ABSTRACT
Tensor mathematics is a beautiful, simple, and useful language for the description of natural phenomena. Tensor fields are the abstract symbols of this language. Each tensor field represents a single physical quantity that is associated with certain places in three-dimensional space and instants of time. Tensor equations express the relationship between physical quantities. Quantities such as the mass of a satellite, the temperature at points in a body, and the charge of an electron have a definite magnitude. They can be represented adequately by pure numbers or scalars. Properties such as the position or velocity of a satellite, the flow of heat in a body, and the electromagnetic force on an electron have both magnitude and direction. They are better represented by directed line segments or vectors. Other quantities such as the stress inside a solid or fluid may be characterized by tensors of order two or higher. Vector algebra can be a powerful tool in geometry.
