Content: |
This is an introduction to Fourier Analysis geared towards advanced undergraduate students from both pure and applied areas. It should be particularly suitable for majors in the sciences and engineering. Topics will include properties of complex numbers, the Discrete Fourier Transform, Fourier series, the Dirichlet and Fejer kernals, convolutions, approximations by trigonometric polynomials, uniqueness of Fourier coefficients, Parseval's identity, properties of trigonometric polynomials, absolutely convergent Fourier series, convergence of Fourier series, applications of Fourier series, and the Fourier transform, including the Poisson summation formula and Plancherel's identity. While the main effort will be to establish the foundations of the subject, applications will include the Fast Fourier Transform, the heat equation, the wave equation, sampling, and signal processing. |