**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.

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