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Domain (mathematical Analysis)
In mathematical analysis, a domain or region is a non-empty connected open set in a topological space, in particular any non-empty connected open subset of the real coordinate space or the complex coordinate space . This is a different concept than the domain of a function, though it is often used for that purpose, for example in partial differential equations and Sobolev spaces. The basic idea of a connected subset of a space dates from the 19th century, but precise definitions vary slightly from generation to generation, author to author, and edition to edition, as concepts developed and terms were translated between German, French, and English works. In English, some authors use the term ''domain'', some use the term ''region'', some use both terms interchangeably, and some define the two terms slightly differently; some avoid ambiguity by sticking with a phrase such as ''non-empty connected open subset''. One common convention is to define a ''domain'' as a connected ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Analysis
Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (mathematics), series, and analytic functions. These theories are usually studied in the context of Real number, real and Complex number, complex numbers and Function (mathematics), functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis. Analysis may be distinguished from geometry; however, it can be applied to any Space (mathematics), space of mathematical objects that has a definition of nearness (a topological space) or specific distances between objects (a metric space). History Ancient Mathematical analysis formally developed in the 17th century during the Scientific Revolution, but many of its ideas can be traced back to earlier mathematicians. Early results in analysis were i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
