# Montana State University Faculty Vita

Department of Mathematical Sciences

John R. Lund

Professor of Mathematics

## Education

- Ph.D., Mathematics, University of Utah, 1978
- M.S., Mathematics, University of Utah, 1973
- B.S., Mathematics, University of Tennessee, 1971

## Experience

- 1993- Head, Department of Mathematical Sciences, Montana State University
- 1989-1993 Professor, Department of Mathematical Sciences, Montana State University
- Sept. 1991 Visiting Professor, Rogaland University, Stavanger, Norway
- May 1991 Visiting Professor, Royal Institute of Technology, Stockholm, Sweden
- Fall 1987,89 Visiting Professor at Texas Tech University, Lubbock, TX
- 1984-1989 Associate Professor, Department of Mathematical Sciences, Montana State University
- 1978-1984 Assistant Professor, Department of Mathematical Sciences, Montana State University
- 1976-1978 Teaching Fellow, University of Utah
- 1975-1976 Graduate Assistant, University of British Columbia
- 1971-1975 Teaching Fellow, University of Utah

**REFEREED PUBLICATIONS:**

- "Advection-Diffusion Equations: Temporal Sinc Methods,"
*Numerical Methods for Partial Differential Equations,*11 (1995), pages 399-422, with K. L. Bowers and T. S. Carlson - "A Sinc-Galerkin Method for Convection Dominated Transport," with T. S. Carlson and
K. Bowers,
*Computation and Control III,*Vol. 15 of the series*Progress in Systems and Control Theory,*Birkhäuser Boston, Inc., 121-139 (1993). - "Numerical Simulations: Boundary Feedback Stabilization," with K. Bowers, Vol. 1 of
the
*Proceedings of the 31st IEEE Conference on Decision and Control,*IEEE Control Systems Society, 809-814 (1992). - "The Sinc-Galerkin Method for Parameter Dependent Self-Adjoint Problems," with K. M. McArthur,
R. C. Smith and K. Bowers,
*Applied Mathematics and Computation,*50(2 3):175-202 (August, 1992). - "Gaussian Quadrature for Trigonometric Polynomials : an Example from Observability,"
accepted by
*Applicable Analysis,*with D. Gilliam and C. Martin. - "A Fully Sinc-Galerkin Method for Euler-Bernoulli Beam Models," with R. C. Smith and
K. Bowers,
*Numerical Methods for Partial Differential Equations,*8(2):171-202 (March, 1992). - "Inverse Parabolic Problems and Discrete Orthogonalities,"
*Numerische Mathematik,*59, (1991), pages 361-383 with D. Gilliam and C. Martin. - "The Sinc-Galerkin Method for Fourth-Order Differential Equations,"
*SIAM Journal on Numerical Analysis,*28 (1991), pages 760-788, with R. Smith, K. Bowers and G. Bogar. - "Fully Sinc-Galerkin Computation for Boundary Feedback Stabilization,"
*Journal of Mathematical Systems, Estimation, and Control,*Vol. 1, (1991), pages 165-182, with T. Carlson and K. Bowers. - "Sinc Approximation Method for Coefficient Identification in Parabolic Systems,"
*Progress in Systems and Control Theory,*Vol. 4 (1990), pages 507-514. - "Quantifying Information Content for Ill-Posed Problems,"
*Inverse Problems,*6 (1990), pages 725-736, with D. Gilliam and C. Vogel. - "Galerkin Schemes and the Sinc-Galerkin Method for Singular Sturm-Liouville Problems,"
*Journal of Computational Physics,*89 (1990), pages 41-62 with K. Bowers and M. Jarratt. - "A Fully Galerkin Method for the Solution of Inverse Problems in Parabolic Partial
Differential Equations,"
*Inverse Problems,*6 (1990), pages 205-217, with C. Vogel. - "The Sinc Method in Multiple Space Dimensions: Model Problems,"
*Numerische Mathematik,*56 (1990), pages 789-816, with K. Bowers and K. McArthur. - "The Trapezoidal Rule for Analytic Functions of Rapid Decrease,"
*Journal of Computational and Applied Mathematics,*27 (1989), pages 389-406, with N. Eggert. - "Accuracy and Conditioning in the Inversion of the Heat Equation,"
*Progress in Systems and Control Theory,*Vol. I (1989), pages 179-196. - "Efficient Numerical Solution of Fourth-Order Problems in the Modeling of Flexible
Structures,"
