Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

MAT 226A: Numerical Methods: Fundamentals
Approved: 2008-06-01, Roland Freund

Units/Lecture:

Fall, alt years; 1st LEC 3.0 hrs/wk; 2nd T-D 1.0 hrs/wk

Suggested Textbook: (actual textbook varies by instructor; check your instructor)

Prerequisites:

128AB or equivalent, or consent of instructor; familiarity with some programming language.

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.

Suggested Schedule:

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
    • LU factorization
    • Newton's method
  • General Principles
    • Conditioning
    • Floating-point arithmetic
    • Stability of algorithms
  • Interpolation
    • B-splines
  • Integration
    • Gaussian integration
    • Adaptive integration
    • High-dimensional integrals
  • Eigenvalue problems
    • QR algorithm
  • Singular Value Decomposition
    • Bidiagonalization
    • QR decomposition
    • Least-squares problem
    • Ill-posed problems
    • Generalizations of SVD

Additional Notes:

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


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.

Assessment:

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