There will be no class in the week of Feb 24. We will have make-up classes
later.
Course Instructor: Shi Jin
Phone: 608-263-3302(o);
E-mail:
jin@math.wisc.edu
Class Hours: TR 11:00-12:15 at B329 Van Vleck
Office Hours: TR:1:30-2:30am, Van Vleck 511,
or by
appointment
References: (reserved in the Math Library)
- G. H. Golub and C.F. van Loan, Matrix Computations,
, John Hopkins Univ Press, 1996
- S.G. Nash and A. Sofer, Linear and Nonlinear Programming,
S.G. Nash and A. Sofer, McGraw-Hill, 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.
-
J.S. Liu, Monte Carlo Strategies in Scientific Computing,
Springer, 2001
-
J.M. Haile, Molecular Dynamics Simulation : Elementary Methods,
Wiley, New York, 1992.
Materials to be covered:
- Numerical algebra:
Direct and iterative methods for linear systems, eigenvalue problems, sparse matrices, nonlinear algebraic equations
- Linear programming and nonlinear optimization:
The Simplex Method, 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
- Monte Carlo methods and molecular dyanmics
Basic probability theory, MC methods for integral, sampling, MC methods in statistical mechanics, molecular
dynamics and applications
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.