ACADEMIC PERSONAL HISTORY

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:

1. Asymptotic Behavior of Feynman Integrals, Thesis, Stanford University, 1967

2. Asymptotic Estimates of Feynman Integrals, Stanford Linear Accelerator Center, Publication SLAC-PUB-356, November 1967

3. Logarithmic Estimates from the Renormalization Group, Phys. Rev. 170 (1968), 1580-1582

4. Asymptotic Estimates of Feynman Integrals, Jour. Math. Phys. 9 (1968), 1389-1400

5. Partial Sums of Vacuum Polarization Graphs, Jour. Math. Phys. 10 (1969), 1440-1441

6. Complete Continuity of the Inverse of a Positive Symmetric Operator, Proc. Amer. Math. Soc. 25 (1970), 147-150

7. Complete Continuity of the Inverse of the Laplacian and GreenUs Function, SIAM Review 13 (1971), 47-54

8. Uniformly Elliptic Operators and Green's Functions, SIAM J. Applied Math. 23 (1972), 153-155

9. Strongly Positive Symmetric Mappings of Banach Spaces, University of Pittsburgh Report

10. Perturbation Expansions for Some Nonlinear Wave Equations (with W. Hall and S. Khalili), SIAM J. Applied Math. 24 (1973), 575-595

11. Entrainment of Frequency in Evolution Equations (with W. Hall), Jour. Diff. Eq. 14 (1973), 9-41

12. A Convergent Two-Time Method for Periodic Differential Equations (with W. Hall and A. Hausrath), Jour. Diff. Eq. 15 (1974), 459-498

13. Discontinuous Periodic Solutions for an Autonomous Nonlinear Wave Equation (with W. Hall and A. Hausrath), Proc. Royal Irish Academy 75A (1975), 195-226

14. 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

15. Lectures on Integration of L^oo-Valued Functions, Fluid Mechanics Research Institute, University of Essex, England, 1977

16. Existence of the Pettis Integral of L^oo-Valued Translation Functions, Fluid Mechanics Research Institute, University of Essex, England, Report No. 93, April 1978

17. The Pettis Integration of a Perturbed Wave Equation, Math. Proc. Camb. Phil. Soc. 86 (1979), 145-159

18. 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

19. 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

20. On the Discretization Error of Parametrized Nonlinear Equations (with W. Rheinboldt), SIAM J. Numer. Anal. 20 (1983), 732-746

21. Solution Manifolds and Submanifolds of Parametrized Equations and Their Discretization Errors (with W. Rheinboldt), Numer. Math. 45 (1984), 323-343

22. The Role of the Tangent Map in Analyzing Bifurcation Behavior (with W. Rheinboldt), Zeit. f. Angew. Math. und Mech. 64 (1984), 407-412

23. Local Error Estimates for Parametrized Nonlinear Equations (with W. Rheinboldt), SIAM J. Numer. Anal. 22 (1985), 729-735

24. Folds on the Solution Manifold of a Parametrized Equation (with W. Rheinboldt), SIAM J. Numer. Anal. 23 (1986), 693-706

25. A Geometric Framework for the Numerical Study of Singular Points (with W. Rheinboldt), SIAM J. Numer. Anal. 24 (1987), 618-633

26. 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

27. Mathematical Modeling, HRI Review, January/February 1988, Holcomb Research Institute, Butler University

28. Curious Behavior of a Groundwater Flow Model, Water Resources Research 26 (1990), 1833-1836

29. 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

30. Can Terminal Velocity Be Exceeded? (with James H. Freeman and Charles R. Hampton), Newsletter for the Consortium for Ordinary Differential Equations, Winter 1994

31. Review of Differential Systems, Software Reviews, The College Mathematics Journal 25 (1994), 329-333

32. 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

33. Can Mathematics Majors Become Engineers?, FOCUS, The Newsletter of the Mathematical Association of America, October 1996

34. Review of Interactive Differential Equations, Software Reviews, The College Mathematics Journal 28 (1997), 63-66

35. The "New" Differential Equations and the "Old" Numerical Analysis, Proceedings of the Third International DERIVE and TI-92 Conference, Gettysburg College, July 1998

36. Differential Equations and Java, Proceedings of the 2000 International Conference on Parallel and Distributed Processing Techniques and Applications (PDPTA'2000), Las Vegas, June 2000

37. 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

38. 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)