Dr. David W. Roach

Associate Professor

Department of Mathematics and Statistics

Murray State University




Courses Taught

Mat 117-Mathematical Concepts    Mat140-College Algebra   

Mat145-Trigonometry                       Mat150-Precalculus

Mat220-Business Calculus

Mat250-Calculus I                             Mat308-Calculus II

Mat411-Differential Equations        

Mat442-Intro Numerical Analysis    Mat542-Numerical Analysis   


Math Videos

The Zero Matrix


Cheri Advertisement for "The Zero Matrix"

Cheri Advertisement with departmental group photo

Cinemark Trailer

The Zero Identity


The AWM Soap Bubble Outreach project



The Euclidean Math Club



Approximation Theory, Splines, Wavelet Analysis


•  Roach, D. W., “Frequency selective parameterized wavelets of length ten", Journal of Concrete and Applicable Mathematics, vol. 8-1, January 2010.

•  Roach, D. W., “The Parameterization of the length Eight Orthogonal Wavelets with No Parameter Constraints”, Approximation Theory XII: San Antonio 2007, M. Neamtu and L. Schumaker (eds.), pp 332-347, 2008.

•  Roach, D. W., and R. Robinson, “Knot removal using the bounding tension spline”, Advances in Constructive Approximation, M. Neamtu and E. B. Saff (eds.), Nashboro Press, pp. 467-476, 2004.

•  Roach, D. W., D. Gibson, and K. Weber, “Why is the square root of 25 not equal to plus or minus five?”, Math ematics Teacher, Vol. 97-1, pp 12-13, Jan 2004.

•  Lai, M.J. and D. W. Roach, “Parameterizations of univariate orthogonal wavelets with short support”, Approximation Theory X , pp. 369—384, Innovations in Applied Math ematics, Vanderbilt Univ. Press , 2002.

•  Lai, M.J. and D. W. Roach, “The nonexistence of bivariate symmetric wavelets with two vanishing moments and short support”, Trends in Approximation Theory, pp. 213-223, Innovations in Applied Math ematics, Vanderbilt Univ. Press, 2001.

•  Christion, M. A., and D. W. Roach, “The numerical performance of Wavelets for PDE’s: The multi-scale Finite Element”, Computational Mechanics , v. 25(23), pp. 230-244, March 2000.

•  Hardin, D. P., and D. W. Roach, “Multiwavelet Prefilters I: Orthogonal prefilters preserving approximation order p<2, IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing , vol. 45-8, pp. 1106-1112, August 1998.

•  Hereford J., D. W. Roach, and R. Pigford, “Image compression using parameterized wavelets with feedback”, Independent Component Analyses, Wavelets, and Neural Networks , A. Bell, M. Vickerhauser, H. Szu, Editors, Proceedings of SPIE, Vol. 5102, pp. 267-277, 2003.

•  Roach, D. W., “Orthogonal approximation order preserving prefilters for multiwavelets”, Wavelets: Application in Signal and Image Processing IX, Andrew F. Laine, Michael A. Unser, Akram Aldroubi, Editors, Proceedings of SPIE Vol. 4478 (2001) pp. 242-253.

•  Lai, M. J. and D. W. Roach, “Nonseparable symmetric wavelets with short support”, Wavelet Applications in Signal and Image Processing VII, Proceedings of SPIE, pp. 132-146, July 1999.

•  Christon, M. A., and D. W. Roach, T.E. Voth, “The numerical performance of wavelets and reproducing kernels for PDE’s”, Proceedings of the International Conference on Computational Engineering Science, 6 pp., October 1998.

•  Christon, M. A., R. S. Baty, S. P. Burns, D. W. Roach, T. G. Trucano, T. E. Voth, J. R. Weatherby, and D. Womble, “An investigation of wavelet bases for grid-based multi-scale simulations-Final Report”, Technical Report SAND98-2456, Sandia National Laboratories, Albuquerque, New Mexico, 142 pp., September 1998.

•  Hardin D. P., and D. W. Roach, “Semi-orthogonal wavelets for elliptic variational problems”, Proceedings of the Tangier 98 International Wavelet Conference on Multi-scale Methods, INRIA, 6 pp., April 1998.

Research Presentations

•  March 2010 Talk-13th International Conference on Approximation Theory , San Antonio , TX .

•  October 2008 Talk-Applied Mathematics and Approximation Theory 2008, Memphis , TN.

•  November 2007 Talk-AMS sectional meeting, special session on wavelets, MTSU, Murfreesboro , TN.

•  November 2007 Seminar talk- The University of Georgia, Athens , GA.

•  March 2007 Talk- 12th International Conference on Approximation Theory , San Antonio , TX .

•  May 2005 Talk-The Application of Splines and Wavelets, Athens , GA.

•  Oct 2004 Talk-AMS South-Eastern Sectional Meeting, Nashville , TN.

•  Mar 2004 Talk-KYMAA state-wide meeting, Murray , KY.

•  May 2003 Talk – International Conference on Advances in Constructive Approximation, Nashville , TN.

•  April 2003 Talk – SPIE Aerosense: Aerospace/Defense Sensing, Simulation, and Controls, Kissimee , FL.

•  March 2003 Talk - Kentucky MAA Annual Meeting, Bellarmine University , Louisville , KY.

•  April 2002 Talk - Kentucky MAA Annual Meeting, Georgetown College , Georgetown , KY.

•  March 2002 Talk - 10 th S. E. Approximation Theory Conference, UGA, Athens , GA.

•  Oct 2001 Invited Talk - Western Kentucky Math Symposium, WKU, Bowling Green , KY.

•  Jul 2001 Invited Talk - SPIE's 46th Annual Meeting, San Diego , CA .

•  Mar 2001 Talk - 10th International Conference on Approximation Theory, UMSL, St. Louis , MO.

  May 2000 Talk - Trends in Approximation Theory an International Symposium, Nashville , TN.

•  Sept 1999 Poster - Image Processing Multiresolution Analysis and Statistics, Georgia Tech, Atlanta, GA.

•  July 1999 Invited Talk – SPIE’s 45 th Annual Meeting, Denver, CO.

•  April 1998 Talk – University of New Mexico Colloquium, Albuquerque , NM .

•  April 1998 Poster – International Wavelet Conference Tangier 98, Tangier, Morocco .

•  Jan 1998 Talk – Ninth International Conference on Approximation Theory, Nashville , TN.

•  May 1997 Talk – Sandia National Laboratories Colloquium, Albuquerque , NM .

•  April 1997 Talk – Ninth Southeastern Approximation Theory Conference, Athens GA.

•  March 1997 Talk – Multiwavelet Conference, Sam Houston State University , Huntsville , TX .

•  Jan 1997 Talk – Special Session of the AMS/MAA Joint Meeting, San Diego , CA .