Random variables; Probability distribution functions; Fourier transform; Mapping of random variables; Sum of random variables; Central limit theorem; Polynomial repre- sentations; Random processes; Brownian motion; Covariance; Spatial random process; Dynamical representation; Modified Helmholtz equation; Random processce in higher dimensions; Polynomial chaos and applications. The course will be in English and each session will last for 1 hour and 15 minutes. This is an introductory course. You only need to know calculus and some basic knowledge of differential equations. And the grade based on homeworks only.
授课教师介绍： Chau-Hsing Su, Kinetic thory; Plasma physics; Water waves; Stochastic PDE.He is Professor of Applied Mathematics at Brown University since 1976. He has published 60 some papers in kinetic theory of gases, plasma physics, stratified fluids, waterwaves and stochastic PDE.
Fourier methods; Galerkin and collocation projections; Polynomial spectral methods (Chebyshev, Legendre, general Jacobi; Hermite); Domain decomposition in complex geometries; spectral elements. The course will be in English and each session will last for 1 hour and 15 minutes. Some knowledge of numerical analysis is required as well as programming in any language. The grade based on computer assignments only。
授课教师介绍：George Karniadakis，MIT (Ph.D 1987; SM 1984); Postdoc at Stanford University; Assistant Professor at Princeton University， is Professor of Applied Mathematics at Brown University since 1994 and Visting Professor of Mechanical Engineering at MIT since 2000. He has published three books and more than 200 research papers on computational mathematics, microfluidics, turbulence, biophysics, and parallel computing.
This course is designed to introduce fluid dynamicists to the way that mathematicians think about fluids. It will cover relatively recent discoveries in the mathematical theory of fluids, such as bounds on the dimension of the attracting set of driven viscous flow. It will also describe problems that remain unsolved, such as those of vortical reconnection and of existence and uniqueness of the initial-value problem in three dimensions. This course will provide an introduction to mathematical fluid dynamics, with emphasis on geometric and topological properties of fluid flow. Homework40%，Exams60%。
授课教师介绍：Bruce M. Boghosian，My research interests center on theoretical and computational fluid dynamics. I am particularly interested in questions of topological fluid dynamics, and also in lattice models of computational hydrodynamics.
I have taught university-level courses in mathematics, physics, and engineering, from the introductory level to the graduate level. I have developed a two-semester sequence of courses on partial differential equations, given in both the Mathematics and Mechanical Engineering departments at Tufts University. I have developed courses on Non-Euclidean Geometry and on Knot Theory for undergraduates. I have also conducted numerous reading courses for undergraduate students, and have advised several graduate students. I was the 2002 recipient of the Undergraduate Initiative in Teaching (UNITE) award at Tufts University.