Definition:Real Function/Multivariable

Definition

Let $f: S_1 \times S_2 \times \cdots \times S_n \to \R$ be a mapping where $S_1, S_2, \ldots, S_n \subseteq \R$.

Then $f$ is defined as a (real) function of $n$ (independent) variables.

The expression:

$y = \map f {x_1, x_2, \ldots, x_n}$

means:

(The dependent variable) $y$ is a function of (the independent variables) $x_1, x_2, \ldots, x_n$.

Also see

• Definition:Real-Valued Function

• Results about real functions can be found here.

Sources

• 1914: G.W. Caunt: Introduction to Infinitesimal Calculus ... (previous) ... (next): Chapter $\text I$: Functions and their Graphs: $2$. Functions
• 1961: David V. Widder: Advanced Calculus (2nd ed.) ... (next): $1$ Partial Differentiation: $\S 1$. Introduction
• 1963: Morris Tenenbaum and Harry Pollard: Ordinary Differential Equations ... (previous) ... (next): Chapter $1$: Basic Concepts: Lesson $2 \text C$: Function of Two Independent Variables: Comment $2.691$
• 1973: G. Stephenson: Mathematical Methods for Science Students (2nd ed.) ... (previous) ... (next): Chapter $1$: Real Numbers and Functions of a Real Variable: $1.3$ Functions of a Real Variable: $\text {(c)}$ Functions of More than One Variable $(3)$