Advanced Engineering Mathematics, 7th Edition

15.3 Fourier Integral

INTRODUCTION

In preceding chapters, Fourier series were used to represent a function f defined on a finite interval (−p, p) or (0, L). When f and f′ are piecewise continuous on such an interval, a Fourier series represents the function on the interval and converges to the periodic extension of f outside the interval. In this way we are justified in saying that Fourier series are associated only with periodic functions. We shall now derive, in a nonrigorous fashion, a means of representing certain kinds of nonperiodic functions that are defined on either an infinite interval (−, ) or a semi-infinite interval (0, ).

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