Education related materials

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 at the Martin Marietta Corporation.

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.

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.

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 assistant 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. Since fall 2001 Sheng has been an Assistant 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. Since 2004 Tarfulea has been an Assistant Professor at Purdue University Calumet.