A Gentle Introduction to Tensors
by Boaz Porat
Publisher: Technion 2010
Number of pages: 87
The book discusses constant tensors and constant linear transformations, tensor fields and curvilinear coordinates, and extends tensor theory to spaces other than vector spaces, namely manifolds. This document was written for the benefits of Engineering students.
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by Ray M. Bowen, C.-C.Wang - Springer
This book presents the basics of vector and tensor analysis for science and engineering students. Volume 1 covers algebraic structures and a modern introduction to the algebra of vectors and tensors. Clear presentation of mathematical concepts.
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 R. M. Brannon - The University of Utah
A step-by-step introduction to tensor analysis that assumes you know nothing but basic calculus. Considerable emphasis is placed on a notation style that works well for applications in materials modeling, but other notation styles are also reviewed.
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.