Georgia Institute of Technology College of Sciences

Review of vector calculus and and its application to partial differential equations.

Approximation of the dynamical structure of a differential equation and preservation of dynamical structure under discretization.

Theoretical and computational aspects of polynomial, rational, trigonometric, spline and wavelet approximation.

Iterative methods for linear and nonlinear systems of equations including Jacobi, G-S, SOR, CG, multigrid, fixed point methods, Newton quasi-Newton, updating, gradient methods. Crosslisted with CSE 6644.

Introduction to the numerical solution of the classic problems of linear algebra including linear systems, least squares, SVD, eigenvalue problems. Crosslisted with CSE 6643.

This course contains the basic numerical and simulation techniques for the pricing of derivative securities.

The fundamental group, covering spaces, core topics in homology and cohomology theory including CW complexes, universal coefficients, and Poincare duality.

This course covers the general mathematical theory of linear stationary and evolution problems plus selected topics chosen on the instructor's interests.

This course is a continuation of MATH 6337. It covers L^p and Hilbert spaces, and an introduction to operator theory and functional analysis.

This course is equivalent to MATH 6580. Students may not obtain credit for both MATH 6580 and MATH 6338.

Complex integration, including Goursat's theorem; classification of singularities, the argument principle, the maximum principle; Riemann Mapping theorem; analytic continuation and Riemann surfaces; range of an analytic function, including Picard's theorem.