Fourier Analysis

This course provides an introduction to Fourier analysis for functions of one real variable.

The following topics are treated:

• Fourier series of periodic functions that are absolutely integrable: basic properties, convergence results, and applications to partial differential equations (PDEs)

• Fourier transform of absolute and square integrable functions: basic properties, inversion formulas, the Poisson summation formula, and the Shannon sampling theorem

• Discrete Fourier transform (DFT): theory and computational aspects.