FOURIER TRANSFORMS

The Fourier transform, named after Joseph Fourier, is a mathematical transform with many applications in physics and engineering. The motivation for the Fourier transform comes from the study of Fourier series. In the study of Fourier series, complicated but periodic functions are written as the sum of simple waves mathematically represented by sines and cosines. The Fourier transform is an extension of the Fourier series that results when the period of the represented function is lengthened and allowed to approach infinity.

L1: Integral Transform - Fourier Integral Theorem - Fourier Sine and Cosine Integrals - Complex Form of Fourier Integral - Fourier Transforms - Inversion Formulae for Fourier Transforms - Properties of Fourier Transforms

L2: Convolution of Two Functions - Convolution Theorem - Finite Fourier Sineand Cosine Transforms - Parseval’s Identity for Fourier Transforms - Fourier Transforms of the Derivatives - Fourier Cosine and Sine Transforms of Derivatives - Relation Between Fourier and Laplace Transforms

L3: Applications of Fourier Transforms to Initial Boundary Value Problems: Heat Conduction - Vibrations of a String - Transmission Lines