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In mathematics, a real-valued function is a function whose values are real numbers. In other words, it is a function that assigns a real number to each member of its domain . Real-valued functions of a real variable (commonly called real functions ) and real-valued functions of several real variables are the main object of study of calculus and ...
A real-valued function of a real variable is a function that takes as input a real number, commonly represented by the variable x, for producing another real number, the value of the function, commonly denoted f(x). For simplicity, in this article a real-valued function of a real variable will be simply called a function. To avoid any ambiguity ...
In introductory calculus, when the word function is used without qualification, it means a real-valued function of a single real variable. The more general definition of a function is usually introduced to second or third year college students with STEM majors, and in their senior year they are introduced to calculus in a larger, more rigorous ...
Real analysis (traditionally, the "theory of functions of a real variable") is a branch of mathematical analysis dealing with the real numbers and real-valued functions of a real variable.
In 3 dimensions, a differential 0-form is a real-valued function (,,); a differential 1-form is the following expression, where the coefficients are functions: + +; a differential 2-form is the formal sum, again with function coefficients: + +; and a differential 3-form is defined by a single term with one function as coefficient: .
Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Originally called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus and integral calculus.
The analytic functions have many fundamental properties. In particular, an analytic function of a real variable extends naturally to a function of a complex variable. It is in this way that the exponential function, the logarithm, the trigonometric functions and their inverses are extended to functions of a complex variable.
A function f from X to Y. The set of points in the red oval X is the domain of f. Graph of the real-valued square root function, f(x) = √ x, whose domain consists of all nonnegative real numbers. In mathematics, the domain of a function is the set of inputs accepted by the function.