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
APPM 2350 - Calculus 3 for Engineers
Primary Instructor
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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
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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
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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
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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
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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.
APPM 5480 - Methods of Applied Mathematics: Approximation Methods
Primary Instructor
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Spring 2020 / Spring 2022 / Spring 2023
Covers asymptotic evaluation of integrals (stationary phase and steepest descent), perturbation methods (regular and singular methods, and inner and outer expansions), multiple scale methods and applications to differential and integral equations. Department enforced prerequisite: APPM 5470.
APPM 7400 - Topics in Applied Mathematics
Primary Instructor
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Spring 2018 / Spring 2019 / Spring 2020
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.
APPM 8300 - Nonlinear Waves Seminar
Primary Instructor
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Spring 2022 / Fall 2023 / Fall 2024
Introduces the core methods in the analysis of nonlinear partial differential and integral equations or systems to graduate students. Provides a vehicle for the development, presentation, and corporative research of new topics in PDE and analysis.
