the separating of any material or abstract entity into its constituent elements (opposed to synthesis).
2.
this process as a method of studying the nature of something or of determining its essential features and their relations: the grammatical analysis of a sentence.
3.
a presentation, usually in writing, of the results of this process: The paper published an analysis of the political situation.
4.
a philosophical method of exhibiting complex concepts or propositions as compounds or functions of more basic ones.
5.
Mathematics.
a.
an investigation based on the properties of numbers.
b.
the discussion of a problem by algebra, as opposed to geometry.
c.
the branch of mathematics consisting of calculus and its higher developments.
d.
a system of calculation, as combinatorial analysis or vector analysis.
e.
a method of proving a proposition by assuming the result and working backward to something that is known to be true. Compare synthesis(def. 4).
6.
Chemistry.
a.
intentionally produced decomposition or separation of materials into their ingredients or elements, as to find their kind or quantity.
b.
the ascertainment of the kind or amount of one or more of the constituents of materials, whether obtained in separate form or not. Compare qualitative analysis, quantitative analysis.
analysis, branch of mathematics that utilizes the concepts and methods of the calculus. It includes not only basic calculus, but also advanced calculus, in which such underlying concepts as that of a limit are subjected to rigorous examination; differential and integral equations, in which the unknowns are functions 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 analysis and tensor analysis; differential geometry; and many other fields.
![[P]](http://cache.lexico.com/g/r/premium_mh.gif){kind=small}
Audio Help [uh-nal-uh-sis] Pronunciation Key 