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Bortz, David Matthew Associate Professor

Positions

Research Areas research areas

Research

research overview

  • 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.

keywords

  • Mathematical Biology, Numerical Analysis, and High Performance Computing.

Publications

selected publications

Teaching

courses taught

  • APPM 2360 - Introduction to Differential Equations with Linear Algebra
    Primary Instructor - Spring 2018
    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
    Primary Instructor - Spring 2019
    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
    Primary Instructor - Fall 2018
    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 5350 - Methods in Applied Mathematics: Fourier Series and Boundary Value Problems
    Primary Instructor - Fall 2018
    Department enforced prerequsite courses: APPM 2350 or MATH 2400 and APPM 2360 and a prerequisite or corequisite course: APPM 3310 or MATH 2130 or MATH 2135. Same as APPM 4350.
  • APPM 5470 - Methods of Applied Mathematics: Partial Differential and Integral Equations
    Primary Instructor - Fall 2019
    Studies properties and solutions of partial differential equations. Covers methods of characteristics, well-posedness, wave, heat and Laplace equations, Green's functions and related integral equations. Department enforced prerequisites: APPM 4350 or MATH 4470 and APPM 4360 or MATH 3450.
  • APPM 8400 - Mathematical Biology Seminar
    Primary Instructor - Spring 2018 / Fall 2018 / Spring 2019 / Fall 2019
    Introduces advanced topics and research in mathematical and computational biology. Instructor consent required.

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