Introduction to Vectors and Tensors: Second Edition–Two Volumes Bound as One (Volume 2) (Dover Books on Mathematics) by Ray M. Bowen (PDF)

Description

This convenient single-volume compilation of two texts offers both an introduction and an in-depth survey. Geared toward engineering and science students rather than mathematicians, its less rigorous treatment focuses on physics and engineering applications, building upon the systematic development of concepts rather than emphasizing mathematical problem-solving techniques. A practical reference for professionals, it is suitable for advanced undergraduate and graduate students. Volume I begins with a brief discussion of algebraic structures followed by detailed explorations of the algebra of vectors and tensors, in addition to aspects of linear and multi-linear algebra. Topics include vector spaces, linear transformations, determinants and matrices, spectral decompositions, and tensor and exterior algebra. 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.

User’s Reviews

Editorial Reviews: About the Author Ray M. Bowen earned his Ph.D. in mechanical engineering from Texas A&M University and later served as president there. He is currently president emeritus with a faculty appointment in mechanical engineering.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I have not gone through the full book, only through a few chapters. The explanations are not terrible, neither are the exercises, but I have seen numerous misprints thus far. I wouldn’t recommend it to anyone that can afford something better. In any case, here is the table of contents in this two volume book:Vol 1Ch 0: Elementary Matrix Theory1: Sets, Relations, and Functions2: Groups, Rings, and Fields3: Vector Spaces4: Linear Transformations5: Determinants and Matrices6: Spectral Decomposition7: Tensor Algebra8: Exterior AlgebraVol 29: Euclidean Manifolds10: Vector Fields and Differential Forms11: Hypersurfaces in a Euclidean Manifold12: Elements of Classical Continuous Groups13: Integration of Fields on Euclidean Manifolds, Hypersurfaces, and continuous Groups

⭐An excellent and thorough two volume book for anyone with a background in mathematics.

⭐Excellent, in depth exposition, from the standpoint of pure math.

⭐i have a graduate degree in physics and wanted to brush up on tensors. This book is a typical example of a couple of academics deriving a bunch of equations. Physical concepts are non existent.

⭐good

⭐This book comes highly recommended and is a great introduction to tensors and all the underlying concepts. Physicists complaining about lack of physics examples are right but also generally in trouble since they never bothered to learn and understand the fundamentals. Which is a huge handicap. So read and understand this book! A rather important personal complaint is that this book like others makes heavy use of capital script for sets etc. however, the font used in the book is unreadable. Ridiculous. Hence the 3 stars.

⭐Stringing together formulas and theorems, presented on poorly featured theory, without any examples and certainly not with any reference to physics or other areas of maths. Tensor calculus as an end in itself or when professors write for the sake of a book publication, but not for the reader. The fact that a large number of misprints were not corrected fits in with this, as well as the use of hardly readable and distinguishable upper case script letters for the denotion of the sets. A plus is the variety of problems, unfortunately without solutions.

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