonometric and Spline-Trigonometric Methods using the
Single-Layer Potential Representation. Ray became a research team
leader in the Computational Mechanics Division of the Navy's David
Taylor Model Basin.
Patrick Noon received his Ph.D. from the
University of Maryland in 1988. His thesis was entitled
The Single Layer Heat Potential and Galerkin Boundary Element
Methods for the Heat Equation. Pat went on to work in the telecommunications industry
and is currently Senior Software Support Engineer at AudioCodes USA.
The first Ph.D. student to finish with me at Penn State was Xiaobo
Liu who received his degree in 1993. Xiaobo wrote his thesis
on
Interior Estimates for Some Nonconforming and Mixed Finite
Element Methods and then joined Parametric Technology Corporation
as a software engineer.
Jinshui (Jason) Qin completed his degree in 1994
with a thesis
On the Convergence of Some Simple Finite Elements
for Incompressible Flows, and then took a job
as assistant professor at the University of Tennessee. He currently works in the
telecommunications industry.
Changyi Chen graduated in 1995 with a thesis
entitled
Asymptotic convergence rates for the Kirchhoff
plate model and went on to work as a research scientist for
Lucent Technologies.
Arup
Mukherjee completed Ph.D. in 1996. His
thesis, An Adaptive Finite
Element Code for Elliptic Boundary Value Problems in three dimensions
with applications in Numerical Relativity, is centered around his
code AMG3DP1. The code uses finite elements on adaptively constructed
tetrahedral meshes to solve nonlinear elliptic boundary value problems
in three dimensions, and, in particular, is applied to obtain accurate
solutions of the initial data problem for colliding black holes.
Having completed a postdoc at Rutgers University,
Arup is now an associate professor at Montclair State University.
Alexandre
Madureira completed Ph.D. in 1999. In his
thesis, Asymptotics
and Hierarchical Modeling of Thin Domains, he obtains new
error estimates for dimensional reduction, the process of replacing
a boundary value problem posed on a thin three-dimensional domain
(a plate) by a boundary value problem posed on a two-dimensional domain.
He is a researcher at the Laboratório Nacional de Computaçio Científica
(LNCC) in Brazil.
Sheng Zhang completed his Ph.D. in 2001.
In his thesis, which is entitled A Linear Shell Theory Based on
Variational Principles, he studies a variational approach to
the derivation of dimensionally reduced models for elastic shells and
obtains rigorous convergence estimates and rates for them.
Sheng is associate professor at Wayne State University.
Nicolae Tarfulea completed his Ph.D. in 2004.
In his thesis, which is entitled Constraint Preserving Boundary
Conditions for Hyperbolic Formulations of Einstein's Equations,
he studies well-posed boundary conditions which preserve given
differential constraints for first order symmetric hyperbolic evolutions
relevant to Einstein's equations in a 3+1 formulation.
Tarfulea is associate professor at Purdue
University Calumet.
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