Dr. Bortz's research is focused on the development and analysis of mathematical models of complex biological, environmental, and medical systems. In particular, he is developing models for the fragmentation of bacterial aggregates. A deeper understanding of the separation mechanism could lead to improvements in bioreactor design for wastewater treatment as well as therapies for blood-borne infections. A part of Dr. Bortz's research at the intersection of biology and mathematics involves experimental design. And, he has a research project which uses experimental design methods to generate accurate meshes for solving PDE models of physical systems.
Mathematical Biology, Numerical Analysis, and High Performance Computing.
APPM 2360 - Introduction to Differential Equations with Linear Algebra
Introduces ordinary differential equations, systems of linear equations, matrices, determinants, vector spaces, linear transformations, and systems of linear differential equations. Credit not granted for this course and both MATH 2130 and MATH 3430.
APPM 3310 - Matrix Methods and Applications
Introduces linear algebra and matrices with an emphasis on applications, including methods to solve systems of linear algebraic and linear ordinary differential equations. Discusses vector space concepts, decomposition theorems, and eigenvalue problems. Degree credit not granted for this course and MATH 2130 and MATH 2135.
APPM 4350 - Methods in Applied Mathematics: Fourier Series and Boundary Value Problems
Reviews ordinary differential equations, including solutions by Fourier series. Physical derivation of the classical linear partial differential equations (heat, wave, and Laplace equations). Solution of these equations via separation of variables, with Fourier series, Fourier integrals, and more general eigenfunction expansions. Same as APPM 5350.
APPM 8400 - Mathematical Biology Seminar
Spring 2018 / Fall 2018 / Spring 2019 / Fall 2019
Introduces advanced topics and research in mathematical and computational biology. Instructor consent required.