Math 2.0

Real functions Concept

Function of several variables

Builds on FunctionEuclidean space

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.

Reading path

To understand this page from the ground up, read these 3 pages in order. The foundations come first.

Show the path as a graph
Euclidean space, object, no evidence levelEuclidean spaceobjectFunction, concept, no evidence levelFunctionconceptFunction of several variables, concept, no evidence levelFunction of several v…concept
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Euclidean space object
  2. Function concept
  3. Function of several variables concept

Where this leads

569 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Function_of_several_real_variables, lead section
About this page
Tag0JPCHTXWG0
URIm2://0JPCHTXWG0
Aliasesmultivariable-function, function-of-several-real-variables
Kindconcept
WritingW0 stub
MSC26B99
UsesFunction, Euclidean space
Same as

Markdown · JSON · Edit on GitHub

What this page needs for W1

  • an inventory row: the row of the inventory that the node accounts for (0 of 1)

The writing levels say how complete the text of a page is. They do not measure its truth.

What links here

Used by