Quick Introduction to Tensor Analysis
by Ruslan Sharipov
Publisher: Samizdat Press 2004
Number of pages: 47
The author wrote this book in a 'do-it-yourself' style so that he gave only a draft of tensor theory, which includes formulating definitions and theorems and giving basic ideas and formulas. All other work such as proving consistence of definitions, deriving formulas, proving theorems or completing details to proofs is left to the reader in the form of numerous exercises. This style makes learning the subject really quick and more effective for understanding and memorizing.
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by Peter Dunsby
Contents: the special theory of relativity, vectors and tensors in special relativity, conceptual basis of general relativity, curved space time and general relativity, Einstein's field equations, Schwarzschild's solution.
by Taha Sochi - viXra
These notes are the second part of the tensor calculus documents. In this text we continue the discussion of selected topics of the subject at a higher level expanding, when necessary, some topics and developing further concepts and techniques.
by Eric Gourgoulhon, Marco Mancini - arXiv.org
These lecture notes present a method for symbolic tensor calculus that runs on fully specified smooth manifolds (described by an atlas), that is not limited to a single coordinate chart or vector frame, and runs even on non-parallelizable manifolds.
by Taha Sochi - arXiv
These are general notes on tensor calculus which can be used as a reference for an introductory course on tensor algebra and calculus. A basic knowledge of calculus and linear algebra with some commonly used mathematical terminology is presumed.