This is a very lucid introduction to spectral methods emphasizing
the mathematical aspects of the theory rather than the many
applications in numerical analysis and the engineering sciences.
The first part is a fairly complete introduction to Fourier series
while the second emphasizes polynomial expansion methods like
Chebyshev's. The author gives rigorous proofs of fundamental
results related to one-dimensional advection and diffusions
equations. The book addresses students as well as practitioners of
numerical analysis.
General
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