Introduction to Tensor Calculus
by Taha Sochi
Publisher: arXiv 2016
Number of pages: 83
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.
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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 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 Edward Nelson - Princeton Univ Pr
The lecture notes for the first part of a one-term course on differential geometry given at Princeton in the spring of 1967. They are an expository account of the formal algebraic aspects of tensor analysis using both modern and classical notations.
by Boaz Porat - Technion
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. Written for the benefits of Engineering students.