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Tensor Geometry
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Book Synopsis Tensor Geometry by : C. T. J. Dodson
Download or read book Tensor Geometry written by C. T. J. Dodson and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: This treatment of differential geometry and the mathematics required for general relativity makes the subject accessible, for the first time, to anyone familiar with elementary calculus in one variable and with some knowledge of vector algebra. The emphasis throughout is on the geometry of the mathematics, which is greatly enhanced by the many illustrations presenting figures of three and more dimensions as closely as the book form will allow.
Book Synopsis Tensor Geometry by : C. T. J. Dodson
Download or read book Tensor Geometry written by C. T. J. Dodson and published by Pitman Publishing. This book was released on 1979 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Tensors: Geometry and Applications by : J. M. Landsberg
Download or read book Tensors: Geometry and Applications written by J. M. Landsberg and published by American Mathematical Soc.. This book was released on 2011-12-14 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensors are ubiquitous in the sciences. The geometry of tensors is both a powerful tool for extracting information from data sets, and a beautiful subject in its own right. This book has three intended uses: a classroom textbook, a reference work for researchers in the sciences, and an account of classical and modern results in (aspects of) the theory that will be of interest to researchers in geometry. For classroom use, there is a modern introduction to multilinear algebra and to the geometry and representation theory needed to study tensors, including a large number of exercises. For researchers in the sciences, there is information on tensors in table format for easy reference and a summary of the state of the art in elementary language. This is the first book containing many classical results regarding tensors. Particular applications treated in the book include the complexity of matrix multiplication, P versus NP, signal processing, phylogenetics, and algebraic statistics. For geometers, there is material on secant varieties, G-varieties, spaces with finitely many orbits and how these objects arise in applications, discussions of numerous open questions in geometry arising in applications, and expositions of advanced topics such as the proof of the Alexander-Hirschowitz theorem and of the Weyman-Kempf method for computing syzygies.
Book Synopsis Tensor and Vector Analysis by : C. E. Springer
Download or read book Tensor and Vector Analysis written by C. E. Springer and published by Courier Corporation. This book was released on 2013-09-26 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assuming only a knowledge of basic calculus, this text's elementary development of tensor theory focuses on concepts related to vector analysis. The book also forms an introduction to metric differential geometry. 1962 edition.
Book Synopsis Tensor Analysis on Manifolds by : Richard L. Bishop
Download or read book Tensor Analysis on Manifolds written by Richard L. Bishop and published by Courier Corporation. This book was released on 2012-04-26 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: DIVProceeds from general to special, including chapters on vector analysis on manifolds and integration theory. /div
Book Synopsis Integral Geometry of Tensor Fields by : V. A. Sharafutdinov
Download or read book Integral Geometry of Tensor Fields written by V. A. Sharafutdinov and published by Walter de Gruyter. This book was released on 2012-01-02 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.
Book Synopsis Introduction to Differential Geometry by : Luther Pfahler Eisenhart
Download or read book Introduction to Differential Geometry written by Luther Pfahler Eisenhart and published by Princeton University Press. This book was released on 2015-12-08 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: Book 3 in the Princeton Mathematical Series. Originally published in 1950. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Book Synopsis TEXTBOOK OF TENSOR CALCULUS AND DIFFERENTIAL GEOMETRY by : PRASUN KUMAR NAYAK
Download or read book TEXTBOOK OF TENSOR CALCULUS AND DIFFERENTIAL GEOMETRY written by PRASUN KUMAR NAYAK and published by PHI Learning Pvt. Ltd.. This book was released on 2011-12-23 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: Primarily intended for the undergraduate and postgraduate students of mathematics, this textbook covers both geometry and tensor in a single volume. This book aims to provide a conceptual exposition of the fundamental results in the theory of tensors. It also illustrates the applications of tensors to differential geometry, mechanics and relativity. Organized in ten chapters, it provides the origin and nature of the tensor along with the scope of the tensor calculus. Besides this, it also discusses N-dimensional Riemannian space, characteristic peculiarity of Riemannian space, intrinsic property of surfaces, and properties and transformation of Christoffel’s symbols. Besides the students of mathematics, this book will be equally useful for the postgraduate students of physics. KEY FEATURES : Contains 250 worked out examples Includes more than 350 unsolved problems Gives thorough foundation in Tensors
Book Synopsis An Introduction to Riemannian Geometry and the Tensor Calculus by : Charles Ernest Weatherburn
