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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.
This course contains the basic numerical and simulation techniques for the pricing of derivative securities.
Applications of mathematical techniques from MATH 6514 to solve real-world problems. Group projects to solve industrial problems in topics chosen by the instructor. (2nd of two courses)
Core topics in differential and Riemannian geometry including Lie groups, curvature, relations with topology.
This course covers the general mathematical theory of linear stationary and evolution problems plus selected topics chosen on the instructor's interests.
Topics include L^p, Banach and Hilbert spaces, basic functional analysis.
Measure and integration theory
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