Scalar field

In the multivariate analysis, vector calculus and differential geometry, a scalar field is a function which assigns to each point of a room is a real number ( scalar). Scalar fields are of great importance in the field description of the physics, and in the multi-dimensional vector analysis. Scalar describe for example, the temperature of each point in space.

Definition

A scalar field is when each point of a plurality is assigned a scalar.

A distinction is made between real-valued scalar fields

And complex scalar fields

Examples

Examples for scalar fields in the physics of the air pressure, temperature, density, potential, or in general ( also referred to as Skalarpotentiale ).

Operations

Important operations in connection with scalar fields are:

• Gradient of a scalar field, which is a vector field.
• Directional derivative of a scalar field.

• Field Theory