Reference:
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"Spectral Methods in MATLAB" by N. Trefethen
"Chebyshev and Fourier Spectral Methods" by J.P. Boyd
"Numerical Recipes"
Matlab
Extra Questions
Lecture notes:
Differentiation 
(econo)
ODE Solvers 
(econo)
Approximation Theory 
(econo)
Spectral Methods (I) 
(econo)
Spectral Methods (II) 
(econo)
Spectral Methods (III) 
(econo)
Wavelets (I) 
(econo)
Computer Programs:
Differentiation
Modified Wavenumber Analysis
ODE Solvers (I)
ODE Solvers (II)
Spectral Methods (I)
Spectral Methods (II)
Spectral Methods (III)
Spectral Methods (IV)
Burgers Eq. (I)
Spectral Methods (V)
Spectral Methods (VI)
Spectral Methods (VII)
Setting for Wavelab
Wavelets (I)
Wavelets (II)
Wavelets (III)
Wavelets (IV)
Miscellaneous:
Reading PDF files
Ethics
Academic Integrity