Level set

In mathematics designated level set amount or level the set of all points of a function ( a scalar field ), which is assigned the same value.

Definition

It had to be an open set, a real-valued function and a value of the target amount, then that means

The level set of the function to the level or levels. It is therefore necessary, that is, the level set is the inverse image of under.

As Subniveaumenge the amount

Referred to, ie.

Applications

Physics

For two-dimensional scalar fields, this amount is usually a line and we speak of isoline or contour line. For three-dimensional scalar fields (for example, for scalar potential fields ), this amount is usually a curved surface and they are called iso-surface or surface level (eg contour lines ). The name is derived from the name of sea level for the near mean sea level extending equipotential surface of the Earth's gravity field. The term level surface but is also used for other force fields, such as an electric field or a magnetic field.

Economics

For a production function and a production level, the amount of all bundles of production factors by which the amount can be generated. The amount is referred to as the level of production isoquant.