Function of a real variable
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In [[mathematics]], a '''function of a real variable''' is a [[mathematical function]] whose [[domain (mathematics)|domain]] is the [[real line]]. More loosely, a function of a real variable is sometimes taken to mean any function whose domain is a subset of the [[real line]].
Functions of a real variable were the classical object of study in [[mathematical analysis]], specifically [[real analysis]]. In that context, a function of a real variable was usually meant a '''real-valued function''' of a real variable, that is, a function whose domain and [[codomain]] were the real numbers. However, because of their convenience in fields such as [[Fourier analysis]], it was also common to consider complex functions of a real variable, that is, a function whose domain was the real numbers and whose range was the complex numbers.
Until the introduction of [[functional analysis]] in the 1920s, the study of functions of a real variable was one of the two major subdivisions of mathematical analysis. The other was the study of [[function of a complex variable|functions of a complex variable]], otherwise known as [[complex analysis]].
[[Category:Mathematical analysis]]
[[Category:Mathematical terminology]]