APPM 6470-3. Advanced Partial Differential Equations.
Continuation of APPM 5470. Advanced study of the properties and solutions of elliptic, parabolic, and hyperbolic partial differential equations. Topics include the study of Sobolev spaces and variational methods as they relate to PDEs, and other topics as time permits. Prereq., APPM 5470.
APPM 6520-3. Mathematics Statistics.
Emphasizes mathematical theory of statistics. Topics include distribution theory, estimation and testing of hypotheses, multivariate analysis, and nonparametric inference, all with emphases on theory. Prereq., APPM 5520 or MATH 5520.
APPM 6550-3. Introduction to Stochastic Processes.
Systematic study of Markov chains and some of the simpler Markoc processes including renewal theory, limit theorems for Markov chains, branching processes, queuing theory, birth and death processes, and Brownian motion. Applications to physical and biological sciences. Prereqs., MATH 4001, MATH 4510 or APPM 3570, or APPM 3570, or APPM 4560, or instructor consent. Same as MATH 6550.
APPM 6610-3. Introduction to Numerical Partial Differential Equations.
Covers finite difference, finite element, finite volume, pseudo-spectral, and spectral methods for elliptic, parabolic, and hyperbolic partial differential equations. Prereq., APPM 5600. Recommended prereq., APPM 5610 or graduate numerical linear algebra.
APPM 6640-3. Multigrid Methods.
Develops a fundamental understanding of principles and techniques of the multigrid methodology, which is a widely used numerical approach for solving many problems in such diverse areas as aerodynamics, astrophysics, chemistry, electromagnetics, hydrology, medical imaging, meteorology/oceanography, quantum mechanics, and statistical physics.
APPM 6900 (1-6) Independent Study.
Introduces graduate students to research foci of the Department of Applied Mathematics. Prereq., instructor consent.
APPM 6940 (1-3) Master's Degree Candidate.
APPM 6950 (1-6). Master's Thesis.
May be repeated up to 12 total credit hours.
APPM 7100-3. Mathematical Methods in Dynamical Systems.
Covers dynamical systems defined by mappings and differential equations. Hamiltonian mechanics, action-angle variables, results from KAM and bifurcation theory, phase plane analysis, Melnikov theory, strange attractors, chaos, etc. Prereq., APPM 5460.
APPM 7300-3. Nonlinear Waves and Integrable Equations.
Includes basic results associated with linear dispersive waves systems, first-order nonlinear wave equations, nonlinear dispersive wave equations, solitons, and the methods of the inverse scattering transform. Prereqs., APPM 5470-5480, PHYS 5210, or instructor consent.
APPM 7400 (1-3). Topics in Applied Mathematics.
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. Prereq., instructor consent.
APPM 7900 (1-3). Independent Study.
Introduces graduate students to research focuses of the Department of Applied Mathematics. Prereq., instructor consent.
APPM 8000-1. Colloquium in Applied Mathematics.
Introduces graduate students to the research focuses of the Department of Applied Mathematics. Prereq., instructor consent.
APPM 8100-2. Seminar in Dynamical Systems.
Introduces advanced topics and research in dynamical systems. Prereqs., instructor consent.
APPM 8300-3. PDE and Analysis Seminar.
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 Analysis. Prereq., APPM 5440.
APPM 8600-1. Seminar in Computational Mathematics.
Introduces advanced topics and research in computational mathematics. Prereq., instructor concent.
APPM 8990 (1-10). Doctoral Dissertation.
All doctoral students must register for no fewer than 30 hours of dissertation credit as part of the requirements for the degree. No more that 10 credit hours may be taken any one semester.