Download or read book An Introduction to Riemannian Geometry and the Tensor Calculus written by Charles Ernest Weatherburn and published by CUP Archive. This book was released on 1938 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Concepts from Tensor Analysis and Differential Geometry by : Tracy Y. Thomas
Download or read book Concepts from Tensor Analysis and Differential Geometry written by Tracy Y. Thomas and published by Elsevier. This book was released on 2016-06-03 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concepts from Tensor Analysis and Differential Geometry discusses coordinate manifolds, scalars, vectors, and tensors. The book explains some interesting formal properties of a skew-symmetric tensor and the curl of a vector in a coordinate manifold of three dimensions. It also explains Riemann spaces, affinely connected spaces, normal coordinates, and the general theory of extension. The book explores differential invariants, transformation groups, Euclidean metric space, and the Frenet formulae. The text describes curves in space, surfaces in space, mixed surfaces, space tensors, including the formulae of Gaus and Weingarten. It presents the equations of two scalars K and Q which can be defined over a regular surface S in a three dimensional Riemannian space R. In the equation, the scalar K, which is an intrinsic differential invariant of the surface S, is known as the total or Gaussian curvature and the scalar U is the mean curvature of the surface. The book also tackles families of parallel surfaces, developable surfaces, asymptotic lines, and orthogonal ennuples. The text is intended for a one-semester course for graduate students of pure mathematics, of applied mathematics covering subjects such as the theory of relativity, fluid mechanics, elasticity, and plasticity theory.
Book Synopsis Cartan for Beginners by : Thomas Andrew Ivey
Download or read book Cartan for Beginners written by Thomas Andrew Ivey and published by American Mathematical Soc.. This book was released on 2003 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to Cartan's approach to differential geometry. Two central methods in Cartan's geometry are the theory of exterior differential systems and the method of moving frames. This book presents thorough and modern treatments of both subjects, including their applications to both classic and contemporary problems. It begins with the classical geometry of surfaces and basic Riemannian geometry in the language of moving frames, along with an elementary introduction to exterior differential systems. Key concepts are developed incrementally with motivating examples leading to definitions, theorems, and proofs. Once the basics of the methods are established, the authors develop applications and advanced topics.One notable application is to complex algebraic geometry, where they expand and update important results from projective differential geometry. The book features an introduction to $G$-structures and a treatment of the theory of connections. The Cartan machinery is also applied to obtain explicit solutions of PDEs via Darboux's method, the method of characteristics, and Cartan's method of equivalence. This text is suitable for a one-year graduate course in differential geometry, and parts of it can be used for a one-semester course. It has numerous exercises and examples throughout. It will also be useful to experts in areas such as PDEs and algebraic geometry who want to learn how moving frames and exterior differential systems apply to their fields.
Book Synopsis Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers by : Hung Nguyen-Schäfer
Download or read book Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers written by Hung Nguyen-Schäfer and published by Springer. This book was released on 2016-08-16 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents tensors and differential geometry in a comprehensive and approachable manner, providing a bridge from the place where physics and engineering mathematics end, and the place where tensor analysis begins. Among the topics examined are tensor analysis, elementary differential geometry of moving surfaces, and k-differential forms. The book includes numerous examples with solutions and concrete calculations, which guide readers through these complex topics step by step. Mindful of the practical needs of engineers and physicists, book favors simplicity over a more rigorous, formal approach. The book shows readers how to work with tensors and differential geometry and how to apply them to modeling the physical and engineering world. The authors provide chapter-length treatment of topics at the intersection of advanced mathematics, and physics and engineering: • General Basis and Bra-Ket Notation • Tensor Analysis • Elementary Differential Geometry • Differential Forms • Applications of Tensors and Differential Geometry • Tensors and Bra-Ket Notation in Quantum Mechanics The text reviews methods and applications in computational fluid dynamics; continuum mechanics; electrodynamics in special relativity; cosmology in the Minkowski four-dimensional space time; and relativistic and non-relativistic quantum mechanics. Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers benefits research scientists and practicing engineers in a variety of fields, who use tensor analysis and differential geometry in the context of applied physics, and electrical and mechanical engineering. It will also interest graduate students in applied physics and engineering.
