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Tensor Spaces and Numerical Tensor Calculus, Hackbusch



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Автор: Hackbusch   (Хакбуш)
Название:  Tensor Spaces and Numerical Tensor Calculus   (Хакбуш: Тензорные пространства и численное тензорное исчисление)
Издательство: Springer
Классификация:
Исчисление и математический анализ
Численный анализ
Прикладная математика
ФИЗИКА
Математическая физика
Физическая химия
Квантовая и теоретическая химия

ISBN: 3642280269
ISBN-13(EAN): 9783642280269
ISBN: 3-642-28026-9
ISBN-13(EAN): 978-3-642-28026-9
Обложка/Формат: Hardback
Страницы: 524
Вес: 0.943 кг.
Дата издания: 01.02.2012
Серия: Springer Series in Computational Mathematics
Язык: English
Издание: 2012 ed.
Иллюстрации: XXIV, 500 p. 9 illus., 3 in color.
Размер: 234 x 160 x 33
Читательская аудитория: Professional & vocational
Ссылка на Издательство: Link
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Поставляется из: Германии
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. ?



Tensor calculus with applications

Название: Tensor calculus with applications
ISBN: 9812385053 ISBN-13(EAN): 9789812385055
Издательство: World Scientific Publishing
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Цена: 7593 р.
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Описание: 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. With regard to applications, the authors construct the general theory of second-degree surfaces, study the inertia t nsor as well as the stress and strain tensors, and consider some problems of crystallophysics.

The last chapter introduces the elements of tensor analysis. 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 and deepen the presented material. There are answers to most of the problems, as well as hints and solutions to selected problems at the end of the book.

Schaums Outline of Tensor Calculus, Revised Edition

Автор: Kay David, Kay David
Название: Schaums Outline of Tensor Calculus, Revised Edition
ISBN: 0071756035 ISBN-13(EAN): 9780071756037
Издательство: McGraw-Hill
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Цена: 2144 р.
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Описание:

The ideal review for your tensor calculus course

More than 40 million students have trusted Schaum's Outlines for their expert knowledge and helpful solved problems. Written by renowned experts in their respective fields, Schaum's Outlines cover everything from math to science, nursing to language. The main feature for all these books is the solved problems. Step-by-step, authors walk readers through coming up with solutions to exercises in their topic of choice. 300 solved problems Coverage of all course fundamentals Effective problem-solving techniques Complements or supplements the major logic textbooks Supports all the major textbooks for tensor calculus courses

An Introduction to Riemannian Geometry and the Tensor Calculus

Автор: Weatherburn
Название: An Introduction to Riemannian Geometry and the Tensor Calculus
ISBN: 0521091888 ISBN-13(EAN): 9780521091886
Издательство: Cambridge Academ
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Цена: 2645 р.
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Описание: The purpose of this book is to bridge the gap between differential geometry of Euclidean space of three dimensions and differential geometry of generalised space.

Tensor Calculus for Engineers and Physicists

Автор: Emil De Souza Sanchez Filho
Название: Tensor Calculus for Engineers and Physicists
ISBN: 3319315196 ISBN-13(EAN): 9783319315195
Издательство: Springer
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Цена: 10449 р.
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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.

Introduction to Tensor Products of Banach Spaces

Автор: Ryan Raymond A.
Название: Introduction to Tensor Products of Banach Spaces
ISBN: 1852334371 ISBN-13(EAN): 9781852334376
Издательство: Springer
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Цена: 10449 р.
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Описание: This volume provides a self-contained introduction to the theory of tensor products of Banach spaces. It is written for graduate students in analysis or for researchers in other fields who wish to become acquainted with this area. The only prerequisites are a basic knowledge of functional analysis and measure theory.Features of particular interest include:- A full treatment of the Grothendieck theory of tensor norms;- Coverage of the Chevet-Saphar norms and their duals, along with the associated classes of nuclear, integral and summing operators;- Chapters on the approximation property and the Radon-Nikodym property;- Topics such as the Bochner and Pettis integrals, the principle of local reflexivity and the Grothendieck inequality placed in a natural setting;- The classes of operators generated by a tensor norm and connections with the theory of operator ideals.Each chapter is accompanied by worked examples and a set of exercises, and two appendices provide essential material on summability in Banach spaces and properties of spaces of measures that may be new to the beginner.

