UW AMath AMath 590, Autumn Quarter, 2013

Approximation Theory and Spectral Methods

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Sample codes

Some other references

There are many other books on approximation theory listed in Trefethen’s ATAP.

Some of the books listed below are SIAM e-books and available free if you access them from a UW computer. Or if you are off-campus, you can gain access by using the UW library off-campus proxy.

Complex analysis

[CarrierKrookPearson]G. F. Carrier, M. K. and C. E. Pearson, Functions of a Complex Variable: Theory and Technique. In the SIAM Classics in Applied Math Series and available as an ebook. Chapters 2 and 3 have a good summary of much of the theory we’ll use.
[Agarwal]R. P. Agarwal, K. Perera, and S. Pinelas, An Introduction to Complex Analysis, Springer, 2011. online
[Ponnusamy]S. Ponnusamy and Herb Silverman, Complex Variables with Applications, Springer, 2006. online


[Driscoll]T. A. Driscoll, Learning MATLAB, SIAM e-book, 2009.
[Higham]D. J. Higham and N. J. Higham, Matlab Guide: Second Edition SIAM e-book, 2005.
[Moler]C. B. Moler, Numerical Computing with MATLAB, SIAM e-book, 2004.


[Dive-into-Python]M. Pilgram, Dive Into Python,.
[Python]G. van Rossum, An Introduction to Python,


[HighamChapter]N. J. Higham, Tex and Latex Chapter from: <i>Handbook of Writing for the Mathematical Sciences</i>, Second Edition, SIAM e-book. (See also Appendix B for latex symbols)
[GriffithsHigham]D.F. Griffiths and D.J. Higham, Learning LaTeX, SIAM, 1997

Spectral Methods

[Boyd]J.P. Boyd, Chebyshev and Fourier Spectral Methods Second edition, freely available from the author’s website
[Fornberg]B. Fornberg, A Practical Guide to Pseudospectral Methods, Cambridge University Press.
[LeVequeFourierNotes]R. J. LeVeque, Fourier Transforms.