What would you like to do?

What is the history of fourier series?

already exists.

Would you like to merge this question into it?

already exists as an alternate of this question.

Would you like to make it the primary and merge this question into it?

exists and is an alternate of .

It is quite complicated, and starts before Fourier. Trigonometric series arose in problems connected with astronomy in the 1750s, and were tackled by Euler and others. In a different context, they arose in connection with a vibrating string (e.g. a violin string) and solutions of the wave equation.

Still in the 1750s, a controversy broke out as to what curves could be represented by trigonometric series and whether every solution to the wave equation could be represented as the sum of a trigonometric series; Daniel Bernoulli claimed that every solution could be so represented and Euler claimed that arbitrary curves could not necessarily be represented. The argument rumbled on for 20 years and dragged in other people, including Laplace. At that time the concepts were not available to settle the problem.

Fourier worked on the heat equation (controlling the diffusion of heat in solid bodies, for example the Earth) in the early part of the 19th century, including a major paper in 1811 and a book in 1822. Fourier had a broader notion of function than the 18th-century people, and also had more convincing examples.

Fourier's work was criticised at the time, and his insistence that discontinuous functions could be represented by trigonometric series contradicted a theorem in a textbook by the leading mathematician of the time, Cauchy.

Nonetheless Fourier was right; Cauchy (and Fourier, and everyone else at that time) was missing the idea of uniform convergence of a series of functions. Fourier's work was widely taken up, and also the outstanding problems (just which functions can be represented by Fourier series?; how different can two functions be if they have the same Fourier series?) were slowly solved.

Source: Morris Kline, Mathematical Thought from Ancient to Modern Times, Oxford University Press, 1972, pages 478-481, 502-514, 671-678,and 964.
26 people found this useful
Thanks for the feedback!

Where did Joseph Fourier live?

Joseph Fourier Fourier was born at Auxerre in the Yonne département of France, the son of a tailor. He was orphaned at age eight. Fourier was recommended to the Bishop of Aux

Can every function be expanded in fouriers series?

no every function cannot be expressed in fourier series... fourier series can b usd only for periodic functions.

What is the difference between fourier series and fourier transform?

As it has been already hinted, Fourier Series is used for periodic signals. It represents the signal by the discrete-time sequence of basis functions with finite and concrete

What is the application of Fourier series in civil engineering?

when we have need to know the temperature in a bar about any distance we can use fourier series to know that and then we can apply sufficient temperature.

What is a fast Fourier transform?

A fast Fourier transform is an efficient algorithm for working out the discrete Fourier transform - which itself is a Fourier transform on 'discrete' data, such as might be he

Difference between fourier series and z-transform?

z transform is related to discrete time signal while fourier series is related to continuous time signal. z transform=sigmalm -infinty to +infinity x(n)z-n

What is the difference between a Fourier series and a Fourier transform?

The Fourier series is an expression of a pattern (such as an electrical waveform or signal) in terms of a group of sine or cosine waves of different frequencies and amplitude.

What is the importance of fourier series?

The Fourier series is important because it allows one to model periodic signals as a sum of distinct harmonic components. In other words, representing signals in this way allo

What is the practical application of a Fourier series?

There are many applications for this complex theory. One of these include the determination of harmonic components in a complex waveform. This is very helpful in analyzing AC

Where fourier series are used in real life?

Fourier analysis is used in many places. Three examples are digital filtering, where a signal is converted to frequency domain, certain bands are removed or processed, and the

Why cannot aperiodic signal be represented using fourier series?

An aperiodic signal cannot be represented using fourier series because the definition of fourier series is the summation of one or more (possibly infinite) sine wave to repres

What is the Fourier Transform?

The Fourier transform is a mathematical transformation used to  transform signals between time or spatial domain and frequency  domain. It is reversible. It refers to both t

What did fourier invent?

In October 1824, Fourier published a scientific paper titled "Remarques generales sur les Temperatures du globe terrestre et des espaces planetaires" in the journal Annales de

What is the practical application of fourier series in electrical engineering?

In electrical engineering, the Fourier series is used to analyse  signal waveforms to find their frequency contest. This is needed to  design communication systems that will