Abstract
Abstract Tensors and tensor algebra are presented. The concept of a tensor is defined in two ways: as something which yields a scalar from a set of vectors, and as something whose components transform a given way. The meaning and use of these definitions is expounded carefully, along with examples. The action of the metric and its inverse (index lowering and raising) is derived. The relation between geodesic coordinates and Christoffel symbols is obtained. The difference between partial differentiation and covariant differentiation is explained at length. The tensor density and Hodge dual are briefly introduced.
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