Math 5661: Numerical Analysis II Spring 2001

Time and place: TR 4:00-5:15 CU 656
Office hours: CU Denver Building 640, Tue 2-3PM, Thu 1-3PM

Textbooks:

1. Required: David R. Kincaid and E. Ward Cheney , Second Edition - Numerical Analysis - Mathematics of Scientific Computing, Brooks/Cole Publishing Company, 1996
2. Supplementary: C. Johnson: Numerical Solution of PDEs by the Finite Element Method Cambridge University Press, 1987.
3. Recommended reading: Lloyd N. Trefethen and David Bau, III: Numerical Linear Algebra, SIAM, 1997

Topics:

Singular values decomposition, least squares, eigenvalue computation
More on numerical differentiation and integration
Numerical solution of ordinary differential equations
Numerical solution of partial differential equations by finite difference methods
Numerical solution of elliptic boundary value problems by finite element methods, sparse matrices

Selection of topics can be adapted according to the interests of students.

Grading: There will be in-class midterm on March 6 and final on May 8, 2001,
and several homeworks and computer projects. All problems are graded on the scale e0-4: 4=OK, 3=minor error, 2=significant progress, 1=some progress, 0=no progress, wrong problem, or misunderstood problem. The letter grades will be A >= 90, A- >= 85, B+ >= 80, B >= 75, B- >=70, C+ >= 65, C >= 60, C- >= 55, D+ >= 50, D >= 45, D- >= 40. Final grade will be 1/3 midterm, 1/3 final, and 1/3 homeworks and projects.

Homeworks and projects will be posted here.

Links

Review topics for in-class Final May 8:

Cea's lemma. This can be found in any introductory or theoretical book on finite elements, e.g. the books by Ciarlet, Johnson, or Brenner and Scott.

Local (a.k.a. truncation) error & order of method for ODE initial value problem

Error of linear interpolation

Error of central difference for second derivative You can use anything you want.