COURSE SYLLABUS

Course Number: MATH6640
Course Title: INTRODUCTION TO NUMERICAL ANALYSIS II
Credit Hours: 3
Prerequisites: MATH2660 and the ability to program in a high level language.
Corequisite: 

Objectives: 
This course treats numerical methods for matrices. It studies general aspects of numerical linear algebra and specifically introduces students to programming and scientific computation. 


Course Content (typical): 
Recall of elementary linear algebra. (1 -- 2 days)

Direct  methods for solving linear systems of equations (5 weeks)
-- Gaussian elimination, scaling and pivoting
-- Matrix factorizations (LU and QR decomposition methods)
-- Cholesky method 

Iterative techniques in matrix computations (3 weeks)
-- Norms, eigenvalues, eigenvectors and the convergence of iterative methods
-- Jacobi, Gauss--Seidel and SOR iteration
-- Iterative refinement
 
Matrix eigenvalue computations (7 weeks)
-- Power method, inverse iteration
-- Orthogonal Hessenberg reduction of matrices
-- QR algorithm with implicit shifts for real matrices

Assign around 5 -- 6 programs from the algorithms above to be programmed and 
tested by the students.

Assign at least one retieval from "net lib" for comparison of the codes and results.

Possible Textbooks: 
Dedicated numerical linear algebra texts:
-- B. N. Datta, Numerical Linear Algebra, 1994, Brooks/Cole
-- D. S. Watkins, Fundamentals of Matrix Computations, Wiley

General numerical analysis texts:
-- K. E. Atkinson, An introduction to Numerical Analysis, Wiley
-- D. Kinkaid and W. Cheney, Numerical Analysis, Brooks/Cole

Grading and Evaluation Procedures:
Programming assignments, tests and final exam at the instructor's discretion.

Statement related to policies on unannounced quizzes and class attendance and participation:
Individual instructors have different policies concerning pop quizzes, class participation, homework grades, and attendance, which are announced at the beginning of the semester.