The focus of this thesis is on the property and the use of Fourier analysis in different fieldsrncontaining differential equations. The Fourier transform of an integrable function f, isrnrnï‚¥rnï€ï‚¥rnF(ï¸ )  f (x)eï€iï¸xdxrnWe present properties of Fourier transform and visit Fourier transform in connection withrnheat transfer in a conducting wire and wave propagation in an infinite bar.