Symbolic Tensor Calculus on Manifolds: a SageMath Implementation
by Eric Gourgoulhon, Marco Mancini
Publisher: arXiv.org 2018
Number of pages: 72
Description:
These lecture notes present a method for symbolic tensor calculus that (i) runs on fully specified smooth manifolds (described by an atlas), (ii) is not limited to a single coordinate chart or vector frame, (iii) runs even on non-parallelizable manifolds and (iv) is independent of the symbolic engine employed to perform calculus at the level of coordinate expressions.
Download or read it online for free here:
Download link
(3.6MB, PDF)
Similar books
Tensors and Relativityby 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.
(12828 views)
Introduction to Tensor Calculusby Kees Dullemond, Kasper Peeters - University of Heidelberg
This booklet contains an explanation about tensor calculus for students of physics and engineering with a basic knowledge of linear algebra. The focus lies on acquiring an understanding of the principles and ideas underlying the concept of 'tensor'.
(4442 views)
Tensor Analysisby 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.
(14634 views)
A Gentle Introduction to Tensorsby 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.
(4845 views)