Educational Background
B.A. Indiana University
B.S. Ball State University
Ph.D. Florida Institute of Technology
Professional Experience
Dr. Shaw has been teaching full time at the university level since 1980 and is a member of the American Mathematical Society and the International Federation of Nonlinear Analysts. At the January 1992 joint meeting of the AMS and MAA conference in Baltimore, Maryland, he presented a talk at the AMS session of Ordinary Differential Equations on “Kronecker Product Self-adjoint Boundary Value Problems,” attended the MAA minicourse on the use of CAS calculators in calculus and linear algebra. He was selected (in June 1993) to attend the Duke University Workshop on Calculus as a Laboratory course, which was funded by the NSF. Dr. Shaw presented a talk at the second international conference of Dynamic Systems and Applications in May 1995 on “Some Qualitative Results of Matrix Differential Equations Using Generalized Norms
Selected Publications
Shaw, M.D. and C. Yakar. September 1998. "Generalized Variation of Parameters with Initial Time Difference and a Comparison Result in Terms of Lyapunov-like Functions;" International Journal of Nonlinear Differential Equations Theory-Methods and Applications.
Shaw, M.D. and C. Yakar.
1998. "Stability Criteria and Slowly Growing Motions with Initial Time Difference," Problems of Nonlinear Analysis in Engineering Systems.
Murty, K.N. and M.D. Shaw. 1998. "On Kronecker Product Self-adjoint Boundary Value
Problems;" Journal of Mathematical and Physical Sciences.
Liu, X. and M.D. Shaw. June 1997. "Boundedness in Terms of Two Measures for Perturbed Systems by Generalized Variation of Parameters;" Communication in Applied Analysis.
Shaw, M.D. 1995. "Generalized Stability of Motion and Matrix Lyapunov Functions;" Journal of Mathematical Analysis and Applications, Vol. 189, pp. 104-114.
Shaw, M.D., Knoll, Johnson and Evans. 1995. Discovering Calculus with Mathematica, 2nd Ed., John Wiley and Sons Inc.
Research
Dr. Shaw’s current research investigates nonlinear variation of parameters with initial time difference and variational comparison results of Lyapunov-like functions and stability criteria and slowly growing motions with initial time difference. His current teaching projects involve the calculus mastery learning program at Florida Tech. He has integrated the use of graphics calculators into the curriculum and is now using computer algebra systems of Mathematica and MATLAB as tools to help students in first- and second-year calculus; in differential equations with linear algebra course, in undergraduate and graduate linear algebra, and in the graduate course Mathematical Methods in Science and Engineering.
Research & Project Interests
Dr. Shaw’s main research is in stability analysis of nonlinear systems. This includes analysis of vector and matrix differential equations (linear and nonlinear) in which generalized variation of parameter methods are quite fruitful. He has studied the boundedness of perturbed systems in terms of two measures and most recently is investigating stability criteria for perturbed and unperturbed differential systems with initial time differences. He has also worked on Kronecker product self-adjoint boundary value problems and on nonlocal sensitivity analysis of general nonlinear Lyapunov systems that arise in a number of areas of control engineering, dynamical systems and optimal filters.
