Author | J. L. Synge | |

ISBN-10 | 9780486141398 | |

Release | 2012-04-26 | |

Pages | 336 | |

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Fundamental introduction of absolute differential calculus and for those interested in applications of tensor calculus to mathematical physics and engineering. Topics include spaces and tensors; basic operations in Riemannian space, curvature of space, more. |

Author | Barry Spain | |

ISBN-10 | 9780486428314 | |

Release | 2003 | |

Pages | 125 | |

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A compact exposition of the theory of tensors, this text also illustrates the power of the tensor technique by its applications to differential geometry, elasticity, and relativity. Explores tensor algebra, the line element, covariant differentiation, geodesics and parallelism, and curvature tensor. Also covers Euclidean 3-dimensional differential geometry, Cartesian tensors and elasticity, and the theory of relativity. 1960 edition. |

Author | Derek F. Lawden | |

ISBN-10 | 0486132145 | |

Release | 2012-03-07 | |

Pages | 224 | |

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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 | Maks A?zikovich Akivis | |

ISBN-10 | 9812385061 | |

Release | 2003 | |

Pages | 367 | |

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This textbook presents the foundations of tensor calculus and the elements of tensor analysis, in addition to considering numerous applications of tensors to geometry, mechanics and physics. While developing tensor calculus, the authors emphasize its relationship with linear algebra. Necessary notions and theorems of linear algebra are introduced and proved in connection with the construction of the apparatus of tensor calculus; prior knowledge is not assumed. For simplicity and to enable the reader to visualize concepts more clearly, all exposition is conducted in three-dimensional space. The principal feature of the book is that the authors use mainly orthogonal tensors, since such tensors are important in applications to physics and engineering. All notions introduced in the book, and also the obtained results, are illustrated with numerous examples discussed in the text. Each section of the book presents problems (a total over 300 problems are given). Examples and problems are intended to illustrate, reinforce textbook presents the foundations of tensor calculus and the elements of tensor analysis, in addition to considering numerous applications of tensors to geometry, mechanics and physics. While developing tensor calculus, the authors emphasize its relationship with linear algebra. Necessary notions and theorems of linear algebra are introduced and proved in connection with the construction of the apparatus of tensor calculus; prior knowledge is not assumed. For simplicity and to enable the reader to visualize concepts more clearly, all exposition is conducted in three-dimensional space. The principal feature of the book is that the authors use mainly orthogonal tensors, sincesuch tensors are important in applications to physics and engineering. All notions introduced in the book, and also the obtained results, are illustrated with numerous examples discussed in the text. Each section of the book p |

Author | Mirjana Dalarsson | |

ISBN-10 | 012200681X | |

Release | 2005 | |

Pages | 280 | |

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This book combines relativity, astrophysics, and cosmology in a single volume, providing an introduction to each subject that enables students to understand more detailed treatises as well as the current literature. The section on general relativity gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes, Penrose processes, and similar topics), and considers the energy-momentum tensor for various solutions. The next section on relativistic astrophysics discusses stellar contraction and collapse, neutron stars and their equations of state, black holes, and accretion onto collapsed objects. Lastly, the section on cosmology discusses various cosmological models, observational tests, and scenarios for the early universe. * Clearly combines relativity, astrophysics, and cosmology in a single volume so students can understand more detailed treatises and current literature * Extensive introductions to each section are followed by relevant examples and numerous exercises * Provides an easy-to-understand approach to this advanced field of mathematics and modern physics by providing highly detailed derivations of all equations and results |

Author | Stanisław Gołąb | |

ISBN-10 | UOM:39015015624342 | |

Release | 1974 | |

Pages | 373 | |

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Tensor calculus has been writing in one form or another for most of life. You can find so many inspiration from Tensor calculus also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Tensor calculus book for free. |

Author | Barry Spain | |

ISBN-10 | UCSD:31822012711719 | |

Release | 1960 | |

Pages | 125 | |

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Tensor calculus has been writing in one form or another for most of life. You can find so many inspiration from Tensor calculus also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Tensor calculus book for free. |

Author | D. C. Agarwal | |

ISBN-10 | ||

Release | 2013 | |

Pages | 291 | |

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Tensor Calculus and Riemannian Geometry has been writing in one form or another for most of life. You can find so many inspiration from Tensor Calculus and Riemannian Geometry also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Tensor Calculus and Riemannian Geometry book for free. |

Author | John G. Papastavridis | |

ISBN-10 | 0849385148 | |

Release | 1998-12-18 | |

Pages | 448 | |

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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. |

