There will be no class on Tuesday, May 3, 2011.

* Course Instructor*: Shi Jin

* Class Hours*: TR 8:00-9:15 at B129 Van Vleck

* References:* (reserved in the Math Library)

- G. H. Golub and C.F. van Loan,
*Matrix Computations,*, John Hopkins Univ Press, 1996

- C. Johnson,
*Numerical Solution of Partial Differential Equations by the Finite Element Method,*, Cambridge University Press, 1987

- S.C. Brenner and L.R. Scott,
*The Mathematical Theory of Finite Element Methods,*Springer-Verlag, 1998

- W.L. Briggs, V.E. Henson and S.F. McCormick,
*A Multigrid Tutorial,*2nd Edition, SIAM 2000.

- M.H. Kalos and P.A. Whitlock,
*Monte Carlo Methods,*John Wiley & Sons, 1986

* Materials to be covered: *

- Numerical algebra:
- Direct and iterative methods for linear systems, eigenvalue problems, sparse matrices, nonlinear algebraic equations,one and multidimensional
optimization, conjugate gradient methods

- Finite element methods for elliptic partial differential equations
- Variational formulation, Galerkin methods, energy estimate and error analysis,
implementation, discontinuous Galerkin, multigrid methods, boundary
element methods

- Monte Carlo methods
- Basic probability theory, MC methods for integral, sampling,
the Metropolis Algorithm, MC methods in statistical mechanics

* Grading:*
The final grade will be determined by
homework assignments including computer projects.

* Homework:* Homeworks, both analytic and
computational, will be
assigned several times during the semester. A basic programing language
(Fortran, C, Matlab, etc.) is essential for the computation projects.
Students should finish the homeworks with their own effort.

- Homework No. 1 , Due Feb 22, 2011
- Homework No. 2 , Due March 10, 2011
- Homework No. 3 , Due April 12, 2011
- Homework No. 4 , Due April 28, 2011
- Homework No. 5 , Due May 10, 2011, at noon