NAME: James Paul Fink

TITLE: Emeritus Professor of Mathematics and Computer Science

EDUCATION:

- Drexel University (B.S. Physics, 1963)
- Stanford University (M.S. Mathematics, 1965; Ph.D. Mathematics, 1967)

PROFESSIONAL EXPERIENCE:

- Engineering Technician, Clifton Precision Products Co., Inc., Clifton
Heights, Pennsylvania, 1959-62
- Physics Instructor, Drexel University, Philadelphia, Pennsylvania, 1962-63
- Professional Summer Employee, IBM, Inc., San Jose, California, Summer, 1964
- Mathematics Instructor, Stanford University, Stanford, California, 1966-67
- Assistant Professor, University of Pittsburgh, Pittsburgh, Pennsylvania,
1967-73
- Associate Professor, University of Pittsburgh, Pittsburgh, Pennsylvania,
1973-86
- Visiting Research Fellow, Fluid Mechanics Research Institute, University of
Essex, England, 1977-78 (sabbatical leave)
- Professor and Department Head, Butler University, Indianapolis, Indiana,
1986-1992
- Professor and Department Chair, Gettysburg College, Gettysburg,
Pennsylvania, 1992-2002
- Visiting Scholar, Department of Mathematics, University of Canterbury,
Christchurch, New Zealand, January-March 2000 (sabbatical leave)
- Professor, Gettysburg College, Gettysburg, Pennsylvania, 2002-2004
- Emeritus Professor, Gettysburg College, Gettysburg, Pennsylvania, 2004-

CURRENT RESEARCH INTERESTS:

- Numerical Analysis
- Continuation Methods
- Differential Equations
- Discretization Error
- Dynamical Systems

GRANT AND FELLOWSHIP AWARDS:

- National Science Foundation Predoctoral Fellow, 1963-67
- Participant in Atomic Energy Commission Grant, 1967-71
- Coinvestigator and Coarranger of National Science Foundation Regional
Conference Grant, July 1970
- Coinvestigator on Air Force Office of Scientific Research Grant, 1981-86
- Co-Principal Investigator on National Science Foundation Equipment Grant,
1981-82
- Co-Principal Investigator on National Science Foundation Equipment Grant,
1984-85
- Principal Investigator on National Science Foundation Research Grant,
1985-87
- Holcomb Research Institute Program Grant, Butler University, 1987-89
- Lilly Endowment Grant, 1990
- Co-Principal Investigator on National Science Foundation Instrumentation Laboratory Improvement Grant, 1991-92

PROFESSIONAL AND HONOR SOCIETIES:

- American Mathematical Society (AMS)
- Mathematical Association of America (MAA)
- Society for Industrial and Applied Mathematics (SIAM)
- Consortium for Mathematics and Its Applications (COMAP)
- Association for Computing Machinery (ACM)
- Phi Kappa Phi Honorary Society
- Sigma Xi Honorary Society
- Associate editor, The UMAP Journal, 1988-
- SIAM representative to UMAP Editorial Board, 1986-
- MAA Committee on Advising, 1994-2002
- Executive Committee, EPADEL section of MAA, 1999-

PUBLICATIONS:

