Course Instructor: Shi Jin
Phone: 608-263-4700(o); E-mail: jin@math.wisc.edu

Class Hours: TR 8:00-9:15 at B129 Van Vleck
Course Homepage: www.math.wisc.edu/~jin/Teaching/S11/m715.html
Office Hours: TR:9:30-10:30, Van Vleck 625 or by appointment

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