Tensor Spaces and Numerical Tensor Calculus, Hackbusch Wolfgang
Автор: Hackbusch Название: Tensor Spaces and Numerical Tensor Calculus ISBN: 3642280269 ISBN-13(EAN): 9783642280269 Издательство: Springer Рейтинг: Цена: 15855.00 р. Наличие на складе: Нет в наличии.
Описание: 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. ?
Автор: Bhaben Chandra Kalita Название: Tensor Calculus and Applications: Simplified Tools and Techniques ISBN: 0367138069 ISBN-13(EAN): 9780367138066 Издательство: Taylor&Francis Рейтинг: Цена: 25265.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The aim of this book is to make the subject easier to understand. This book provides clear concepts, tools, and techniques to master the subject of Tensors, and can be used in many fields of research. Special applications are discussed in the book, in order to remove any confusion, and for absolute understanding of the subject.
This volume of lecture notes briefly introduces the basic concepts needed in any computational physics course: software and hardware, programming skills, linear algebra, and differential calculus. It then presents more advanced numerical methods to tackle the quantum many-body problem: it reviews the numerical renormalization group and then focuses on tensor network methods, from basic concepts to gauge invariant ones. Finally, in the last part, the author presents some applications of tensor network methods to equilibrium and out-of-equilibrium correlated quantum matter.
The book can be used for a graduate computational physics course. After successfully completing such a course, a student should be able to write a tensor network program and can begin to explore the physics of many-body quantum systems. The book can also serve as a reference for researchers working or starting out in the field.
Автор: Emil De Souza Sanchez Filho Название: Tensor Calculus for Engineers and Physicists ISBN: 3319315196 ISBN-13(EAN): 9783319315195 Издательство: Springer Рейтинг: Цена: 12196.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This textbook provides a rigorous approach to tensor manifolds in several aspects relevant for Engineers and Physicists working in industry or academia. With a thorough, comprehensive, and unified presentation, this book offers insights into several topics of tensor analysis, which covers all aspects of n-dimensional spaces.
The main purpose of this book is to give a self-contained yet simple, correct and comprehensive mathematical explanation of tensor calculus for undergraduate and graduate students and for professionals. In addition to many worked problems, this book features a selection of examples, solved step by step. Although no emphasis is placed on special and particular problems of Engineering or Physics, the text covers the fundamentals of these fields of science. The book makes a brief introduction into the basic concept of the tensorial formalism so as to allow the reader to make a quick and easy review of the essential topics that enable having the grounds for the subsequent themes, without needing to resort to other bibliographical sources on tensors.
Chapter 1 deals with Fundamental Concepts about tensors and chapter 2 is devoted to the study of covariant, absolute and contravariant derivatives. The chapters 3 and 4 are dedicated to the Integral Theorems and Differential Operators, respectively. Chapter 5 deals with Riemann Spaces, and finally the chapter 6 presents a concise study of the Parallelism of Vectors. It also shows how to solve various problems of several particular manifolds.
Автор: de Souza Sбnchez Filho Emil Название: Tensor Calculus for Engineers and Physicists ISBN: 3319810561 ISBN-13(EAN): 9783319810560 Издательство: Springer Рейтинг: Цена: 10976.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
Chapter 1. Fundamental Concepts
1.1. Basic Concepts
1.2. N Dimensional Spaces
1.3. Homogeneous and Isotropic Spaces
1.4. Kronecker Delta
1.5. Metric Tensor
1.6. Angle between Curves
1.7. Some Useful Formulas
Chapter 2. Covariant, Absolute and Contravariant Differentiation
2.1. Initial Notes
2.2. Cartesian Tensor Differentiation
2.3. Base Vectors Differentiation
2.4. Christoffel Symbols
2.5. Covariant Differentiation
2.5.1. Contravariant Tensor
2.5.2. Covariant Tensor
2.5.3. Mixed Tensor
2.5.4. Covariant Differentiation: Addition and Product of Tensors
2.5.5. Covariant Differentiation of the Tensors
2.5.6. Particularities of the Covariant Derivative
2.6. Covariant Differentiation of the Relative Tensors
2.7. Intrinsic or Absolute Differentiation
2.8. Contravariant Differentiation
Chapter 3. Integral Theorems
3.1. Initial Concepts
3.2. Green Theorem
3.3. Stokes Theorem
3.4. Gauss-Ostrogadsky Theorem
Chapter 4. Differential Operators
4.1. Scalar, Vectorial and Tensorial Fields
4.2. Gradient
4.3. Divergent
4.4 Curl
4.5. Successive Applications of the Nabla Operator
1 Introduction.- 2 Notes on point set topology.- 3 The finite dimensional real vector space.- 4 Tensor Algebra.- 5 Affine space and euclidean space.- 6 Tensor analysis in euclidean space.- 7 A primer on smooth manifolds.- B Further Reading.
1 Introduction.- 2 Notes on point set topology.- 3 The finite dimensional real vector space.- 4 Tensor Algebra.- 5 Affine space and euclidean space.- 6 Tensor analysis in euclidean space.- 7 A primer on smooth manifolds.- B Further Reading.
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.- Appendices.
Автор: Ilya L. Shapiro Название: A Primer in Tensor Analysis and Relativity ISBN: 3030268942 ISBN-13(EAN): 9783030268947 Издательство: Springer Рейтинг: Цена: 5487.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: 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.
Описание: The types of Galerkin methods covered are: continuous Galerkin methods (i.e., finite/spectral elements), discontinuous Galerkin methods, and hybridized discontinuous Galerkin methods using both nodal and modal basis functions.
Автор: Strathearn Aidan Название: Modelling Non-Markovian Quantum Systems Using Tensor Networks ISBN: 3030549747 ISBN-13(EAN): 9783030549749 Издательство: Springer Рейтинг: Цена: 15855.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: Ralph Abraham; Jerrold E. Marsden; Tudor Ratiu Название: Manifolds, Tensor Analysis, and Applications ISBN: 1461269903 ISBN-13(EAN): 9781461269908 Издательство: Springer Рейтинг: Цена: 15855.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book presents core material in nonlinear analysis, offering working knowledge of manifolds, dynamical systems, tensors and differential forms. Coverage includes Hamiltonian mechanics, fluid mechanics, electromagnetism, plasma dynamics and control theory.
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