Tensor Analysis for Physicists, Second Edition

By Jan Arnoldus Schouten

Book Overview

This rigorous and advanced mathematical explanation of classic tensor analysis was written by one of the founders of tensor calculus. Its concise exposition of the mathematical basis of the discipline is integrated with well-chosen physical examples of the theory, including those involving elasticity, classical dynamics, relativity, and Dirac''s matrix calculus. 1954 edition.

• Format: Paperback
• Language: English
• ISBN: 0486655822
• ISBN13: 9780486655826
• Release Date: December 2011
• Publisher: Dover Publications
• Length: 320 Pages
• Weight: 1.16 lbs.
• Dimensions: 0.6" x 5.3" x 8.4"

Customer Reviews

An abridged version of Schouten's earlier treatise

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 this style of tensor analysis does not uphold the standards of rigor set forth by the Bourbaki school of presentation, but, in light of the fact that the language has changed so drastically since the writing of this book, 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 more complete than the present book. In the interest of saving space for the physical applications in the second half of the text, the author omitted important details, such as an adequate definition of 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 Noll: Finite Dimensional Spaces; Choquet-Bruhat et al: Analysis, Manifolds and Physics, Part I and II; Spivak: A Comprehensive Introduction to Differential Geometry, Volume 1; Loomis: Advanced Calculus; and Helgason: Differential Geometry, Lie Groups and Symmetric Spaces all to be exceptionally well written.

This is a no easy book!

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.

Great Book

I would suggest this book for relativity lovers, who loves to undrestand General relativity deeply. This book is easy to learn and it takes very little time to read but the benefits are very large.