Mohammed, Seid (PhD)Jenber, Dagnachew2018-07-122023-11-042018-07-122023-11-042012-01http://etd.aau.edu.et/handle/123456789/8314This project discusses the concept of Fourier transform of a function in Space with its properties theorem, inversion theorem, Fourier sine and cosine transforms theorem, Plancherel’s and Parseval’s identities theorem and the applications of Fourier transform in partial differential equations, Shannon’s sampling theorem and Heisenberg’s inequality. Therefore the purpose of this project is to solving certain problems in partial differential equations like for example Heat equation, Wave equation , and Laplace equation, to solve some complicated integrals shortly and simply, and it works in Shannon’s sampling theorem and Heisenberg’s inequality. This project uses some definitions and theorems as a preliminary from some real analysis and Fourier analysis booksenAnalysis of Fourier TransformThesis