New Developments in the Visualization and Processing of Tensor Fields

Автор: Laidlaw
Название: New Developments in the Visualization and Processing of Tensor Fields
ISBN: 3642273424 ISBN-13(EAN): 9783642273421
Издательство: Springer
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Цена: 17241 р.
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Описание: Bringing together key researchers in disciplines ranging from visualization and image processing to applications in structural mechanics, fluid dynamics, elastography, and numerical mathematics, the workshop that generated this edited volume was the third in the successful Dagstuhl series. Its aim, reflected in the quality and relevance of the papers presented, was to foster collaboration and fresh lines of inquiry in the analysis and visualization of tensor fields, which offer a concise model for numerous physical phenomena. Despite their utility, there remains a dearth of methods for studying all but the simplest ones, a shortage the workshops aim to address. Documenting the latest progress and open research questions in tensor field analysis, the chapters reflect the excitement and inspiration generated  by this latest Dagstuhl workshop, held in July 2009. The topics they address range from applications of the analysis of tensor fields to purer research into their mathematical and analytical properties. They show how cooperation and the sharing of ideas and data between those engaged in pure and applied research can open new vistas in the study of tensor fields.

Visualization and Processing of Tensor Fields

Автор: Weickert Joachim, Hagen Hans
Название: Visualization and Processing of Tensor Fields
ISBN: 3540250328 ISBN-13(EAN): 9783540250326
Издательство: Springer
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Цена: 17241 р.
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Описание: Matrix-valued data sets – so-called second order tensor fields – have gained significant importance in scientific visualization and image processing due to recent developments such as diffusion tensor imaging. This book is the first edited volume that presents the state of the art in the visualization and processing of tensor fields. It contains some longer chapters dedicated to surveys and tutorials of specific topics, as well as a great deal of original work by leading experts that has not been published before. It serves as an overview for the inquiring scientist, as a basic foundation for developers and practitioners, and as as a textbook for specialized classes and seminars for graduate and doctoral students.

Tensor Analysis and Continuum Mechanics

Автор: Talpaert Y.R.
Название: Tensor Analysis and Continuum Mechanics
ISBN: 1402010559 ISBN-13(EAN): 9781402010552
Издательство: Springer
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Цена: 14629 р.
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Описание: This volume combines an illustration of the theory of tensors and the foundations of continuum mechanics. Firstly, a detailed tensor analysis is developed in Cartesian and general coordinates. Definitions, propositions, and examples relative to operations on tensors, canonical isomorphism, Euclidean vector spaces, exterior algebra, point spaces, metric element, Christoffel symbols, covariant and absolute derivatives, adjoint, differential operators, and many other concepts are introduced in a rigorous and practical way. The topic is not merely viewed as an autonomous mathematical discipline, but as a preparation for theories of physics such as general relativity theory, fluid-dynamics, engineering, and differential geometry. Secondly, developed in symbiosis with tensor analysis, continuum mechanics thoroughly covers Lagrangian and Eulerian descriptions, deformations, kinematics of continua, fundamental laws, principle of virtual work, linear elasticity and more. This work lays the groundwork for more technical subjects as strength of materials, plasticity, viscoelasticity, and nonlinear continuum mechanics. The material is presented with great pedagogical care, a summary of formulae and a glossary of symbols are provided, as well as ninety-five solved problems. The book is suitable as a text for third year students of mathematics, physics and engineering, and for anyone wishing to acquire insight into the mathematics of mechanics, the mathematics of physics, the mathematics of engineering, continuum mechanics, elasticity and viscoelasticity, linear and multilinear algebra, or matrix theory.

