December 2020
Intermediate to advanced
1064 pages
49h 13m
English
Content preview from Advanced Engineering Mathematics, 7th Edition
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15.4 Fourier Transforms
INTRODUCTION
Up to now we have studied and used only one integral transform: the Laplace transform. But in Section 15.3 we saw that the Fourier integral had three alternative forms: the cosine integral, the sine integral, and the complex or exponential form. In the present section we shall take these three forms of the Fourier integral and develop them into three new integral transforms naturally called Fourier transforms. In addition, we shall expand on the concept of a transform pair, that is, an integral transform and its inverse. We shall also see that the inverse of an integral transform is itself another integral transform.
Transform Pairs
The Laplace transform F(s) of a function f(t) is defined by an integral, ...
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