Fourier research is a vital zone of arithmetic, particularly in mild of its value in physics, chemistry, and engineering. but it appears this topic is never provided to undergraduates. This booklet introduces Fourier research in its 3 such a lot classical settings: The Discrete Fourier rework for periodic sequences, Fourier sequence for periodic capabilities, and the Fourier rework for features at the actual line. The presentation is on the market for college students with simply 3 or 4 phrases of calculus, however the ebook is usually meant to be compatible for a junior-senior path, for a capstone undergraduate direction, or for starting graduate scholars. fabric wanted from genuine research is quoted with no evidence, and problems with Lebesgue degree conception are taken care of particularly informally. incorporated are a few functions of Fourier sequence, and Fourier research in greater dimensions is in short sketched. A scholar may perhaps ultimately are looking to movement directly to Fourier research mentioned in a extra complex method, both in terms of extra basic orthogonal structures, or within the language of Banach areas, or of in the community compact commutative teams, however the adventure of the classical surroundings presents a psychological snapshot of what's occurring in an summary surroundings.