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Czubak, Magdalena

Associate Professor

Positions

Research Areas research areas

Research

research overview

  • Partial differential equations (PDE), looking from the geometrical point of view, and making connections between PDE, differential geometry, harmonic analysis, and mathematical physics: fluid flows on manifolds, dispersive pde, and equations with fractional diffusion.

keywords

  • Differential Geometry, Navier-Stokes Equations, Dispersive equations

Publications

selected publications

Teaching

courses taught

  • MATH 3001 - Analysis 1
    Primary Instructor - Spring 2021 / Fall 2021
    Provides a rigorous treatment of the basic results from elementary Calculus. Topics include the topology of the real line, sequences of numbers, continuous functions, differentiable functions and the Riemann integral.
  • MATH 3430 - Ordinary Differential Equations
    Primary Instructor - Fall 2018 / Spring 2019 / Fall 2019 / Spring 2024
    Involves an elementary systematic introduction to first-order scalar differential equations, nth order linear differential equations, and n-dimensional linear systems of first-order differential equations. Additional topics are chosen from equations with regular singular points, Laplace transforms, phase plane techniques, basic existence and uniqueness and numerical solutions. Formerly MATH 4430.
  • MATH 4001 - Analysis 2
    Primary Instructor - Fall 2019
    Provides a rigorous treatment of infinite series, sequences of functions and an additional topic chosen by the instructor (for example, multivariable analysis, the Lebesgue integral or Fourier analysis). Same as MATH 5001.
  • MATH 4470 - Partial Differential Equations
    Primary Instructor - Spring 2018 / Fall 2020 / Spring 2022 / Fall 2023
    Studies initial, boundary, and eigenvalue problems for the wave, heat, and potential equations. Solution by separation of variables, Green's function, and variational methods. Same as MATH 5470.
  • MATH 5001 - Analysis 2
    Primary Instructor - Fall 2019
    Provides a rigorous treatment of infinite series, sequences of functions and an additional topic chosen by the instructor (for example, multivariable analysis, the Lebesgue integral or Fourier analysis). Same as MATH 4001.
  • MATH 5470 - Partial Differential Equations
    Primary Instructor - Spring 2018 / Fall 2020 / Spring 2022 / Fall 2023
    Studies initial boundary and eigenvalue problems for the wave, heat and potential equations. Solution by separation of variables, Green's function, and variational methods. Department enforced prerequisite: MATH 3430 or MATH 5430. Instructor consent required for undergraduates. Same as MATH 4470.
  • MATH 6230 - Introduction to Differential Geometry 1
    Primary Instructor - Spring 2020 / Spring 2021 / Spring 2024
    Introduces topological and differential manifolds, vector bundles, differential forms, de Rham cohomology, integration, Riemannian metrics, connections and curvature. Department enforced prerequisites: MATH 2130 and MATH 4001. Instructor consent required for undergraduates.
  • MATH 6240 - Introduction to Differential Geometry 2
    Primary Instructor - Fall 2018 / Fall 2024
    Continuation of MATH 6230. Department enforced prerequisite: MATH 6230. Instructor consent required for undergraduates.
  • MATH 8234 - Topics in Differential Geometry
    Primary Instructor - Fall 2021
    Presents advanced topics in Differential Geometry, such as index theory, partial differential equations on manifolds, exterior differential systems, and Cartan's methods.

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