Differential Geometry And Tensors

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Differential Geometry and Tensors

Author : K.K. Dube
Publisher : I. K. International Pvt Ltd
ISBN 13 : 9380026587
Total Pages : 377 pages
Book Rating : 4.3/5 (8 download)

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Book Synopsis Differential Geometry and Tensors by : K.K. Dube

Download or read book Differential Geometry and Tensors written by K.K. Dube and published by I. K. International Pvt Ltd. This book was released on 2013-12-30 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to give a simple, lucid, rigorous and comprehensive account of fundamental notions of Differential Geometry and Tensors. The book is self-contained and divided in two parts. Section A deals with Differential Geometry and Section B is devoted to the study of Tensors. Section A deals with: " Theory of curves, envelopes and developables. " Curves on surfaces and fundamental magnitudes, curvature of surfaces and lines of curvature. " Fundamental equations of surface theory. " Geodesics. Section B deals with: " Tensor algebra. " Tensor calculus. " Christoffel symbols and their properties. " Riemann symbols and Einstein space, and their properties. " Physical components of contravariant and covariant vectors. " Geodesics and Parallelism of vectors. " Differentiable manifolds, charts, atlases.

Tensor and Vector Analysis

Author : C. E. Springer
Publisher : Courier Corporation
ISBN 13 : 048632091X
Total Pages : 258 pages
Book Rating : 4.4/5 (863 download)

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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 258 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.

TEXTBOOK OF TENSOR CALCULUS AND DIFFERENTIAL GEOMETRY

Author : PRASUN KUMAR NAYAK
Publisher : PHI Learning Pvt. Ltd.
ISBN 13 : 812034507X
Total Pages : 551 pages
Book Rating : 4.1/5 (23 download)

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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

Concepts from Tensor Analysis and Differential Geometry

Author : Tracy Y. Thomas
Publisher : Elsevier
ISBN 13 : 1483263711
Total Pages : 128 pages
Book Rating : 4.4/5 (832 download)

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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.

Tensor Calculus and Differential Geometry for Engineers

Author : Shahab Sahraee
Publisher : Springer Nature
ISBN 13 : 3031339533
Total Pages : 684 pages
Book Rating : 4.0/5 (313 download)

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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.

Tensors, Differential Forms, and Variational Principles

Author : David Lovelock
Publisher : Courier Corporation
ISBN 13 : 048613198X
Total Pages : 402 pages
Book Rating : 4.4/5 (861 download)

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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 402 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.

Introduction to Differential Geometry with Tensor Applications

Author : Dipankar De
Publisher : John Wiley & Sons
ISBN 13 : 1119795621
Total Pages : 516 pages
Book Rating : 4.1/5 (197 download)

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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

Tensor Analysis on Manifolds

Author : Richard L. Bishop
Publisher : Courier Corporation
ISBN 13 : 0486139239
Total Pages : 290 pages
Book Rating : 4.4/5 (861 download)

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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 290 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

Tensors and Riemannian Geometry

Author : Nail H. Ibragimov
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110379503
Total Pages : 198 pages
Book Rating : 4.1/5 (13 download)

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Book Synopsis Tensors and Riemannian Geometry by : Nail H. Ibragimov

Download or read book Tensors and Riemannian Geometry written by Nail H. Ibragimov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2015-08-31 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the experience of teaching the subject by the author in Russia, France, South Africa and Sweden. The author provides students and teachers with an easy to follow textbook spanning a variety of topics on tensors, Riemannian geometry and geometric approach to partial differential equations. Application of approximate transformation groups to the equations of general relativity in the de Sitter space simplifies the subject significantly.

Tensor Geometry

Author : C. T. J. Dodson
Publisher : Springer Science & Business Media
ISBN 13 : 3642105149
Total Pages : 449 pages
Book Rating : 4.6/5 (421 download)

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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.

Concepts from Tensor Analysis and Differential Geometry by Tracy Y Thomas

Author :
Publisher : Elsevier
ISBN 13 : 0080957781
Total Pages : 129 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Concepts from Tensor Analysis and Differential Geometry by Tracy Y Thomas by :

Download or read book Concepts from Tensor Analysis and Differential Geometry by Tracy Y Thomas written by and published by Elsevier. This book was released on 2000-04-01 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression. - Best operator approximation,- Non-Lagrange interpolation,- Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering

Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers

Author : Hung Nguyen-Schäfer
Publisher : Springer
ISBN 13 : 3662484978
Total Pages : 389 pages
Book Rating : 4.6/5 (624 download)

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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.

Tensor Geometry

Author : C. T. J. Dodson
Publisher : Pitman Publishing
ISBN 13 : 9780273010401
Total Pages : 598 pages
Book Rating : 4.0/5 (14 download)

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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 Pitman Publishing. This book was released on 1979 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt:

TENSORS

Author : AHSAN, ZAFAR
Publisher : PHI Learning Pvt. Ltd.
ISBN 13 : 812035088X
Total Pages : 242 pages
Book Rating : 4.1/5 (23 download)

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Book Synopsis TENSORS by : AHSAN, ZAFAR

Download or read book TENSORS written by AHSAN, ZAFAR and published by PHI Learning Pvt. Ltd.. This book was released on 2015-05-21 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: The principal aim of analysis of tensors is to investigate those relations which remain valid when we change from one coordinate system to another. This book on Tensors requires only a knowledge of elementary calculus, differential equations and classical mechanics as pre-requisites. It provides the readers with all the information about the tensors along with the derivation of all the tensorial relations/equations in a simple manner. The book also deals in detail with topics of importance to the study of special and general relativity and the geometry of differentiable manifolds with a crystal clear exposition. The concepts dealt within the book are well supported by a number of solved examples. A carefully selected set of unsolved problems is also given at the end of each chapter, and the answers and hints for the solution of these problems are given at the end of the book. The applications of tensors to the fields of differential geometry, relativity, cosmology and electromagnetism is another attraction of the present book. This book is intended to serve as text for postgraduate students of mathematics, physics and engineering. It is ideally suited for both students and teachers who are engaged in research in General Theory of Relativity and Differential Geometry.

Modern Differential Geometry for Physicists

Author : Chris J. Isham
Publisher : Allied Publishers
ISBN 13 : 9788177643169
Total Pages : 308 pages
Book Rating : 4.6/5 (431 download)

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Book Synopsis Modern Differential Geometry for Physicists by : Chris J. Isham

Download or read book Modern Differential Geometry for Physicists written by Chris J. Isham and published by Allied Publishers. This book was released on 2002 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Tensors: Geometry and Applications

Author : J. M. Landsberg
Publisher : American Mathematical Soc.
ISBN 13 : 0821869078
Total Pages : 464 pages
Book Rating : 4.8/5 (218 download)

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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.

Introduction to Differential Geometry

Author : Luther Pfahler Eisenhart
Publisher : Princeton University Press
ISBN 13 : 1400877865
Total Pages : 315 pages
Book Rating : 4.4/5 (8 download)

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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.