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The Fourier series is an example of a trigonometric series. [2] By expressing a function as a sum of sines and cosines, many problems involving the function become easier to analyze because trigonometric functions are well understood. For example, Fourier series were first used by Joseph Fourier to find solutions to the heat equation. This ...
The method of Fourier-transform spectroscopy can also be used for absorption spectroscopy. The primary example is " FTIR Spectroscopy ", a common technique in chemistry. In general, the goal of absorption spectroscopy is to measure how well a sample absorbs or transmits light at each different wavelength.
In the study of heat conduction, the Fourier number, is the ratio of time, , to a characteristic time scale for heat diffusion, . This dimensionless group is named in honor of J.B.J. Fourier , who formulated the modern understanding of heat conduction. [ 1 ]
An Elementary Treatise on Fourier's Series: And Spherical, Cylindrical, and Ellipsoidal Harmonics, with Applications to Problems in Mathematical Physics (2 ed.). Ginn. p. 30. Carslaw, Horatio Scott (1921). "Chapter 7: Fourier's Series". Introduction to the Theory of Fourier's Series and Integrals, Volume 1 (2 ed.). Macmillan and Company. p. 196.
In addition, the improved sensitivity and speed have opened up new areas of application. Spectra can be measured in situations where very little energy reaches the detector. Fourier transform infrared spectroscopy is used in geology, [11] chemistry, materials, botany [12] and biology research fields. [13]
The subject of Fourier series investigates the idea that an 'arbitrary' periodic function is a sum of trigonometric functions with matching periods. According to the definition above, some exotic functions, for example the Dirichlet function, are also periodic; in the case of Dirichlet function, any nonzero rational number is a period.
A number of authors, notably Jean le Rond d'Alembert, and Carl Friedrich Gauss used trigonometric series to study the heat equation, [20] but the breakthrough development was the 1807 paper Mémoire sur la propagation de la chaleur dans les corps solides by Joseph Fourier, whose crucial insight was to model all functions by trigonometric series ...
The first four partial sums of the Fourier series for a square wave. Fourier series are an important tool in real analysis. Fourier series are an important tool in real analysis. Fourier series decomposes periodic functions or periodic signals into the sum of a (possibly infinite) set of simple oscillating functions, namely sines and cosines ...