Fast Fourier Transforms

Basic aspects of fourier series; definition of fourier series; examples of fourier series; fourier series of real functions; pointwise convergence of fourier series; further aspects of convergence of fourier series; fourier sine series and cosine series; convergence of fourier sine and cosine series; the discrete fourier transform (DFT); the fast fourier transform (FFT); some applications of fourier series; fourier transforms; properties of fourier transforms; inversion of fourier transforms; convolution - an introduction; the convolution theorem; an application of convolution in quantum mechanics; filtering, frequency detection, and removal of noise; summation kernals arising from poisson summation; fourier optics; fresnel diffraction; fraunhofer diffraction; circular apertures; the phase transformation induced by a thin lens; imaging with a single lens; user's manual for fourier analysis software; some computer programmes; the schwarz inequality.