Geometrical properties of vectors and convectors : an introductory survey of differentiable manifolds, tensors and forms / Joaquim M. Domingos.

Format:

Book

Author/Creator:

Domingos, Joaquim M.

Contributor:

Harry E. Humphreys Book Fund.

Language:

English

Subjects (All):

Vector analysis.

Manifolds (Mathematics).

Physical Description:

vii, 73 pages : illustrations ; 24 cm

Place of Publication:

Hackensack, NJ : World Scientific, [2006]

Summary:

This is a brief introduction to some geometrical topics including topological spaces, the metric tensor, Euclidean space, manifolds, tensors, r-forms, the orientation of a manifold and the Hodge star operator. It provides the reader who is approaching the subject for the first time with a deeper understanding of the geometrical properties of vectors and covectors. The material prepares the reader for discussions on basic concepts such as the differential of a function as a covector, metric dual, inner product, wedge product and cross product. Book jacket.

Contents:

1 Topological Spaces 1

2 Metric Tensor 7

3 Differentiable Manifolds 13

3.2 Tangent vectors and spaces 17

3.3 Parallelization 24

4 Metric Dual 27

5 Tensors 39

6 r-Forms 45

7 Orientation of a Manifold 55

8 Hodge Star Operator 61

9 Wedge Product and Cross Product 65.

Notes:

Includes bibliographical references (pages 69-70) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Harry E. Humphreys Book Fund.

ISBN:

9812700447

OCLC:

123955282