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Function of a real variable 实函数 Funzione di variabile reale
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实函数(Real function),指定义域和值域均为实数集的子集的函数。實函數的特性之一是可以在坐標平面上畫出圖形。 Una funzione di variabile reale è una funzione che prende valori sull'insieme dei numeri reali e restituisce altri numeri reali. Più precisamente, una tale funzione ha come dominio e codominio o un suo sottoinsieme. È possibile generalizzare il dominio e considerare il prodotto cartesiano di con sé stesso un numero arbitrario di volte. La funzione prenderà uno o più numeri reali e restituirà uno o più numeri reali. Si dice dunque che l'argomento della funzione è una -upla di numeri reali, o un vettore di . Rappresentazione di un campo vettoriale In mathematical analysis, and applications in geometry, applied mathematics, engineering, and natural sciences, a function of a real variable is a function whose domain is the real numbers , or a subset of that contains an interval of positive length. Most real functions that are considered and studied are differentiable in some interval.The most widely considered such functions are the real functions, which are the real-valued functions of a real variable, that is, the functions of a real variable whose codomain is the set of real numbers.
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In mathematical analysis, and applications in geometry, applied mathematics, engineering, and natural sciences, a function of a real variable is a function whose domain is the real numbers , or a subset of that contains an interval of positive length. Most real functions that are considered and studied are differentiable in some interval.The most widely considered such functions are the real functions, which are the real-valued functions of a real variable, that is, the functions of a real variable whose codomain is the set of real numbers. Nevertheless, the codomain of a function of a real variable may be any set. However, it is often assumed to have a structure of -vector space over the reals. That is, the codomain may be a Euclidean space, a coordinate vector, the set of matrices of real numbers of a given size, or an -algebra, such as the complex numbers or the quaternions. The structure -vector space of the codomain induces a structure of -vector space on the functions. If the codomain has a structure of -algebra, the same is true for the functions. The image of a function of a real variable is a curve in the codomain. In this context, a function that defines curve is called a parametric equation of the curve. When the codomain of a function of a real variable is a finite-dimensional vector space, the function may be viewed as a sequence of real functions. This is often used in applications. Una funzione di variabile reale è una funzione che prende valori sull'insieme dei numeri reali e restituisce altri numeri reali. Più precisamente, una tale funzione ha come dominio e codominio o un suo sottoinsieme. È possibile generalizzare il dominio e considerare il prodotto cartesiano di con sé stesso un numero arbitrario di volte. La funzione prenderà uno o più numeri reali e restituirà uno o più numeri reali. Si dice dunque che l'argomento della funzione è una -upla di numeri reali, o un vettore di . Rappresentazione di un campo vettoriale Le funzioni si dividono in funzioni scalari, se il codominio è un sottoinsieme di , e funzioni vettoriali se il codominio è un sottoinsieme di per un certo . In particolare, si dirà campo vettoriale una funzione da (un sottoinsieme di) (con ) in stesso. In generale le possibilità sono quattro (considerando ): * : la situazione più classica; * : una funzione scalare in variabili; * : una funzione vettoriale di una variabile (ad esempio quella che dato un numero restituisce parte intera e parte frazionaria); * : una funzione vettoriale in variabili. Le funzioni (scalari) di una variabile reale si classificano in funzioni algebriche e funzioni trascendenti. 实函数(Real function),指定义域和值域均为实数集的子集的函数。實函數的特性之一是可以在坐標平面上畫出圖形。
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