John Davis, Ph.D.
Associate Department Chair Professor of Mathematics
Ph.D., Auburn University, 1998 Phi Beta Kappa
Academic Interests and Research
Ordinary and partial differential equations, interplay between discrete and continuous (hybrid) dynamical systems, nonlinear systems theory, adaptive control theory, applied mathematics.
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, "Non-regressivity 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.
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 Non-autonomous Linear Dynamic Systems on Time Scales
Matthew K. Brammer, M.S. 2003
Thesis: Nonlinear Dynamics and Bifurcations in the Belousov-Zhabotinskii Reaction