Complex and Fourier Analysis with Applications to Art, Science and Engineering

Harvard FAS

Complex analysis: complex numbers, functions, mappings, Laurent series, differentiation, integration, contour integration and residue theory, conformal mappings. Applications to visualization, art (especially M.C. Escher). Anamorphic images. Fourier Analysis: orthogonality, Fourier Series, Fourier transforms. Signal processing: sampling theorems (Nyquist, Shannon), fast Fourier transforms. Applications to image, audio analysis: filtering and deblurring.