I
Field of mathematics that incorporates the methods of algebra and calculus
specifically of limit s, continuity , and infinite series
to analyze classes of function s and equation s having general properties (e.g., differentiability).
Analysis builds on the work of Isaac Newton by exploring the applications of the derivative and the integral . Several distinct but related subfields have developed, including the calculus of variations, differential equation s, Fourier analysis (see Fourier transform ), complex analysis, vector and tensor analysis , real analysis, and functional analysis . See also numerical analysis .
II
In chemistry, the determination of the properties and composition of samples of materials; qualitative analysis establishes what is there, and quantitative analysis measures how much.
A large body of systematic procedures (analytical chemistry) has evolved in close association with other branches of the physical sciences since their beginnings. A sample of a single compound may be analyzed to establish its elemental composition (see element , molecular weight ) or molecular structure; many measurements use spectroscopy and spectrophotometry . A mixed sample is usually analyzed by separating, detecting, and identifying its components by methods that depend on differences in their properties (e.g., volatility, mobility in an electric or gravitational field, distribution between liquids that do not mix). The many types of chromatography are increasingly useful, particularly with biological and biochemical samples.
III
[c mediumvioletred] (as used in expressions)
algorithms analysis of
blood analysis
cost benefit analysis
dimensional analysis
functional analysis
input output analysis
{{link=numerical analysis">numerical analysis
spectrochemical analysis
systems analysis
tensor analysis