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Beylkin, Gregory

Professor

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Research

research overview

  • Gregory Beylkin's research is focused on analysis and development of fast algorithms for solving integral and differential equations. Applications include quantum chemistry, gravity field evaluation and estimation, wave propagation and inverse problems. A number of algorithms developed by Gregory Beylkin and his group have been implemented and are used in practical applications.

keywords

  • numerical analysis, harmonic analysis, wavelets, signal processing, wave propagation, inverse problems

Publications

selected publications

Teaching

courses taught

  • APPM 3310 - Matrix Methods and Applications
    Primary Instructor - Fall 2019 / Spring 2021 / Fall 2021 / Spring 2022 / Fall 2022 / Spring 2023 / Fall 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 5610 - Numerical Analysis 2
    Primary Instructor - Spring 2018 / Spring 2020 / Spring 2021 / Spring 2022 / Spring 2024
    Numerical linear algebra, eigenvalue problems, optimization problems, and ordinary and partial differential equations. Department enforced prerequisite: APPM 5600 or MATH 5600.
  • APPM 5620 - Numerical Linear Algebra
    Primary Instructor - Spring 2024
    Develops and analyzes methods for the solution of square nonsingular linear systems, linear least squares problems, eigenvalue problems, and rank estimation. Direct and iterative methods are covered, as well as methods for dense and sparse problems. Requires solid background in linear algebra and proficiency with scientific computing.
  • APPM 6610 - Introduction to Numerical Partial Differential Equations
    Primary Instructor - Fall 2020 / Fall 2022
    Covers finite difference, finite element, finite volume, pseudo-spectral, and spectral methods for elliptic, parabolic, and hyperbolic partial differential equations. Department enforced prerequisite: APPM 5600. Recommended prerequisite: APPM 5610 or graduate numerical linear algebra.
  • APPM 7400 - Topics in Applied Mathematics
    Primary Instructor - Fall 2019
    Provides a vehicle for the development and presentation of new topics with the potential of being incorporated into the core courses in applied mathematics. May be repeated up to 6 total credit hours.
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