Expertise
My main research interests are in the area of differential equations, primarily related to models in mathematical biology. Most models that I have developed and/or studied are nonlinear, both for ordinary and (parabolic) partial differential equations. Current applications of interest include population dynamics and invasive species, with a side interest in epidemiology. Earlier work looked at optimal control, with projects involving porous media flow, and cancer treatment.
I am also interested in research associated with teaching and learning calculus, as well as applied math topics. Current projects involve examining data for differences in educational gain among groups of students in calculus, and improving student success in integral calculus.
I have mentored eight graduate students (seven at FGCU), and nine undergraduate research projects (14 students total). Topics have included modeling the spread of the Zika virus, oyster-mussel competition dynamics, zombies, musical instruments and Fourier analysis, and an age-based compartmental model of star populations. Additionally, I have been on three master's thesis committees (including two in biology).