Textbook Of Tensor Calculus And Differential Geometry
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Textbook Of Tensor Calculus And Differential Geometry
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Author : PRASUN KUMAR NAYAK
language : en
Publisher: PHI Learning Pvt. Ltd.
Release Date : 2011-12-23
Textbook Of Tensor Calculus And Differential Geometry written by PRASUN KUMAR NAYAK and has been published by PHI Learning Pvt. Ltd. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-23 with Mathematics categories.
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
Textbook Of Tensor Calculus And Differential Geometry
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Author : Prasun Kumar Nayak
language : en
Publisher:
Release Date : 2012
Textbook Of Tensor Calculus And Differential Geometry written by Prasun Kumar Nayak and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Calculus of tensors categories.
Textbook Of Tensor Calculus And Differential Geometry And Their Applications
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Author : Quddus Khan
language : en
Publisher: Misha Books
Release Date : 2020-12-29
Textbook Of Tensor Calculus And Differential Geometry And Their Applications written by Quddus Khan and has been published by Misha Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-29 with Mathematics categories.
This book is intended to serve as a Textbook for Undergraduate and Post - graduate students of Mathematics. It will be useful to the researchers working in the field of Differential geometry and its applications to general theory of relativity and other applied areas. It will also be helpful in preparing for the competitive examinations like IAS, IES, NET, PCS, and UP Higher Education exams. The text starts with a chapter on Preliminaries discussing basic concepts and results which would be taken for general later in the subsequent chapters of this book. This is followed by the Study of the Tensors Algebra and its operations and types, Christoffel's symbols and its properties, the concept of covariant differentiation and its properties, Riemann's symbols and its properties, and application of tensor in different areas in part – I and the study of the Theory of Curves in Space, Concepts of a Surface and Fundamental forms, Envelopes and Developables, Curvature of Surface and Lines of Curvature, Fundamental Equations of Surface Theory, Theory of Geodesics, Differentiable Manifolds and Riemannian Manifold and Application of Differential Geometry in Part –II. KEY FEATURES: Provides basic Concepts in an easy to understand style; Presentation of the subject in a natural way; Includes a large number of solved examples and illuminating illustrations; Exercise questions at the end of the topic and at the end of each chapter; Proof of the theorems are given in an easy to understand style; Neat and clean figures are given at appropriate places; Notes and remarks are given at appropriate places.
Textbook Of Tensor Calculus Differential Geometry And Their Applications
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Author :
language : en
Publisher:
Release Date : 2020
Textbook Of Tensor Calculus Differential Geometry And Their Applications written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with categories.
Tensors Differential Forms And Variational Principles
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Author : David Lovelock
language : en
Publisher: Courier Corporation
Release Date : 2012-04-20
Tensors Differential Forms And Variational Principles written by David Lovelock and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-20 with Mathematics categories.
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 Tensor Analysis And The Calculus Of Moving Surfaces
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Author : Pavel Grinfeld
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-09-24
Introduction To Tensor Analysis And The Calculus Of Moving Surfaces written by Pavel Grinfeld and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-24 with Mathematics categories.
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.
Tensor Analysis On Manifolds
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Author : Richard L. Bishop
language : en
Publisher: Courier Corporation
Release Date : 1980-12-01
Tensor Analysis On Manifolds written by Richard L. Bishop and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980-12-01 with Mathematics categories.
Striking just the right balance between formal and abstract approaches, this text proceeds from generalities to specifics. Topics include function-theoretical and algebraic aspects, manifolds and integration theory, several important structures, and adaptation to classical mechanics. "First-rate. . . deserves to be widely read." — American Mathematical Monthly. 1980 edition.
Tensors
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Author : AHSAN, ZAFAR
language : en
Publisher: PHI Learning Pvt. Ltd.
Release Date : 2015-05-21
Tensors written by AHSAN, ZAFAR and has been published by PHI Learning Pvt. Ltd. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-21 with Mathematics categories.
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.
Tensor Calculus And Analytical Dynamics
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Author : John G. Papastavridis
language : en
Publisher: Routledge
Release Date : 2018-12-12
Tensor Calculus And Analytical Dynamics written by John G. Papastavridis and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-12 with Mathematics categories.
Tensor Calculus and Analytical Dynamics provides a concise, comprehensive, and readable introduction to classical tensor calculus - in both holonomic and nonholonomic coordinates - as well as to its principal applications to the Lagrangean dynamics of discrete systems under positional or velocity constraints. The thrust of the book focuses on formal structure and basic geometrical/physical ideas underlying most general equations of motion of mechanical systems under linear velocity constraints. Written for the theoretically minded engineer, Tensor Calculus and Analytical Dynamics contains uniquely accessbile treatments of such intricate topics as: tensor calculus in nonholonomic variables Pfaffian nonholonomic constraints related integrability theory of Frobenius The book enables readers to move quickly and confidently in any particular geometry-based area of theoretical or applied mechanics in either classical or modern form.