Math/CS 715 -- Methods of Computational Mathematics II
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
Course Homepage: www.math.wisc.edu/~jin/Teaching/S11/m715.html
Office Hours: TR:9:30-10:30, Van Vleck 625
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,
- 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
- Monte Carlo methods
Basic probability theory, MC methods for integral, sampling,
the Metropolis Algorithm, MC methods in statistical mechanics
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