Mathematical Methods for Physicists: A concise introduction - Site Map

4
Fourier series and integrals
Fourier series are in®nite series of sines and cosines which are capable of representing
almost any periodic function whether continuous or not. Periodic functions
that occur in physics and engineering problems are often very complicated
and it is desirable to represent them in terms of simple periodic functions.
Therefore the study of Fourier series is a matter of great practical importance
for physicists and engineers.
The ®rst part of this chapter deals with Fourier series. Basic concepts, facts, and
techniques in connection with Fourier series will be introduced and developed,
along with illustrative examples. They are followed by Fourier integrals and
Fourier transforms.
Periodic functions
If function f …x† is de®ned for all x and there is some positive constant P such that
f …x ‡ P† ˆf …x†
…4:1†
then we say that f …x† is periodic with a period P (Fig. 4.1). From Eq. (4.1) we also
Figure 4.1.
A general periodic function.
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