1) General: The separation of an intellectual or material whole into its
constituent parts for individual study. The study of such constituent
parts and their interrelationships in making up a whole
(opposite of → synthesis).
From M.L. analysis, from Gk. analysis "a breaking up," from analyein "unloose," from ana- "up, throughout" + lysis "a loosening," from lyein "to loosen, release, untie". The L. cognate and counterpart of this Gk. word, i.e. luere has formed the words solve, dissolve, solution. The Skt. cognate lu, lunoti "to cut, sever, mow, pluck, tear asunder, destroy," lava "cutting, plucking; what is cut; fragment, piece;" PIE *leu- "to loosen, divide, cut apart". The Eng. lose, loose and Ger. los derive from this root.
Ânâlas, from ânâ-, → ana-, +
las "loose" ([Mo'in], Gilaki, Tabari, Tâleši, Aftari). We do not
know the Av./O.Pers. counterparts of these Gk. las, lysis, lyein,
believe that las and the following words probably derive from
the above-mentioned PIE *leu-:
ânâlas-e dadehâ, ânâkâvi-ye ~
Fr.: analyse de données
The evaluation of reduced data; → data reduction.
ânâlas-e vâmuni, ânâkâvi-ye ~
Fr.: analyse dimensionnelle
A technique used in physics based on the fact that the various terms in a
physical equation must have identical → dimensional formulae
if the equation is to be true for all consistent systems of unit. Its main uses are:
Fr.: analyse de Fourier
The process of decomposing any function of time or space into a sum of sinusoidal functions using the → Fourier series and → Fourier transforms. In other words, any data analysis procedure that describes or measures the fluctuations in a time series by comparing them with sinusoids. Fourier analysis is an essential component of much of modern applied and pure mathematics. It forms an exceptionally powerful analytical tool for solving various problems in many areas of mathematics, physics, engineering, biology, finance, etc. and has opened up new realms of knowledge.
After the French mathematician Baron Jean Baptiste Joseph Fourier (1768-1830), whose work had a tremendous impact on the physical applications of mathematics; → analysis.
Fr.: analyse numérique
The study of methods for approximation of solutions of various classes of mathematical problems including error analysis.
Fr.: analyse optique
The mathematical evaluation of an optical system to determine its basic optical properties and image quality characteristics.
Fr.: analyse quantitative
The analysis of a chemical sample to derive its precise percentage composition in terms of elements, radicals, or compounds.
Fr.: analyse de régression
A statistical technique used to determine the values of parameters for a function that best fits a given set of data.
Fr.: analyse tensorielle
A method of calculation in higher mathematics based on the properties of tensors.
Fr.: analyse vectorielle
Fr.: analyse de forme d'onde
The resolution of a complex waveform into a sum of simple periodic waves, usually by computer means.