Differential Equations

7

Fourier Integral Transforms

7.1 INTRODUCTION

Integral transforms are useful in solving initial and boundary value problems and in evaluating certain integrals. Laplace and Fourier transforms are two important transforms which are widely used in engineering and physical applications. They are used in the solution of conduction of heat, vibration of strings, oscillations of elastic beams, transmission lines, etc.

Here we define Fourier transform together with Fourier sine and cosine transforms, their inverses and study their properties and consider evaluation of certain integrals.

7.2 INTEGRAL TRANSFORMS

A linear integral transform or simply an integral transform of a function f(x) is defined by

 

 

where K(s, x), called the Kernel of the ...