
“real: chapter_11” — 2011/5/23 — 0:43 — page1—#1
11
Fourier Series
11.1 INTRODUCTION
In 1807, Fourier discovered that several arbitrary functions (not even
continuous) could be associated to a finite or infinite linear combina-
tion of sine and cosine functions. These are the so-called trigonometric
polynomials or the Fourier series and have become an indispensable
tool in the analysis of periodic events such as vibrations, planetary
motions and wave motions, which are studied in depth in physics and
engineering. Many important mathematical questions have also been
raised in the study of the Fourier series and mathematical analysis
has been deeply influenced ...