Book Synopsis Introduction to Tensor Analysis and the Calculus of Moving Surfaces by : Pavel Grinfeld
Download or read book Introduction to Tensor Analysis and the Calculus of Moving Surfaces written by Pavel Grinfeld and published by Springer Science & Business Media. This book was released on 2013-09-24 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is distinguished from other texts on the subject by the depth of the presentation and the discussion of the calculus of moving surfaces, which is an extension of tensor calculus to deforming manifolds. Designed for advanced undergraduate and graduate students, this text invites its audience to take a fresh look at previously learned material through the prism of tensor calculus. Once the framework is mastered, the student is introduced to new material which includes differential geometry on manifolds, shape optimization, boundary perturbation and dynamic fluid film equations. The language of tensors, originally championed by Einstein, is as fundamental as the languages of calculus and linear algebra and is one that every technical scientist ought to speak. The tensor technique, invented at the turn of the 20th century, is now considered classical. Yet, as the author shows, it remains remarkably vital and relevant. The author’s skilled lecturing capabilities are evident by the inclusion of insightful examples and a plethora of exercises. A great deal of material is devoted to the geometric fundamentals, the mechanics of change of variables, the proper use of the tensor notation and the discussion of the interplay between algebra and geometry. The early chapters have many words and few equations. The definition of a tensor comes only in Chapter 6 – when the reader is ready for it. While this text maintains a consistent level of rigor, it takes great care to avoid formalizing the subject. The last part of the textbook is devoted to the Calculus of Moving Surfaces. 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.
Book Synopsis Tensors, Differential Forms, and Variational Principles by : David Lovelock
Download or read book Tensors, Differential Forms, and Variational Principles written by David Lovelock and published by Courier Corporation. This book was released on 2012-04-20 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques. Includes problems.
Book Synopsis Tensor Geometry by : C. T. J. Dodson
Download or read book Tensor Geometry written by C. T. J. Dodson and published by . This book was released on 1979 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Differential Geometry with Tensor Applications by : Dipankar De
Download or read book Introduction to Differential Geometry with Tensor Applications written by Dipankar De and published by John Wiley & Sons. This book was released on 2022-05-24 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: INTRODUCTION TO DIFFERENTIAL GEOMETRY WITH TENSOR APPLICATIONS This is the only volume of its kind to explain, in precise and easy-to-understand language, the fundamentals of tensors and their applications in differential geometry and analytical mechanics with examples for practical applications and questions for use in a course setting. Introduction to Differential Geometry with Tensor Applications discusses the theory of tensors, curves and surfaces and their applications in Newtonian mechanics. Since tensor analysis deals with entities and properties that are independent of the choice of reference frames, it forms an ideal tool for the study of differential geometry and also of classical and celestial mechanics. This book provides a profound introduction to the basic theory of differential geometry: curves and surfaces and analytical mechanics with tensor applications. The author has tried to keep the treatment of the advanced material as lucid and comprehensive as possible, mainly by including utmost detailed calculations, numerous illustrative examples, and a wealth of complementing exercises with complete solutions making the book easily accessible even to beginners in the field. Groundbreaking and thought-provoking, this volume is an outstanding primer for modern differential geometry and is a basic source for a profound introductory course or as a valuable reference. It can even be used for self-study, by students or by practicing engineers interested in the subject. Whether for the student or the veteran engineer or scientist, Introduction to Differential Geometry with Tensor Applications is a must-have for any library. This outstanding new volume: Presents a unique perspective on the theories in the field not available anywhere else Explains the basic concepts of tensors and matrices and their applications in differential geometry and analytical mechanics Is filled with hundreds of examples and unworked problems, useful not just for the student, but also for the engineer in the field Is a valuable reference for the professional engineer or a textbook for the engineering student
Book Synopsis Tensor Calculus and Differential Geometry for Engineers by : Shahab Sahraee
Download or read book Tensor Calculus and Differential Geometry for Engineers written by Shahab Sahraee and published by Springer Nature. This book was released on 2023-12-12 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains the basics of tensor algebra as well as a comprehensive description of tensor calculus, both in Cartesian and curvilinear coordinates. Some recent developments in representation theorems and differential forms are included. The last part of the book presents a detailed introduction to differential geometry of surfaces and curves which is based on tensor calculus. By solving numerous exercises, the reader is equipped to properly understand the theoretical background and derivations. Many solved problems are provided at the end of each chapter for in-depth learning. All derivations in this text are carried out line by line which will help the reader to understand the basic ideas. Each figure in the book includes descriptive text that corresponds with the theoretical derivations to facilitate rapid learning.
