analysis, branch of mathematics mathematics, deductive study of numbers, geometry, and various abstract constructs, or structures; the latter often "abstract" the features common to several models derived from the empirical, or applied, sciences, although many emerge from purely mathematical or
..... Click the link for more information. that utilizes the concepts and methods of the calculus calculus, branch of mathematics that studies continuously changing quantities. The calculus is characterized by the use of infinite processes, involving passage to a limit —the notion of tending toward, or approaching, an ultimate value.
..... Click the link for more information. . It includes not only basic calculus, but also advanced calculus, in which such underlying concepts as that of a limit limit, in mathematics, value approached by a sequence or a function as the index or independent variable approaches some value, possibly infinity. For example, the terms of the sequence 1-2, 1-4, 1-8, 1-16, … are obviously getting smaller and smaller; since,
..... Click the link for more information. are subjected to rigorous examination; differential and integral equations, in which the unknowns are functions function, in mathematics, a relation f that assigns to each member x of some set X a corresponding member y of some set Y; y is said to be a function of x, usually denoted f(x) (read "f of x
..... Click the link for more information. rather than numbers, as in algebraic equations; complex variable analysis, in which the variables are of the form z=x+iy, where i is the imaginary unit; vector U [−3,1] and V [5,2], one can add their corresponding components to find the resultant vector R [2,3], or one can graph U and V on a set of coordinate axes and complete the parallelogram formed with U and V
..... Click the link for more information. analysis and tensor tensor, in mathematics, quantity that depends linearly on several vector variables and that varies covariantly with respect to some variables and contravariantly with respect to others when the coordinate axes are rotated (see Cartesian coordinates ).
..... Click the link for more information. analysis; differential geometry r moves along a curve at arc length s from some fixed point, then t = dr/ds is a unit tangent vector to the curve at r. The normal vector n
..... Click the link for more information. ; and many other fields.

analysis

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.

analysis

Field of mathematics that incorporates the methods of algebra and calculus—specifically of limits, continuity, and infinite series—to analyze classes of functions and equations having general properties (e.g., differentiability). Analysis builds on the work of G.W. Leibniz and 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 equations, Fourier analysis (see Fourier transform), complex analysis, vector and tensor analysis, real analysis, and functional analysis. See also numerical analysis.

analysis

See systems analysis & design and computer forensics.

analysis

1. short for psychoanalysis

2. Chem

a. the decomposition of a substance into its elements, radicals, or other constituents in order to determine the kinds of constituents present (qualitative analysis) or the amount of each constituent (quantitative analysis)

b. the result obtained by such a determination

3. Maths the branch of mathematics principally concerned with the properties of functions, largely arising out of calculus

4. Philosophy (in the writings of Kant) the separation of a concept from another that contains it

analysis [ə′nal·ə·səs]

(analytical chemistry)

The determination of the composition of a substance.

(mathematics)

The branch of mathematics most explicitly concerned with the limit process or the concept of convergence; includes the theories of differentiation, integration and measure, infinite series, and analytic functions. Also known as mathematical analysis.

(meteorology)

A detailed study in synoptic meteorology of the state of the atmosphere based on actual observations, usually including a separation of the entity into its component patterns and involving the drawing of families of isopleths for various elements.

analysis (redirected from in the ultimate analysis)

analysis

analysis

analysis

analysis
(redirected from in the ultimate analysis)