Syllabus

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.

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.

Recommended background

Applied Math 584-5-6 or similar background is strongly recommended, along with programming experience in Matlab and/or Python and some knowledge of complex analysis.

Textbooks

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

• L. N. Trefethen, Approximation Theory and Approximation Practice, SIAM 2013.

  [Download m-files]

• L. N. Trefethen, Spectral Methods in Matlab, SIAM 2000.

  Note that this is freely available online as an ebook From off-campus computers you can use the UW libraries proxy.

  [Download m-files]

Outline (tentative)

I hope to cover the following:

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