*Progress in Systems and Control Theory,*Vol. I (1989), pages 283-297, with R. Smith and K. Bowers. - "A Discrete Sampling Inversion Scheme for the Heat Equation,"
*Numerische Mathematik,*54 (1989), pages 493-506, with D. Gilliam and C. Martin. - "Complex Variable and Regularization Methods of Inversion of the Laplace Transform,"
*Mathematics of Computation,*53 (1989), pages 589-608, with F. Stenger and D.D. Ang. - "Symmetrization of the Sinc-Galerkin Method with Block Techniques for Elliptic Equations,"
*I.M.A. Journal of Numerical Analysis,*9 (1989), pages 29-46, with K. Bowers and K. McArthur. - "Analytic and Numerical Aspects of the Observation of the Heat Equation,"
*Proceedings of the 1987 IEEE Conference on Decision and Control,*pages 975-976, with D. Gilliam and C. Martin. - "Spectral Representation of the Laplace and Stieltjes Transforms,"
*Mat. Aplic. Comp.,*7 (1988), pages 101-107, with D. Gilliam and J. Schulenberger. - "Numerical Implementation of the Sinc-Galerkin Method for Second-Order Hyperbolic
Equations,"
*Numerical Methods for Partial Differential Equations,*3 (1987), pages 169-185, with K. L. Bowers and K. M. McArthur. - "Sinc Function Computation of the Eigenvalues of Sturm-Liouville Problems,"
*Journal of Computational Physics,*69 (1987), pages 209-229, with N. Eggert and M. Jarratt. - "The Space-Time Sinc-Galerkin Method for Parabolic Problems,"
*International Journal for Numerical Methods in Engineering,*24 (1987), pages 1629-1644, with D. Lewis and K. Bowers. - "The Numerical Solution of Singular Poisson Equations by the Sinc-Galerkin Method,"
*SIAM Journal on Numerical Analysis,*24 (1987), pages 36-51, with K. Bowers. - "Symmetrization of the Sinc-Galerkin Method for Boundary Value Problems,"
*Mathematics of Computation,*47 (1986), pages 571-588. - "Spectral Representation of the Laplace Transform and Related Operators in ," Computational and Combinatorial Methods in Systems Theory, North Holland (1986), pages 69-73, with D. Gilliam and J.R. Schulenberger.
- "Bessel Transforms and Rational Extrapolation,"
*Numerische Mathematik,*47 (1985), pages 1-14. - "A Sinc-Collocation Method for the Computation of the Eigenvalues of the Radial Schrodinger
Equation,"
*I.M.A. Journal of Numerical Analysis,*4 (1984), pages 83-98, with B. Riley. - "A Geometric Property of the Regular Unit N-gon and Its Application to a Special Integral,"
*Proceedings of the Montana Academy of Sciences,*43 (1984), pages 194-200, with M. Jarratt. - "Examples of Functions Whose Sequence of Strong Unicity Constants is Unbounded,"
*Journal of Approximation Theory,*41 (1984), pages 244-252, with N. Eggert. - "Dense Rational Systems in the Hilbert Spaces ,"
*Applicable Analysis,*18 (1984), pages 267-281, with N. Eggert. - "Sinc Function Quadrature Rule for the Fourier Integral,"
*Mathematics of Computation,*41 (1983), pages 103-113. - "Probabilities and Upper Quantiles for the Studentized Range" (two algorithms),
*J. of Royal Statistical Society,*AS190, pages 204-210, 1983. These algorithms are available in IMSL (International Math and Statistical Library). - "The Cardinality of Extreme Sets of Rational Functions,"
*Approximation Theory III,*E.W. Cheney, editor (1979), pages 377-383, with N. Eggert.

## Books

*Sinc Methods for Quadrature and Differential Equations,*, SIAM, Philadelphia, 304 pages, 1992 (with K. Bowers). This is an introductory graduate text in the numerical solution of ordinary and partial differential equations using the Galerkin method with the Sinc basis.*Computation and Control III, Proceedings of the 1992 Bozeman Conference.*Volume 15 in the Birkhäuser series "Progress in Systems and Control Theory", 1993 (with K. Bowers).*Computation and Control II, Proceedings of the 1990 Bozeman Conference.*Volume 11 in the Birkhäuser series "Progress in Systems and Control Theory", 1991 (with K. Bowers).*Computation and Control, Proceedings of the 1988 Bozeman Conference.*Volume I in the Birkhäuser series "Progress in Systems and Control Theory", 1989 (with K. Bowers).