Analysis / Part Two: Integration, Distributions, Holomorphic Functions, Tensor and Harmonic Analysis

Автор: Maurin Krzysztof
Название: Analysis / Part Two: Integration, Distributions, Holomorphic Functions, Tensor and Harmonic Analysis
ISBN: 1402003145 ISBN-13(EAN): 9781402003141
Издательство: Springer
Цена: 9404 р.
Наличие на складе: Поставка под заказ.

Tensor Analysis and Nonlinear Tensor Functions

Автор: Dimitrienko I.
Название: Tensor Analysis and Nonlinear Tensor Functions
ISBN: 140201015X ISBN-13(EAN): 9781402010156
Издательство: Springer
Цена: 19333 р.
Наличие на складе: Есть у поставщика Поставка под заказ.

Описание: Tensor Analysis and Nonlinear Tensor Functions embraces the basic fields of tensor calculus: tensor algebra, tensor analysis, tensor description of curves and surfaces, tensor integral calculus, the basis of tensor calculus in Riemannian spaces and affinely connected spaces, - which are used in mechanics and electrodynamics of continua, crystallophysics, quantum chemistry etc.The book suggests a new approach to definition of a tensor in space R3, which allows us to show a geometric representation of a tensor and operations on tensors. Based on this approach, the author gives a mathematically rigorous definition of a tensor as an individual object in arbitrary linear, Riemannian and other spaces for the first time. It is the first book to present a systematized theory of tensor invariants, a theory of nonlinear anisotropic tensor functions and a theory of indifferent tensors describing the physical properties of continua. The book will be useful for students and postgraduates of mathematical, mechanical engineering and physical departments of universities and also for investigators and academic scientists working in continuum mechanics, solid physics, general relativity, crystallophysics, quantum chemistry of solids and material science.

Cosmology in Scalar-Tensor Gravity

Автор: Faraoni Valerio
Название: Cosmology in Scalar-Tensor Gravity
ISBN: 1402019882 ISBN-13(EAN): 9781402019883
Издательство: Springer
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Цена: 16602 р.
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Описание: Cosmology in Scalar-Tensor Gravity covers all aspects of cosmology in scalar-tensor theories of gravity. Considerable progress has been made in this exciting area of physics and this book is the first to provide a critical overview of the research. Among the topics treated are: -Scalar-tensor gravity and its limit to general relativity, -Effective energy-momentum tensors and conformal frames, -Gravitational waves in scalar-tensor cosmology, -Specific scalar-tensor theories, -Exact cosmological solutions and cosmological perturbations, -Scalar-tensor scenarios of the early universe and inflation, -Scalar-tensor models of quintessence in the present universe and their far-reaching consequences for the ultimate fate of the cosmos.

Tensor Algebra and Tensor Analysis for Engineers

Автор: Itskov
Название: Tensor Algebra and Tensor Analysis for Engineers
ISBN: 3540360468 ISBN-13(EAN): 9783540360469
Издательство: Springer
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Цена: 4697 р.
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Описание: There is a large gap between the engineering course in tensor algebra on the one hand and the treatment of linear transformations within classical linear algebra on the other hand. The aim of the book is to bridge this gap by means of the consequent and fundamental exposition. The book is addressed primarily to engineering students with some initial knowledge of matrix algebra. Thereby the mathematical formalism is applied as far as it is absolutely necessary. Numerous exercises provided in the book are accompanied by solutions enabling an autonomous study. The last chapters of the book deal with modern developments in the theory of isotropic an anisotropic tensor functions and their applications to continuum mechanics and might therefore be of high interest for PhD-students and scientists working in this area. In the last decades, the absolute notation for tensors has become widely accepted and is now a current state of the art for publications in solid and structural mechanics. This is opposed to a majority of books on tensor calculus referring to index notation. The latter one complicates the understanding of the matter especially for readers with initial knowledge. Thus, this book aims at being a modern textbook on tensor calculus for engineers in line with the contemporary way of scientific publications.


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