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Bortz, David

Professor

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Research Areas research areas

Research

research overview

  • Dr. Bortz's research in focused on the methodology of data-driven modeling and scientific machine learning as applied to complex biological, environmental, and medical systems including: cellular migration, infectious diseases, bacterial community population dynamics, and designs for an artificial pancreas.

keywords

  • Data-driven modeling, Scientific Machine Learning, Applied Mathematics, Mathematical Biology

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 / Fall 2019 / Fall 2021 / Fall 2022 / Spring 2023
    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 4390 - Modeling in Mathematical Biology
    Primary Instructor - Spring 2020 / Spring 2021
    Investigates how complex systems in biology can be studied using applied mathematics. Examines several case studies which include topics from microbiology, enzyme reaction kinetics, neuroscience, ecology, epidemiology, physiology and bioengineering. Same as APPM 5390.
  • APPM 4720 - Open Topics in Applied Mathematics
    Primary Instructor - Spring 2022 / Spring 2023
    Provides a vehicle for the development and presentation of new topics that may be incorporated into the core courses in applied mathematics. Department enforced prerequisite: variable, depending on the topic, see instructor. May be repeated up to 15 total credit hours. Same as APPM 5720.
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