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Title: Tensor Analysis for Physicists, Second Edition by J. A. Schouten ISBN: 0-486-65582-2 Publisher: Dover Pubns Pub. Date: 01 July, 1989 Format: Paperback Volumes: 1 List Price(USD): $13.95 |
Average Customer Rating: 4 (4 reviews)
Rating: 4
Summary: An Abridged Version of the Author's Treatise
Comment: In recent times it has become fashionable to derogate the classical tensor analysis cultivated by such pioneers as Levi-Civita, Schouten and Eisenhart. Modern critics refer to such works as a "sea of indices", the reading of which is likened to "chasing shadows". It is true that tensor analysis predating ~1960 does not uphold the standards of rigor set by modern mathematical analysis, but, in light of the fact that the language has changed so drastically during the intervening years, it would be fair to treat the classical theory as a separate subject, of interest in its own right.
This book offers a valuable, yet not entirely self-contained, introduction to classical tensor analysis. As a beginner, I found the text to be too terse and was forced to consult other sources, such as Levi-Civita's "Absolute Differential Calculus" and Eisenhart's "Riemannian Geometry". Once I had gained some familiarity with the basic notions, Schouten's book became the preferred reference. The author develops an extremely precise notation which he calls the "kernel-index method" and systematically applies it as a problem solving tool throughout the book. Looking back, it is difficult to say how I ever got along without it.
Unfortunately, the book's terseness is due in part to the fact that the first five chapters are basically abridged excerpts from the author's lengthier 1954 treatise "Ricci-Calculus". In nearly every respect, the aforementioned title is better than the present book, for, in the interest of economizing space, the author omitted important details, such as the definition of a manifold and the role of the vector field which generates the infinitesimal transformations used in discussing Lie derivatives.
For classical tensor analysis, Schouten's "Ricci-Calculus" (1954) and "Pfaff's Problem and its Generalizations" (1949, but still in print) are both excellent. For the modern theory, I have found Munkres' "Analysis on Manifolds" and Noll's "Finite Dimensional Spaces" to be exceptionally well written.
Rating: 4
Summary: This is a no easy book!
Comment: First that everything should have present that this it is not an introduction book. Don't hope to learn tensor analysis in this book. From the first chapter it begins to demand you and to tell you what you should know and to understand the subject to follow their reading. Definitively you have to have the clear subject in your mind to enjoy the book. But that doesn't mean that it is bad book, or that the book takes a lie title : the book is for exact science graduates (or science advanced undergraduates). The notation, inclusive, you will notice it heavy, difficult. You can divide the book in three parts: the part corresponding to the chapters 1-5 where it introduces all the elements of the tensor analysis . A second part, the chapter 6, dedicated to the study of the physical objects and their dimensions, and a third part that it includes the remaining chapters, dedicated to applications. It is not an easy book. This is a book on tensors where you won't learn on tensors. It is a beautiful synthesis of the content of the tensor analysis (chapters 1-5). The rest, obviously is impossible to find everything in a single book. Not yet it is enough with to have a general knowledge of the topic for this book. You have to have a solid one.
Possible books that you can read before being faced with this book: A. I. Borisenko (Classic, elementary), Synge, Goldberg, Levi-Civita, Akivis (Elementary, very elementary), Kreiszig (differential Geometry, elementary to intermediate level), etc.
Rating: 3
Summary: Nice reference, however very incomplete
Comment: This book has no introduction! I mean the book has no "preparation" for studying pure tensor analysis, thus it cannot be taken as an introduction to the subject but as a reference for classes (unless you have many other books of geometry and algebra so you can get the "introduction" there). Also, the book has few information of used notations, making it harder to understand and the subject of tensor analysis, according to the author, is not fully explored - its just an "introduction" (Really?). So if you buy this book you rather buy few others together. About the title, I really didn't understand why it is called "for physicists". The author understood that applications make the book truly interesting for physicists. Is that so?
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Title: Tensor Calculus by J. L. Synge, A. Schild ISBN: 0486636127 Publisher: Dover Pubns Pub. Date: 01 July, 1978 List Price(USD): $14.95 |
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Title: Tensors, Differential Forms, and Variational Principles by David Lovelock, Hanno Rund ISBN: 0486658406 Publisher: Dover Pubns Pub. Date: 01 April, 1989 List Price(USD): $15.95 |
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Title: Vector and Tensor Analysis with Applications by A. I. Borisenko, I. E. Tarapov ISBN: 0486638332 Publisher: Dover Pubns Pub. Date: 01 October, 1979 List Price(USD): $12.95 |
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Title: Div, Grad, Curl, and All That: An Informal Text on Vector Calculus by Harry M. Schey ISBN: 0393969975 Publisher: W.W. Norton & Company Pub. Date: August, 1997 List Price(USD): $17.95 |
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Title: Schaum's Outline of Tensor Calculus (Schaum's) by David C. Kay ISBN: 0070334846 Publisher: McGraw-Hill Trade Pub. Date: 01 April, 1988 List Price(USD): $16.95 |
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