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Author: Ilya L. Shapiro Publisher: Springer Nature ISBN: 3030268950 Category : Science Languages : en Pages : 324
Book Description
This undergraduate textbook provides a simple, concise introduction to tensor algebra and analysis, as well as special and general relativity. With a plethora of examples, explanations, and exercises, it forms a well-rounded didactic text that will be useful for any related course. The book is divided into three main parts, all based on lecture notes that have been refined for classroom teaching over the past two decades. Part I provides students with a comprehensive overview of tensors. Part II links the very introductory first part and the relatively advanced third part, demonstrating the important intermediate-level applications of tensor analysis. Part III contains an extended discussion of general relativity, and includes material useful for students interested primarily in quantum field theory and quantum gravity. Tailored to the undergraduate, this textbook offers explanations of technical material not easily found or detailed elsewhere, including an understandable description of Riemann normal coordinates and conformal transformations. Future theoretical and experimental physicists, as well as mathematicians, will thus find it a wonderful first read on the subject.
Author: Ilya L. Shapiro Publisher: Springer Nature ISBN: 3030268950 Category : Science Languages : en Pages : 324
Book Description
This undergraduate textbook provides a simple, concise introduction to tensor algebra and analysis, as well as special and general relativity. With a plethora of examples, explanations, and exercises, it forms a well-rounded didactic text that will be useful for any related course. The book is divided into three main parts, all based on lecture notes that have been refined for classroom teaching over the past two decades. Part I provides students with a comprehensive overview of tensors. Part II links the very introductory first part and the relatively advanced third part, demonstrating the important intermediate-level applications of tensor analysis. Part III contains an extended discussion of general relativity, and includes material useful for students interested primarily in quantum field theory and quantum gravity. Tailored to the undergraduate, this textbook offers explanations of technical material not easily found or detailed elsewhere, including an understandable description of Riemann normal coordinates and conformal transformations. Future theoretical and experimental physicists, as well as mathematicians, will thus find it a wonderful first read on the subject.
Author: Ilya Lvovitch Shapiro Publisher: ISBN: 9783030268961 Category : Calculus of tensors Languages : en Pages :
Book Description
This undergraduate textbook provides a simple, concise introduction to tensor algebra and analysis, as well as special and general relativity. With a plethora of examples, explanations, and exercises, it forms a well-rounded didactic text that will be useful for any related course. The book is divided into three main parts, all based on lecture notes that have been refined for classroom teaching over the past two decades. Part I provides students with a comprehensive overview of tensors. Part II links the very introductory first part and the relatively advanced third part, demonstrating the important intermediate-level applications of tensor analysis. Part III contains an extended discussion of general relativity, and includes material useful for students interested primarily in quantum field theory and quantum gravity. Tailored to the undergraduate, this textbook offers explanations of technical material not easily found or detailed elsewhere, including an understandable description of Riemann normal coordinates and conformal transformations. Future theoretical and experimental physicists, as well as mathematicians, will thus find it a wonderful first read on the subject.
Author: Anadi Jiban Das Publisher: Springer Science & Business Media ISBN: 0387694692 Category : Science Languages : en Pages : 300
Book Description
Here is a modern introduction to the theory of tensor algebra and tensor analysis. It discusses tensor algebra and introduces differential manifold. Coverage also details tensor analysis, differential forms, connection forms, and curvature tensor. In addition, the book investigates Riemannian and pseudo-Riemannian manifolds in great detail. Throughout, examples and problems are furnished from the theory of relativity and continuum mechanics.
Author: Derek F. Lawden Publisher: Courier Corporation ISBN: 9780486132143 Category : Science Languages : en Pages : 224
Book Description
This elementary introduction pays special attention to aspects of tensor calculus and relativity that students tend to find most difficult. Its use of relatively unsophisticated mathematics in the early chapters allows readers to develop their confidence within the framework of Cartesian coordinates before undertaking the theory of tensors in curved spaces and its application to general relativity theory. Topics include the special principle of relativity and Lorentz transformations; orthogonal transformations and Cartesian tensors; special relativity mechanics and electrodynamics; general tensor calculus and Riemannian space; and the general theory of relativity, including a focus on black holes and gravitational waves. The text concludes with a chapter offering a sound background in applying the principles of general relativity to cosmology. Numerous exercises advance the theoretical developments of the main text, thus enhancing this volume’s appeal to students of applied mathematics and physics at both undergraduate and postgraduate levels. Preface. List of Constants. References. Bibliography.
Author: Bipin Singh Koranga Publisher: CRC Press ISBN: 1000795918 Category : Mathematics Languages : en Pages : 127
Book Description
The subject of Tensor Analysis deals with the problem of the formulation of the relation between various entities in forms which remain invariant when we pass from one system of coordinates to another. The invariant form of equation is necessarily related to the possible system of coordinates with reference to which the equation remains invariant. The primary purpose of this book is the study of the invariance form of equation relative to the totally of the rectangular co-ordinate system in the three-dimensional Euclidean space. We start with the consideration of the way the sets representing various entities are transformed when we pass from one system of rectangular co-ordinates to another. A Tensor may be a physical entity that can be described as a Tensor only with respect to the manner of its representation by means of multi-sux sets associated with different system of axes such that the sets associated with different system of co-ordinate obey the transformation law for Tensor. We have employed sux notation for tensors of any order, we could also employ single letter such A,B to denote Tensors.
Author: Quddus Khan Publisher: Partridge Publishing ISBN: 1482850680 Category : Mathematics Languages : en Pages : 215
Book Description
This book is intended to serve as a textbook for undergraduate and postgraduate 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 other higher education tests. The text starts with the basic concepts and results, which shall refer throughout this book and is followed by the study of the tensor algebra and its calculus, consisting the notion of tensor, its operations, and its different types; Christoffels symbols and its properties, the concept of covariant differentiation of tensors and its properties, tensor form of gradient, divergence, laplacian and curl, divergence of a tensor, intrinsic derivatives, and parallel displacement of vectors, Riemanns symbols and its properties, and application of tensor in different areas.
Author: Jan Arnoldus Schouten Publisher: Courier Corporation ISBN: 0486655822 Category : Science Languages : en Pages : 322
Book Description
This rigorous and advanced mathematical explanation of classic tensor analysis was written by one of the founders of tensor calculus. Its concise exposition of the mathematical basis of the discipline is integrated with well-chosen physical examples of the theory, including those involving elasticity, classical dynamics, relativity, and Dirac's matrix calculus. 1954 edition.
Author: James G. Simmonds Publisher: Springer Science & Business Media ISBN: 1441985220 Category : Mathematics Languages : en Pages : 124
Book Description
In this text which gradually develops the tools for formulating and manipulating the field equations of Continuum Mechanics, the mathematics of tensor analysis is introduced in four, well-separated stages, and the physical interpretation and application of vectors and tensors are stressed throughout. This new edition contains more exercises. In addition, the author has appended a section on Differential Geometry.
Author: Ilya L. Shapiro
Author: Ilya L. Shapiro
Author: Ilya Lvovitch Shapiro
Author: Anadi Jiban Das
Author: Derek F. Lawden
Author: Bipin Singh Koranga
Author: Derek Frank Lawden
Author: Quddus Khan
Author: Jan Arnoldus Schouten
Author: James G. Simmonds
Author: Matthew S Smith