1st semester 
20 credits / 30 lectures

The aim of this course is to introduce students to some of the fundamental ideas and techniques of spectral methods. It can be considered as an extension to the courses on numerical analysis of ODEs and PDEs. The topics include:

• Differentiation matrices
• Fourier transforms: semidiscrete, discrete, FFT
• Clustered grids, Chebyshev spectral differentiation
• Chebyshev, Fourier and Laurent series
• Applications to boundary-value, eigenvalue and evolution problems