MATH 417 - Real Analysis

★ 3 (fi 6)(EITHER, 3-0-0)

Brief review of set operations and countable sets. Measure theory, integration theory, Lebesgue measure and integrals on R^n, product measure, Tonelli-Fubini theorem. Functions of bounded variation, absolutely continuous functions. Prerequisite: MATH 317 or 414.

MATH 514 - Measure Theory I

★ 3 (fi 6)(EITHER, 3-0-0)

Brief review of set operations and countable sets. Measure theory, integration theory, Lebesgue measure and integrals on R^n, product measure, Tonelli-Fubini theorem. Functions of bounded variation, absolutely continuous functions. Prerequisites: Math 317.

MATH 536 - Numerical Solutions of Partial Differential Equations I

★ 3 (fi 6)(EITHER, 3-0-0)

Finite difference and finite element methods for boundary-value problems of elliptic equations. Numerical algorithms for large systems of linear algebraic equations: direct, classical relaxation, multigrid and preconditioned conjugate gradient methods. Algorithms for vector/parallel computers and the domain decomposition method. Prerequisites: MATH 337, 436 or equivalent and some computer programming.