This note covers the following
topics: Fourier Analysis, Least Squares, Normwise Convergence, The Discrete
Fourier Transform, The Fast Fourier Transform, Taylor Series, Contour
integration, Laurent series, Chebyshev series, Signal smoothing and root
finding, Differentiation and integration, Spectral methods, Ultraspherical
spectral methods, Functional analysis, Spectrum, Infinite-dimensional linear
algebra, Linear partial differential equations, Laplace's equation,
Riemann–Hilbert problems, Matrix-valued Riemann–Hilbert.