## Manuscripts

- "Development and Direction of the Sinc-Galerkin Method for Differential Equations," with K. Bowers and F. Stenger.
- "Numerical Quadratures for Integral Transforms," Ph.D. thesis, University of Utah, 1978.
- "Properly Discontinuous Groups and Fundamental Regions," Master's thesis, University of Utah, 1973.

## Ph.D. Dissertations Directed

**Timothy Carlson**"Sinc Procedures for the Discretization of Convection Diffusion Problems," 1994**Randy Doyle**"Extensions to the Development of the Sinc-Galerkin Method for Parabolic Problems," 1990**David Lewis**"A Fully Galerkin Method for Parabolic Problems," 1990**Mary Jarratt**"Approximation of Eigenvalues of Sturm-Liouville Differential Equations by the Sinc-Collocation Method," (Second Advisor), 1987**Kelly McArthur**"Sinc-Galerkin Solution of Second-Order Hyperbolic Problems in Multiple Space Dimensions,"(Second Advisor), 1987**Bruce Riley**"Galerkin Schemes for Elliptic Boundary Value Problems," 1982

## Invited Talks: 1989-Present

- "Numerical Methods for Burgers' Equation with Large Reynold's Number" University of Linkoping, Linkoping, Sweden, October, 1991.
- "The Sinc Method in Numerical Analysis" Danish Technical Institute, Copenhagen, Denmark, August, 1991.
- "The Sinc Function, Numerical Integration and Boundary Value Problems" to the Systems and Optimization Group at The Royal Institute of Technology, Stockholm, Sweden. This talk occured during the authors visit to the Royal Institute from May 1 to June 1, 1991.
- "The Sinc Method as a Numerical Tool" to the Engineering School at Washington University, St. Louis, MO., February, 1991.
- "Towards Stabilizing Burger's Equation" in the mini-symposium: Inverse Eigenvalue Problems at the SIAM Conference on Linear Algebra, San Francisco, CA., November, 1990.
- "Stabilization of Parabolic Problems via Boundary Feedback" Virginia Polytechnic Institute, V.P.I. Blacksburg, Virginia, September, 1990.
- "Sinc Methods in Elementary Numerical Analysis" Radford University, Radford, Virginia, September, 1990.
- "Discrete Orthogonality and Numerical Methods" Texas Tech University, Lubbock, Texas, September, 1990.
- "A Survey of Sinc Methods for Boundary Value Problems," Royal Institute, Stockholm, Sweden, June, 1989.
- "Parameter Identification of Distributed Parameter Systems via Sinc Methods," at MTNS-89, Amsterdam, The Netherlands, June, 1989.
- Numerical and Theoretical Methods in Observability Minisymposium: "Parameter Identification in Parabolic Systems via Sinc Methods" at the SIAM Conference on Control in the 90's, May, 1989.
- Survey of Sinc Methods in Ill-Posed Problems" at the University of Colorado-Denver, January, 1989.

## Grants and Awards

- "Proposal for the `Third Conference on Computation and Control'," MSU Research and Creative Activity Grant, $2,000 and MSU Foundation Grant, $1,000, 1992 (with K. Bowers).
- Received NSF-MONTS grant for the proposal "A Fully Galerkin Method for Transport Problems." This provided summer salary for 1991 (with K. Bowers).
- Received an NSF grant for ($9,000) to fund the Second Conference on Computation and Control (August 1-August 7, 1990) at MSU.
- Received MSU Foundation ($2,000) and MONTS ($1,500) grants for funding of the Second Conference in Computation and Control (August 1-August 7, 1990).
- Received a grant from ONR ($9,000) and the MSU Foundation ($3,000) to support the Conference on Computation and Control, held August 1-11, 1988 at MSU.
- Received "Award of Excellence" from Bozeman Chamber of Commerce and Montana State University Alumni Office for undergraduate teaching and advising.
- Received NSF-MONTS grant for the proposal "Spectral Conjectures Concerning the Matrices of the Sinc-Galerkin Method." This provided summer salary for 1987 (with K. Bowers).
- Received Research/Creativity grant funding travel to Salt Lake City, Utah to work with Professor Frank Stenger for a week in the Spring of 1986.
- Received NSF-MONTS grant for the proposal "Computational Analysis of the Sinc-Galerkin Method Applied to Singular Elliptic Equations" (1985) (with K. Bowers).
- Received Research/Creativity grant for "Strong Unicity and Rational Functions" for the summer of 1981.

