Scalar Field

High Quality Content by WIKIPEDIA articles! In mathematics and physics, a scalar field associates a scalar value to every point in a space. The scalar may either be a mathematical number, or a physical quantity. Scalar fields are often used in physics, for instance to indicate the temperature distribution throughout space, or the air pressure. Mathematically, a scalar field on a region U is a real or complex-valued function on U. The region U may be a set in some Euclidean space, or more generally a subset of a manifold, and it is typical to impose further conditions on the field, such that it be continuous or often continuously differentiable to some order. In a mathematical context, the term "scalar field" may be used to distinguish a function of this kind with a more general tensor field, density, or differential form.

Klappentext

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics and physics, a scalar field associates a scalar value to every point in a space. The scalar may either be a mathematical number, or a physical quantity. Scalar fields are often used in physics, for instance to indicate the temperature distribution throughout space, or the air pressure. Mathematically, a scalar field on a region U is a real or complex-valued function on U. The region U may be a set in some Euclidean space, or more generally a subset of a manifold, and it is typical to impose further conditions on the field, such that it be continuous or often continuously differentiable to some order. In a mathematical context, the term "scalar field" may be used to distinguish a function of this kind with a more general tensor field, density, or differential form.