UW AMath AMath 590, Autumn Quarter, 2013

Approximation Theory and Spectral Methods

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Course information


  • Prof. Randall LeVeque
    • Office: Lewis 328
    • netid for email: rjl
    • Office hours: Tuesday 1:30-2:30, Thursday 12:30-1:30, or by appointment.


  • MW 3:30 - 4:45 pm in LOW 105 Note room change


  • Homework: 75%, final project: 25%.
  • There will probably be 5 homework assignments.
  • See Homework and project for more information and due dates.


This course will be an introduction to interpolation and approximation of data and functions by polynomials, piecewise polynomials, and trigonometric series. Practical aspects of implementation such as FFTs and the chebfun software will be covered. See Software for the course.

Spectral methods for solving differential equations will serve as the main motivating application, along with other approximation problems and a brief introduction to finite element methods.


Note that SIAM members can purchase these books directly from SIAM at a big discount, and that UW students can join SIAM free

See also the books in the Some other references, particularly [Boyd] and [Fornberg] on spectral methods.

Outline (tentative)

I hope to cover the following:

  • Most of Chapters 1 - 17 and 21-23 of ATAP,
  • Most of Chapters 1 - 10 from MMS (there is some overlap with ATAP),
  • Introduction to piecewise polynomials and finite element methods.