Author | Uday Chand De | |

ISBN-10 | 1842654489 | |

Release | 2008 | |

Pages | 163 | |

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Tensor Calculus has been writing in one form or another for most of life. You can find so many inspiration from Tensor Calculus also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Tensor Calculus book for free. |

Author | David Kay | |

ISBN-10 | 0070334846 | |

Release | 1988-04-01 | |

Pages | 228 | |

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This lucid introduction for undergraduates and graduates proves fundamental for pactitioners of theoretical physics and certain areas of engineering, like aerodynamics and fluid mechanics, and exteremely valuable for mathematicians. This study guide teaches all the basics and efective problem-solving skills too. |

Author | PRASUN KUMAR NAYAK | |

ISBN-10 | 9788120345072 | |

Release | 2011-12-23 | |

Pages | 552 | |

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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 |

Author | Iulian Beju | |

ISBN-10 | 0856263303 | |

Release | 1983-01 | |

Pages | 303 | |

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Euclidean Tensor Calculus with Applications has been writing in one form or another for most of life. You can find so many inspiration from Euclidean Tensor Calculus with Applications also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Euclidean Tensor Calculus with Applications book for free. |

Author | ||

ISBN-10 | ||

Release | ||

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An Introduction to RIEMANNIAN GEOMETRY AND THE TENSOR CALCULUS has been writing in one form or another for most of life. You can find so many inspiration from An Introduction to RIEMANNIAN GEOMETRY AND THE TENSOR CALCULUS also informative, and entertaining. Click DOWNLOAD or Read Online button to get full An Introduction to RIEMANNIAN GEOMETRY AND THE TENSOR CALCULUS book for free. |

Author | Dwight E. Neuenschwander | |

ISBN-10 | 9781421415642 | |

Release | 2014-11-04 | |

Pages | 248 | |

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Understanding tensors is essential for any physics student dealing with phenomena where causes and effects have different directions. A horizontal electric field producing vertical polarization in dielectrics; an unbalanced car wheel wobbling in the vertical plane while spinning about a horizontal axis; an electrostatic field on Earth observed to be a magnetic field by orbiting astronauts—these are some situations where physicists employ tensors. But the true beauty of tensors lies in this fact: When coordinates are transformed from one system to another, tensors change according to the same rules as the coordinates. Tensors, therefore, allow for the convenience of coordinates while also transcending them. This makes tensors the gold standard for expressing physical relationships in physics and geometry. Undergraduate physics majors are typically introduced to tensors in special-case applications. For example, in a classical mechanics course, they meet the "inertia tensor," and in electricity and magnetism, they encounter the "polarization tensor." However, this piecemeal approach can set students up for misconceptions when they have to learn about tensors in more advanced physics and mathematics studies (e.g., while enrolled in a graduate-level general relativity course or when studying non-Euclidean geometries in a higher mathematics class). Dwight E. Neuenschwander's Tensor Calculus for Physics is a bottom-up approach that emphasizes motivations before providing definitions. Using a clear, step-by-step approach, the book strives to embed the logic of tensors in contexts that demonstrate why that logic is worth pursuing. It is an ideal companion for courses such as mathematical methods of physics, classical mechanics, electricity and magnetism, and relativity. |

Author | A. Lichnerowicz | |

ISBN-10 | 9780486811864 | |

Release | 2016-04-10 | |

Pages | 176 | |

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This classic introductory text, geared toward undergraduate students of mathematics, is the work of an internationally renowned authority on tensor calculus. The two-part treatment offers a rigorous presentation of tensor calculus as a development of vector analysis as well as discussions of the most important applications of tensor calculus. Starting with a chapter on vector spaces, Part I explores affine Euclidean point spaces, tensor algebra, curvilinear coordinates in Euclidean space, and Riemannian spaces. Part II examines the use of tensors in classical analytical dynamics and details the role of tensors in special relativity theory. The book concludes with a brief presentation of the field equations of general relativity theory. |

Author | Wolfgang Hackbusch | |

ISBN-10 | 9783642280276 | |

Release | 2012-02-23 | |

Pages | 500 | |

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Special numerical techniques are already needed to deal with nxn matrices for large n.Tensor data are of size nxnx...xn=n^d, where n^d exceeds the computer memory by far. They appear for problems of high spatial dimensions. Since standard methods fail, a particular tensor calculus is needed to treat such problems. The monograph describes the methods how tensors can be practically treated and how numerical operations can be performed. Applications are problems from quantum chemistry, approximation of multivariate functions, solution of pde, e.g., with stochastic coefficients, etc. |