Bowen R., Wang C. Introduction to Vectors and Tensors. Volume 2 - Vector and Tensor Analysis

2nd Edition. — Online self-publishing version of the 2008 Dover Publications 2nd edition. — Mineola, New York: Dover Publications Inc., 2008. — XXI, 295-520 pp.Exactly coincides with the Dover 2nd edition.Volume II opens with a discussion of Euclidean manifolds and proceeds to the development of analytical and geometrical aspects of vector and tensor fields. Subsequent chapters survey the integration of fields on Euclidean manifolds, hypersurfaces, and continuous groups.This is the second volume of a two-volume work on vectors and tensors. Volume I is concerned with the algebra of vectors and tensors, while this volume is concerned with the geometrical aspects of vectors and tensors. This volume begins with a discussion of Euclidean manifolds. The principal mathematical entity considered in this volume is a field, which is defined on a domain in a Euclidean manifold. The values of the field may be vectors or tensors. We investigate results due to the distribution of the vector or tensor values of the field on its domain. While we do not discuss general differentiable manifolds, we do include a chapter on vector and tensor fields defined on hypersurfaces in a Euclidean manifold.Vector and Tensor Analysis
Euclidean Manifolds
Vector Fields and Differential Forms
Hypersurfaces in a Euclidean Manifold
Elements of Classical Continuous Groups
Integration of Fields on Euclidean Manifolds, Hypersurfaces, and Continuous Groups