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John Davis

Professor of Mathematics
Undergraduate Program Director
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Professor of Mathematics
Education:

Ph.D., Auburn University, 1998 Phi Beta Kappa

Academic Interests and Researc

Ordinary and partial differential equations, interplay between discrete and continuous (hybrid) dynamical systems, nonlinear systems theory, adaptive control theory, applied mathematics.

Research Funding

NSF Grant EHS #0410685
Real-Time Distributed Control Networks: Dynamic Bandwidth Allocation via Adaptive Sampling, 2004-2008. $311,000

NSF Grant CMMI #0726996
Mu-Dynamics on Time Scales: Adaptive Time Domains for Dynamical Systems, 2007-2010. $143,952

Selected (Recent) Publications:

R.J. Marks II, I.A. Gravagne, J.M. Davis, "A generalized Fourier transform and convolution on time scales," Journal of Mathematical Analysis and Applications 340 (2008), 901�919.

J.M. Davis, I.A. Gravagne, B.J. Jackson, R.J. Marks II, A.A. Ramos, "The Laplace transform on time scales revisited," Journal of Mathematical Analysis and Applications 332 (2007), 1291�1307.

R.J. Marks II, I.A. Gravagne, J.M. Davis, and J.J. DaCunha, "Nonregressivity in switched linear circuits and mechanical systems," Mathematical and Computer Modelling 43 (2006), 1383�1392.

Q. Sheng, M. Fadag, J. Henderson, and J.M. Davis, "An exploration of combined dynamic derivatives on time scales and their applications," Nonlinear Analysis 7 (2006), 395�413.

I.A. Gravagne, J.M. Davis, R.J. Marks II, "How deterministic must a real-time controller be?" Proceedings of 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems, (IROS 2005), Alberta, Canada, Aug. 2005, 3856�3861.

Research Group

Dr. Ian A. Gravagne, Associate Professor of Electrical and Computer Engineering, Baylor University

Dr. Robert J. Marks II, Distinguished Professor of Electrical and Computer Engineering, Baylor University

Graduate Students Directed

Alice A. Ramos, Ph.D. student currently working with me

Billy J. Jackson, Ph.D. 2007
Thesis: A General Linear Systems Theory on Time Scales: Transforms, Stability, and Control

Jeffrey J. DaCunha, Ph.D. 2004
Thesis: Lyapunov Stability and Floquet Theory for Nonautonomous Linear Dynamic Systems on Time Scales

Matthew K. Brammer, M.S. 2003
Thesis: Nonlinear Dynamics and Bifurcations in the Belousov-Zhabotinskii Reaction

DEPARTMENT OF MATHEMATICS

Sid Richardson Science Building
One Bear Place #97328
Waco, TX 76798

(254) 710-3561