- Asymptotic Behavior of Feynman Integrals, Thesis, Stanford University, 1967
- Asymptotic Estimates of Feynman Integrals, Stanford Linear Accelerator
Center, Publication SLAC-PUB-356, November 1967
- Logarithmic Estimates from the Renormalization Group, Phys. Rev. 170 (1968),
1580-1582
- Asymptotic Estimates of Feynman Integrals, Jour. Math. Phys. 9 (1968),
1389-1400
- Partial Sums of Vacuum Polarization Graphs, Jour. Math. Phys. 10 (1969),
1440-1441
- Complete Continuity of the Inverse of a Positive Symmetric Operator, Proc.
Amer. Math. Soc. 25 (1970), 147-150
- Complete Continuity of the Inverse of the Laplacian and GreenUs Function,
SIAM Review 13 (1971), 47-54
- Uniformly Elliptic Operators and Green's Functions, SIAM J. Applied Math. 23
(1972), 153-155
- Strongly Positive Symmetric Mappings of Banach Spaces, University of
Pittsburgh Report
- Perturbation Expansions for Some Nonlinear Wave Equations (with W. Hall and
S. Khalili), SIAM J. Applied Math. 24 (1973), 575-595
- Entrainment of Frequency in Evolution Equations (with W. Hall), Jour. Diff.
Eq. 14 (1973), 9-41
- A Convergent Two-Time Method for Periodic Differential Equations (with W.
Hall and A. Hausrath), Jour. Diff. Eq. 15 (1974), 459-498
- Discontinuous Periodic Solutions for an Autonomous Nonlinear Wave Equation
(with W. Hall and A. Hausrath), Proc. Royal Irish Academy 75A (1975), 195-226
- Discontinuous Periodic Solutions of an Autonomous Nonlinear Wave Equation
(with W. Hall and A. Hausrath), in Dynamical Systems, An International
Symposium, vol. 1, ed. by L. Cesari, J. K. Hale, J. P. LaSalle, Academic Press
(1976), 267-271
- Lectures on Integration of L
^{oo}-Valued Functions, Fluid Mechanics Research Institute, University of Essex, England, 1977 - Existence of the Pettis Integral of L
^{oo}-Valued Translation Functions, Fluid Mechanics Research Institute, University of Essex, England, Report No. 93, April 1978 - The Pettis Integration of a Perturbed Wave Equation, Math. Proc. Camb. Phil.
Soc. 86 (1979), 145-159
- On the Error Behavior of the Reduced-Basis Technique for Nonlinear
Finite-Element Approximations (with W. Rheinboldt), Zeit. f. Angew. Math. und
Mech. 63 (1983), 21-28
- Some Analytic Techniques for Parametrized Nonlinear Equations and Their
Discretizations (with W. Rheinboldt), in Numerical Methods, Proceedings of the
International Workshop Held at Caracas, June 14-18, 1982, Lecture Notes in
Mathematics, vol. 1005, ed. by V. Pereyra and A. Reinoza, Springer-Verlag
(1983), 108-119
- On the Discretization Error of Parametrized Nonlinear Equations (with W.
Rheinboldt), SIAM J. Numer. Anal. 20 (1983), 732-746
- Solution Manifolds and Submanifolds of Parametrized Equations and Their
Discretization Errors (with W. Rheinboldt), Numer. Math. 45 (1984), 323-343
- The Role of the Tangent Map in Analyzing Bifurcation Behavior (with W.
Rheinboldt), Zeit. f. Angew. Math. und Mech. 64 (1984), 407-412
- Local Error Estimates for Parametrized Nonlinear Equations (with W.
Rheinboldt), SIAM J. Numer. Anal. 22 (1985), 729-735
- Folds on the Solution Manifold of a Parametrized Equation (with W.
Rheinboldt), SIAM J. Numer. Anal. 23 (1986), 693-706
- A Geometric Framework for the Numerical Study of Singular Points (with W.
Rheinboldt), SIAM J. Numer. Anal. 24 (1987), 618-633
- The Numerical Treatment of Fold Points on Cuts of a Manifold, University of
Pittsburgh, Inst. for Comp. Math. and Applications, Technical Report ICMA-86-93,
1986
- Mathematical Modeling, HRI Review, January/February 1988, Holcomb Research
Institute, Butler University
- Curious Behavior of a Groundwater Flow Model, Water Resources Research 26
(1990), 1833-1836
- A Capillarity Correction for Free Surface Flow Revisited (with J.-Y.
Parlange, W. Brutsaert, and A. I. El-Kadi), Water Resources Research 26 (1990),
1691-1692
- Can Terminal Velocity Be Exceeded? (with James H. Freeman and Charles R.
Hampton), Newsletter for the Consortium for Ordinary Differential Equations,
Winter 1994
- Review of Differential Systems, Software Reviews, The College Mathematics
Journal 25 (1994), 329-333
- Comment on: "A Multi-Scale Theory of Swelling Porous Media: I. Application
to One-Dimensional Consolidation" (with J.-Y. Parlange, W. Brutsaert, and A. I.
El-Kadi), Transport in Porous Media 23 (1996), 355-356
- Can Mathematics Majors Become Engineers?, FOCUS, The Newsletter of the
Mathematical Association of America, October 1996
- Review of Interactive Differential Equations, Software Reviews, The College
Mathematics Journal 28 (1997), 63-66
- The "New" Differential Equations and the "Old" Numerical Analysis,
Proceedings of the Third International DERIVE and TI-92 Conference, Gettysburg
College, July 1998
- Differential Equations and Java, Proceedings of the 2000 International
Conference on Parallel and Distributed Processing Techniques and Applications
(PDPTA'2000), Las Vegas, June 2000
- One Last Visit to the Capillarity Correction for Free Surface Flow
(with J.-Y. Parlange and Aly I. El-Kadi), Water Resources Research 37 (2001),
827-829
- Growing Ideas with Derive: An Object-Oriented Approach to Learning Mathematics (with L. Carl Leinbach), Proceedings of the Vienna International Symposium on Including Technology in Mathematics Education, October 2002

BOOKS:

- Methods of Local and Global Differential Geometry in General Relativity (coeditor with D. Farnsworth, J. Porter, A. Thompson), Springer-Verlag Lecture Notes in Physics, No. 14 (1972)