Tensors

Abstract

In this chapter we develop the concept of tensors, their meaning, and how they arise from vectors. Emphasis is placed on tensor transformations, covariance between coordinate systems, and relation to the metric. The concept of metric connection and the Christoffel symbols is introduced in three dimensions via the easily visualizable idea of parallel transport. Derivatives and intergrals in covariant form are discussed. The first two chapters are designed to familiarize the reader with the language that is the bread and butter of the general theory of relativity and other higher geometric theories.