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Fourier Analysis

In mathematics, Fourier analysis is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fourier, who showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer.

Today, the subject of Fourier analysis encompasses a vast spectrum of mathematics. In the sciences and engineering, the process of decomposing a function into oscillatory components is often called Fourier analysis, while the operation of rebuilding the function from these pieces is known as Fourier synthesis. For example, determining what component frequencies are present in a musical note would involve computing the Fourier transform of a sampled musical note. One could then re-synthesize the same sound by including the frequency components as revealed in the Fourier analysis. In mathematics, the term Fourier analysis often refers to the study of both operations. (from wikipedia.org)

Harmonious Math: Fourier Analysis


Related Links
Fourier Analysis - wikipedia
In mathematics, Fourier analysis is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions.
Fourier's Series
Joseph Fourier was interested in the mathematical study of the diffusion of heat in solid bodies which he described using infinite trigonometric series which are now known as Fourier series.
Fourier Analysis, Time Evolution of Pulses on Strings
In addition to the traditional topics of mechanical vibrations and waves, coupled oscillators, and electro-magnetic radiation, other interesting topics are covered in this course.
The Fourier Transform and Its Applications
Instructor: Professor Brad Osgood. In this course the emphasis is on relating the theoretical principles to solving practical engineering and science problems.

e-Books
The Analytical Theory of Heat
This is a collection of eBooks of Joseph Fourier's The Analytical Theory of Heat, first published in 1822.
An Introduction to Fourier Analysis
By R.D. Stuart. Topics: Mathematics; Fourier Series; Fourier Integrals; Periodic Waveforms. Collection: folkscanomy_mathematics; folkscanomy; additional_collections.