## Professional Activities

- President of the Rocky Mountain Mathematics Consortium (1991-92).
- Vice-President of the Rocky Mountain Mathematics Consortium (1990-91).
- Associate editor for
*Journal of Mathematical Systems, Estimation, and Control.* - Referee papers for
*Mathematics of Computation, The Journal of Computational and Applied Mathematics*,*The Journal of Computational Physics*and*Automatica.* - Review proposals for NSF.

## Professional Memberships

- Phi Beta Kappa
- Phi Kappa Phi
- Pi Mu Epsilon, President, Utah chapter, 1974
- SIAM

## Professional Service

- Organized and ran (with K. Bowers) the Third Conference on Computation and Control II, hosted by the MSU Mathematical Sciences Department, August 5-11, 1992. This conference was funded by the the MSU Foundation. Editor (with K. Bowers) of the proceedings from this conference, published as Volume 15 in the series "Progress in Systems and Control Theory", by Birkhäuser, Boston 1993.
- Organized and ran (with K. Bowers) the minisymposium
*Computational Control of Distributed Parameter Systems*at the SIAM Conference on Control and Its Applications, Minneapolis, Minnesota, September 17-19, 1992. - Organized a summer seminar series (Summer, 1991) which included local speakers as well as the following : David Gilliam, Texas Tech University, Lubbock, Texas "Boundary Stabilization for Distributed Parameter Systems", Sven Åke Gustafson, Rogaland University, Stavanger, Norway, Convergence Acceleration Methods Applied to Sinc Approximation with Application to Approximation of , James P. Keener, University of Utah, Salt Lake City, Utah, "Spiral Waves in Excitable Media : The Core of the Spiral", Frank Stenger, University of Utah, Salt Lake City, Utah, "Sinc Functions : Future Directions", Gordon Wade, U.C.L.A., Los Angeles, Ca., "Convergence Theory for a Fully Galerkin Approximation to Inverse Problems from Parabolic P.D.E.'s", and Ward Whitt, AT T Bell Laboratories, Murray Hill, N.J., "The Fourier Series Method for Inverting Transforms of Probability Distributions".
- Organized the mini-symposium "Computational Sinc Procedures for Time-Dependent Problems in Mathematical Physics" at ICIAM (International Conference on Industrial and Applied Mathematics), Washington, D.C. (July, 1991)
- Organized the mini-symposium "Inverse Eigenvalue Problems" at the SIAM Conference on Linear Algebra in San Francisco (November 5-8, 1990).
- Organized and ran (with K. Bowers) the Second Conference on Computation and Control II, hosted by the MSU Mathematical Sciences Department, August 1-7, 1990. This conference was funded by the NSF, the MSU Foundation and MONTS. Editor (with K. Bowers) of the proceedings from this conference, published as Volume 11 in the series "Progress in Systems and Control Theory", by Birkhäuser, Boston 1991.
- Organized the session "Discrete Observability and Numerical Methods" at the MTNS-89 meeting, Amsterdam, The Netherlands, June, 1989.
- Organizer of a mini-symposium on "Computational Methods in Parameter Identification" at the SIAM Conference on Control in the 90's, San Francisco, California, May 17-19, 1989.
- Organized and ran (with K. Bowers) the Conference on Computation and Control, hosted by the MSU Mathematical Sciences Department, August 1-11, 1988. The conference was funded in part by ONR, MSU Foundation and MONTS. Editor of proceedings (with K. Bowers) from this conference, published as Volume I in the series "Progress in Systems and Control Theory", by Birkhäuser, Boston 1989.
- Organized and ran (with N. Eggert) a Conference in Approximation Theory, Montana State University, summer 1981.

Updated on: June 17, 1998.