• Multilevel Iterative Methods for Discretized PDEs
This is a special summer course given by Dr. Qingguo Hong in 315 McAllister building at 3:30 pm – 4:50 pm every Wednesday from June 8, 2017 to August 17, 2017. This course develops the theory of multilevel iterative methods for discretized PDEs. The course covers the following topics: basic linear iterative methods, preconditioned conjugate methods, fast Auxiliary space preconditioning methods, subspace corrections methods, domain decomposition method and basic multigrid methods.
• MATH 503 – Functional Analysis
This course develops the theory needed to treat linear integral and differential equations, within the framework of infinite-dimensional linear algebra. Applications to some classical equations are presented. The course covers the following topics: Banach and Hilbert spaces, dual spaces, linear operators, distributions, weak derivatives, Sobolev spaces, applications to linear differential equations.
• MATH 513 – Partial Differential Equation I
First order equations, the Cauchy problem, Cauchy-Kowalevski theorem, Laplace equation, wave equation, heat equation.
• MATH 514 – Partial Differential Equations II
Sobolev spaces and Elliptic boundary value problems, Schauder estimates. Quasilinear symmetric hyperbolic systems, conservation laws.
• MATH 518 – Probability Theory
Measure theoretic foundation of probability, distribution functions and laws, types of convergence, central limit problem, conditional probability, special topics.
• MATH 523 – Numerical Analysis I
Approximation and interpolation, numerical quadrature, direct methods of numerical linear algebra, numerical solutions of nonlinear systems and optimization.
• MATH 524 – Numerical Linear Algebra
This course provides a graduate level foundation in numerical linear algebra. It covers the mathematical theory behind numerical algorithms for the solution of linear systems of equations and eigenvalue problems. Specific topics include: matrix decompositions, direct methods of numerical linear algebra, eigenvalue computations, iterative methods.
• MATH 551 – Numerical Solution of Ordinary Differential Equations
Methods for initial value and boundary value problems; convergence and stability analysis, automatic error control, stiff systems, boundary value problems.
• MATH 597 C – Multiscale Methods
Formal courses given on a topical or special interest subject which may be offered infrequently; several different topics may be taught in one year or term.
• MATH 597 D – Applied Math Methods in Biology Sciences
Formal courses given on a topical or special interest subject which may be offered infrequently; several different topics may be taught in one year or term.
• AE 559 – Computational Fluid Dynamics in Building Design
Theory and applications of building environmental modeling with Computational Fluid Dynamics (CFD)
• IE 519 – Dynamic Programming
Theory and application of dynamic programming; Markov decision processes with emphasis on applications in engineering systems, supply chain and information systems.
• IE 521 – Nonlinear Programming
Fundamental theory of optimization including classical optimization, convex analysis, optimality conditions and duality, algorithmic solution strategies, variational methods.
• IE 597 A – Advanced Linear Programming
This is a graduate level course on linear programming (LP) and its extensions emphasizing the underlying mathematical structures, geometrical ideas, and algorithms. The topics covered include: the geometry of linear optimization, duality theory, the simplex method, sensitivity analysis, large scale linear problems, network flows, the ellipsoid method as a poloynomial time algorithm for LP, and interior point methods.
• ME 523 – Numerical Solutions Applied to Heat Transfer and Fluid Mechanics Problems
Application of finite difference methods to the study of potential and viscous flows and conduction and convection heat transfer.
• PNG 512 – Numerical Reservoir Simulation
Mathematical analysis of complex reservoir behavior and combination drives; numerical methods for the solution of behavior equations; recent developments.
Maintained by Qipin Chen.