Applications are predominantly to problems in fluid dynamics.
This time, I plan spend the bulk of the time on spectral element and spectral multidomain methods, including recent work on the development of methods for compressible flows. No text will be required, however several books are now available on the subject. Polynomial Approximation of Differential Equations, By D. Funaro, Springer-Verlag, 1992. Chebyshev and Fourier Spectral Methods by J.P. Boyd, Springer-Verlag, 1989. Graded homework, typically involving the use of a computer, will be periodically assigned.