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.
APPM 2360 - Introduction to Differential Equations with Linear Algebra
Primary Instructor
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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
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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
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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
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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
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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.
APPM 5390 - Modeling in Mathematical Biology
Primary Instructor
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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. Department enforced prerequisites: APPM 2360 and APPM 3310 or MATH 2130 or MATH 2135 or instructor consent required. Same as APPM 4390.
APPM 5720 - Open Topics in Applied Mathematics
Primary Instructor
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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 6 total credit hours. Same as APPM 4720.
APPM 8400 - Mathematical Biology Seminar
Primary Instructor
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Spring 2018 / Fall 2018 / Spring 2019 / Spring 2020 / Fall 2020
Introduces advanced topics and research in mathematical and computational biology. Instructor consent required.
