Prepared by Roland Freund and approved by the campus in Spring 2008.

Course Request Summary

Department Submitting Request: Mathematics

Request for Action: NEW

Effective: 200910

Course Subject Area: Mathematics

Subject Code: MAT

Course Number: 226A

Descriptive Title: Numerical Methods: Fundamentals

Abbreviated Title: Numerical Methods

Units: 4

Learning Activity

1st LEC 3.0 hrs/wk

2nd T-D 1.0 hrs/wk

In Progress Grading: None

Consent of Instructor: No

Prerequisite(s): 128AB or equivalent, or consent of instructor; familiarity with some programming language.

Restrictions on Enrollment: None

Course Description: Fundamental principles and methods in numerical analysis, including the concepts of stability of algorithms and conditioning of numerical problems, numerical methods for interpolation and integration, eigenvalue problems, singular value decomposition and its applications.

General Education: No GE certification

Topical Breadth:

Diversity:

Writing Experience:

Cross Listing:

Justification:

Repeat Credit: No

Credit Limitations: None

Mode of Grading: Letter

Quarters to be Offered: I, Alternate Years

Instructors Name(s): Staff, Chair in Charge

Title(s):

Remarks:

Expanded Course Description

1. SUMMARY OF COURSE CONTENTS:

The course is designed to give students an in-depth introduction to the fundamental principles and methods of numerical analysis. The techniques covered in this course are the fundamental building blocks used in modern numerical methods for the solution of computational problems in the sciences, engineering, and many other applications areas.

Outline of the major topics:

- Two Examples of Numerical Methods

                o LU factorization

                o Newton's method

- General Principles

                o Conditioning

                o Floating-point arithmetic

                o Stability of algorithms

- Interpolation

                o B-splines

- Integration

                o Gaussian integration

                o Adaptive integration

                o High-dimensional integrals

- Eigenvalue problems

                o QR algorithm

- Singular Value Decomposition

                o Bidiagonalization

                o QR decomposition

                o Least-squares problem

                o Ill-posed problems

                o Generalizations of SVD

2. ILLUSTRATIVE READING:

No required textbook. Optional references:

- G. Dahlquist and A. Bjoerck, Numerical Methods, Dover Publications, 2003

- L.N. Trefethen and D. Bau, III, Numerical Linear Algebra, SIAM, 1997

- C.B. Moler, Numerical Computing With Matlab, SIAM, 2004

3. FINAL EXAMINATION REQUIREMENT:

Homework assignments, covering both theory and computational problems: 50%.

Final project and report: 50%

4. JUSTIFICATION OF UNITS:

Student workload is 3 hours of lecture, 6 hours of outside preparation, and 3 hours of term paper research and writing for a total of 12 hours per week.

5. POTENTIAL COURSE OVERLAP:

With the cancellation of MAT 229AB, which is being replaced by the new MAT226ABC series, there is no overlap of this proposed course with any other graduate-level course offered by the Department of Mathematics.

Some of the topics of this proposed course are also covered in ECS 230, but the focus in ECS 230 is on applications and software-related aspects of these topics. The focus of this course, however, is on a rigorous mathematical treatment of these topics. Therefore, the potential overlap of CS 230 and this proposed course is minimal.

6. GENERAL EDUCATION JUSTIFICATION: None

7. ADDITIONAL INFORMATION FOR STUDENTS: None.