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Differential Geometry and Tensors

Differential Geometry and Tensors
Author: K.K. Dube
Publisher: I. K. International Pvt Ltd
Total Pages: 377
Release: 2013-12-30
Genre: Mathematics
ISBN: 9380026587
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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.

TEXTBOOK OF TENSOR CALCULUS AND DIFFERENTIAL GEOMETRY

TEXTBOOK OF TENSOR CALCULUS AND DIFFERENTIAL GEOMETRY
Author: PRASUN KUMAR NAYAK
Publisher: PHI Learning Pvt. Ltd.
Total Pages: 551
Release: 2011-12-23
Genre: Mathematics
ISBN: 812034507X
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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

Tensor and Vector Analysis

Tensor and Vector Analysis
Author: C. E. Springer
Publisher: Courier Corporation
Total Pages: 258
Release: 2013-09-26
Genre: Mathematics
ISBN: 048632091X
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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.

Tensor Calculus and Differential Geometry for Engineers

Tensor Calculus and Differential Geometry for Engineers
Author: Shahab Sahraee
Publisher: Springer Nature
Total Pages: 684
Release: 2023-12-12
Genre: Technology & Engineering
ISBN: 3031339533
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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.

Tensor Geometry

Tensor Geometry
Author: C. T. J. Dodson
Publisher: Springer Science & Business Media
Total Pages: 449
Release: 2013-04-17
Genre: Mathematics
ISBN: 3642105149
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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.

Tensors, Differential Forms, and Variational Principles

Tensors, Differential Forms, and Variational Principles
Author: David Lovelock
Publisher: Courier Corporation
Total Pages: 402
Release: 2012-04-20
Genre: Mathematics
ISBN: 048613198X
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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

Introduction to Differential Geometry with Tensor Applications
Author: Dipankar De
Publisher: John Wiley & Sons
Total Pages: 516
Release: 2022-05-24
Genre: Mathematics
ISBN: 1119795621
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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

Concepts from Tensor Analysis and Differential Geometry

Concepts from Tensor Analysis and Differential Geometry
Author: Tracy Y. Thomas
Publisher: Elsevier
Total Pages: 128
Release: 2016-06-03
Genre: Mathematics
ISBN: 1483263711
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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 Geometry

Tensor Geometry
Author: C. T. J. Dodson
Publisher: Pitman Publishing
Total Pages: 598
Release: 1979
Genre: Calculus of tensors
ISBN: 9780273010401
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Concepts from Tensor Analysis and Differential Geometry by Tracy Y Thomas

Concepts from Tensor Analysis and Differential Geometry by Tracy Y Thomas
Author:
Publisher: Elsevier
Total Pages: 129
Release: 2000-04-01
Genre: Technology & Engineering
ISBN: 0080957781
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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