Math 2.0

concept

Function of several variables

Summary

A function of several real variables is a function f ⁣:D→Rf \colon D \to \mathbb{R} whose domain DD is a subset of Euclidean space Rn\mathbb{R}^n for some n≥2n \ge 2. Its value at a point x=(x1,…,xn)x = (x_1, \dots, x_n) of DD is written f(x)f(x) or f(x1,…,xn)f(x_1, \dots, x_n). Examples are f(x,y)=x2+y2f(x, y) = x^2 + y^2 on R2\mathbb{R}^2 and g(x,y,z)=xyzg(x, y, z) = xyz on R3\mathbb{R}^3.

Remarks

When the values lie in Rm\mathbb{R}^m with m≥2m \ge 2, the function is a vector-valued function of several variables. The domain is often an open subset of Rn\mathbb{R}^n, so that each point of the domain has a whole ball around it in the domain.

Explanations

L1 human

A function of two variables takes two numbers and gives one number. An example is the height of a hill above the point (x,y)(x, y) of a map. Each input is now a point of the plane or of space, not a point of a line.

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Sources

  1. Web https://en.wikipedia.org/wiki/Function_of_several_real_variables, lead section

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