**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

**Quick Introduction to Tensor Analysis**

by

**Ruslan Sharipov**-

**Samizdat Press**

The author gives only a draft of tensor theory, he formulates definitions and theorems and gives basic ideas and formulas. Proving consistence of definitions, deriving formulas, proving theorems or completing details to proofs is left to the reader.

(

**10948**views)

**A Gentle Introduction to Tensors**

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.

(

**3644**views)

**Introduction to Tensor Calculus**

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.

(

**2855**views)

**Tensor Calculus**

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.

(

**2305**views)