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Lists with This Book. This book is not yet featured on Listopia. Community Reviews. Showing Rating details. Sort order. Feb 08, WarpDrive rated it really liked it Shelves: owned , science-and-maths , ebooks. A quite good, conceptually rigorous introduction to tensor calculus. It is not perfect, but probably one of the most readable on the subject, requiring only knowledge of linear algebra and multivariate calculus at undergraduate level.
Introduction To Tensor Analysis And The Calculus Of Moving Surfaces
The only issues I have with the book are: - in relation to the number of typos there are a fe A quite good, conceptually rigorous introduction to tensor calculus. Also note that this book delivers a general introduction to tensor calculus, and as such it is not particularly targeted at general relativity. A solid, readable introductory work on the subject, designed at advanced undergraduate level. View 2 comments. May 11, David Grimmer rated it really liked it. This book was my first real introduction to those fantastic objects from geometry called tensors, and thank god I read this before being poorly indoctrinated in college lectures.
This book is not perfect, it avoids the topological setting upon which tensors are modernly understood.
There is no talk of charts, overlap, diffeomorphism, ect. But you do not need any of that unnecessary topology to appreciate what you will learn from this book.
If you are a physicist struggling to learn about Relativ This book was my first real introduction to those fantastic objects from geometry called tensors, and thank god I read this before being poorly indoctrinated in college lectures. If you are a physicist struggling to learn about Relativity theory, you don't need to know about smooth manifolds you need to know how to calculate.
This book is a perfect first step, you learn mathematics by doing it and applying it to problems in mathematics or physics. It is the first textbook exposition of this important technique and is one of the gems of this text. A number of exciting applications of the calculus are presented including shape optimization, boundary perturbation of boundary value problems and dynamic fluid film equations developed by the author in recent years. Furthermore, the moving surfaces framework is used to offer new derivations of classical results such as the geodesic equation and the celebrated Gauss-Bonnet theorem.
Looking at Pavel Grinfeld's Tensor Analysis Book
Show more Show less. From the book reviews: "The textbook is meant for advanced undergraduate and graduate audiences. It is a common language among scientists and can help students from technical fields see their respective fields in a new and exiting way. Both undergraduate and graduate students have a chance to take a fresh look at previously learned material through the prism of tensor calculus.
Pavel Grinfeld is currently a professor of mathematics at Drexel University, teaching courses in linear algebra, tensor analysis, numerical computation, and financial mathematics. Topological spaces and groups are not mentioned. A few other books do a good job in this regard, including [2, 8, 31, 46].
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The book  is particularly concise and offers the shortest path to the general relativity theory. For an excellent book with an emphasis on elasticity, see . Along with eschewing formalism, this book also strives to avoid vagueness associated with such notions as the infinitesimal differentials dx i. While a number of fundamental concepts are accepted without definition, all subsequent elements of the calculus are derived in a consistent and rigorous way.
The description of Euclidean spaces centers on the basis vectors Zi. These important and geometrically intuitive objects are absent from many textbooks. Furthermore, the use of vector quantities goes a long way towards helping the student see the world in a way that is independent of Cartesian coordinates. The notation is of paramount importance in mastering the subject. To borrow a sentence from A. As a result, the framework is described in a natural context that makes the effectiveness of the rules and conventions apparent.
This is unlike most other textbooks which introduce the tensor notation in advance of the actual content. In spirit and vision, this book is most similar to A. Since a heavy emphasis in placed on vector-valued quantities, it is important to have good familiarity with geometric vectors viewed as objects on their own terms rather than elements in Rn.
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A number of textbooks discuss the geometric nature of vectors in great depth. First and foremost is J. Danielson  also gives a good introduction to geometric vectors and offers an excellent discussion on the subject of differentiation of vector fields. The following books enjoy a good reputation in the modern differential geometry community: [3, 6, 23, 29, 32, 41].
Other popular textbooks, including [38, 43] are known for taking the formal approach to the subject.