Introduction to Vectors and Tensors Vol 2 (Bowen 246). - Index of

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PREFACE
To Volume 2
This is the second volume of a two-volume work on vectors and tensors. Volume 1 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.
This volume contains frequent references to Volume 1. However, references are limited to
basic algebraic concepts, and a student with a modest background in linear algebra should be able
to utilize this volume as an independent textbook. As indicated in the preface to Volume 1, this
volume is suitable for a one-semester course on vector and tensor analysis. On occasions when we
have taught a one –semester course, we covered material from Chapters 9, 10, and 11 of this
volume. This course also covered the material in Chapters 0,3,4,5, and 8 from Volume 1.
We wish to thank the U.S. National Science Foundation for its support during the
preparation of this work. We also wish to take this opportunity to thank Dr. Kurt Reinicke for
critically checking the entire manuscript and offering improvements on many points.
Houston, Texas
R.M.B.
C.-C.W.
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