Raegan Higgins, Ph.D.

My research is in the area of time scales.   The calculus of time scales was developed to unify and extend results obtained for differential equations and difference equations.  Currently, my focus is on oscillation criteria for certain linear and nonlinear second order dynamic equations. I am also interested in applications of time scales to mathematical biology and issues that affect pre-service teachers ability to teach mathematics.

Current Collaborators

Dr. Vlajko Kocic and Dr. Yevgeniy Kostrov at Xavier University of Louisiana

Dr. Elvan Akin at Missouri University of Science and Technology

Publications

Journal Articles

M. Advir, E. Akin, and R. Higgins, Oscillatory behavior of solutions of third-order delay and advanced dynamic equations, Journal of Inequalities and Applications , (2014), no 1, 1-15.

T. Stevens, Z. Aguirre-Munoz, G. Harris, R. Higgins, and X. Liu, Middle Level Mathematics Teachers' Self-Efficacy Growth through Professional Development: Differences Based on Mathematical Background, Australian Journal of Teacher Education, 38 (2013), no 4.

R. Higgins, Oscillation of a Second-order Linear Delay Dynamic Equation, Communications in Applied Analysis, 16 (2012), no 3, 403-414.

T. Stevens, G. Harris, and R. Higgins, A professional development model for middle school of mathematics, International Journal of Mathematical Education in Science and Technology, 42 (2011), no 7, 951-961.

R. Higgins, Oscillation of second-order dynamic equations, International Journal of Dynamical Systems and Differential Systems, 3 (2011), no 1/2, 189-205.

R. Higgins, Asymptotic behavior of second-order nonlinear dynamic equations on time scales, Discrete and Continuous Dynamical Systems Series B, 13 (2010), no 13, 609-622.

R. Higgins, Oscillation results for second-order delay dynamic equations, International Journal of Difference Equations, 5 (2010), no 1, 41-54.

R. Higgins, Some oscillation criteria for second-order delay dynamic equations, Applicable Analysis and Discrete Mathematics, 4 (2010), no 2, 322-337.

R. Higgins, Some oscillation results for second order functional dynamic equations, Advances in Dynamical Systems and Applications, 5 (2010) no 1, 87-105.

L. Erbe and R. Higgins, Some oscillation results for second order functional dynamic equations, Advances in Dynamical Systems and Applications, 3 (2008), no 1, 73-88.

Conference Proceedings

T. Stevens, G. Harris, R. Higgins, Z. Aguirre-Munoz, and X. Liu, Rigorous Math Courses for Middle-school Math Teachers, Proceedings of the 41st Annual Meeting of the Research Council on Mathematics Learning, (2014), 17-24.

R. J. Higgins and A. Peterson, Cauchy Functions and Taylor's Formula for Time Scales,  Proceedings of the the Sixth International Conference on  Difference Equations, (2004), 299-308.

Thesis

R. J. Higgins, Oscillation Theory of Dynamic Equations on Time Scales, Department of Mathematics and Statistics, University of Nebraska-Lincoln, 2008.