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Publications in VIVO

# Czubak, Magdalena Assistant Professor

## Research

### research overview

• My research interests are in partial differential equations (PDE), looking from the geometrical point of view, and making connections between PDE, differential geometry, harmonic analysis, gauge theory, mathematical physics, and very recently, probability. I have worked in broad areas of PDE, which include fluid flows on manifolds, dispersive pde, and equations with fractional diffusion.

### keywords

• Dispersive equations, Navier-Stokes Equations, Differential Geometry

## Teaching

### courses taught

• MATH 3430 - Ordinary Differential Equations
Primary Instructor - Fall 2018 / Spring 2019 / Fall 2019
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 4470 - Partial Differential Equations
Primary Instructor - Spring 2018
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 5470 - Partial Differential Equations
Primary Instructor - Spring 2018
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
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
Continuation of MATH 6230. Department enforced prerequisite: MATH 6230. Instructor consent required for undergraduates.

• Ph.D., 2008
• B.S., 2001
• B.S., 2001