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Publications in VIVO

Hoefer, Mark

Professor

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Research Areas research areas

Research

research overview

  • Multiscale nonlinear wave phenomena in physical systems, including fluid dynamics, geophysical systems, condensed matter, superfluids, and nonlinear optics; modulation theory of nonlinear waves including multiphase and multidimensional waves; dispersive hydrodynamics, dispersive shock waves, solitons, solitary waves, and singular limits of nonlinear PDE; dispersive hydrodynamic-type laboratory experiments in fluid dynamics; methods of applied mathematics including perturbation theory, singular asymptotics, scientific computing, and mathematical modeling

keywords

  • Nonlinear Waves, Shock Waves, Fluid Dynamics, Solitons, Asymptotic Methods, Partial Differential Equations, Scientific Computing, Magnetization Dynamics, Spin Waves, Spin Hydrodynamics

Publications

selected publications

Teaching

courses taught

  • APPM 2350 - Calculus 3 for Engineers
    Primary Instructor - Fall 2018 / Fall 2023
    Covers multivariable calculus, vector analysis, and theorems of Gauss, Green, and Stokes. Degree credit not granted for this course and MATH 2400.
  • APPM 2360 - Introduction to Differential Equations with Linear Algebra
    Primary Instructor - Spring 2022
    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 4360 - Methods in Applied Mathematics: Complex Variables and Applications
    Primary Instructor - Spring 2024
    Introduces methods of complex variables, contour integration and theory of residues. Applications include solving partial differential equations by transform methods, Fourier and Laplace transforms and Reimann-Hilbert boundary-value problems, conformal mapping to ideal fluid flow and/or electrostatics. Same as APPM 5360.
  • APPM 5360 - Methods in Applied Mathematics: Complex Variables and Applications
    Primary Instructor - Spring 2024
    Introduces methods of complex variables, contour integration and theory of residues. Applications include solving partial differential equations by transform methods, Fourier and Laplace transforms and Reimann-Hilbert boundary-value problems, conformal mapping to ideal fluid flow and/or electrostatics. Department enforced prerequisites: APPM 2350 or MATH 2400 and APPM 2360 and a prerequisite or corequisite course of APPM 3310 or MATH 3130 or MATH 3135. Same as APPM 4360.
  • APPM 5470 - Methods of Applied Mathematics: Partial Differential and Integral Equations
    Primary Instructor - Fall 2021 / Fall 2023
    Studies properties and solutions of partial differential equations. Covers methods of characteristics, well-posedness, wave, heat and Laplace equations, Green's functions and related integral equations. Department enforced prerequisites: APPM 4350 or MATH 4470 and APPM 4360 or MATH 3450.
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