Spring 2019

Archived:

## Math Methods of Applied Sciences II

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

## Numerical Methods for Dynamical Systems

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

## Numerical Approximation Theory

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

## Iterative Methods for Systems of Equations

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.

## Numerical Methods in Finance

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

## Differential Geometry I

Core topics in differential and Riemannian geometry including Lie groups, curvature, relations with topology.

## Partial Differential Equations II

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

## Real Analysis I

Lebesgue measure and integration, differentiation, abstract measure theory.

This course is equivalent to MATH 6579. Students should not be able to obtain credit for both MATH 6579 and MATH 6337.

## Complex Analysis

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.

## Ordinary Differential Equations II

This sequence develops the qualitative theory for systems of differential equations. Topics include stability, Lyapunov functions, Floquet theory, attractors, invariant manifolds, bifurcation theory, and normal forms. (2nd of two courses)