Tensor Spaces And Numerical Tensor Calculus

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Tensor Spaces and Numerical Tensor Calculus

Wolfgang Hackbusch
Tensor Spaces and Numerical Tensor Calculus Book PDF

Author : Wolfgang Hackbusch
Publisher : Springer Nature
Page : 605 pages
File Size : 40,8 Mb
Release : 2019-12-16
Category : Mathematics
ISBN : 9783030355548

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Tensor Spaces and Numerical Tensor Calculus by Wolfgang Hackbusch Pdf

Special numerical techniques are already needed to deal with n × n matrices for large n. Tensor data are of size n × n ×...× n=nd, where nd 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. This monograph describes the methods by which tensors can be practically treated and shows how numerical operations can be performed. Applications include problems from quantum chemistry, approximation of multivariate functions, solution of partial differential equations, for example with stochastic coefficients, and more. In addition to containing corrections of the unavoidable misprints, this revised second edition includes new parts ranging from single additional statements to new subchapters. The book is mainly addressed to numerical mathematicians and researchers working with high-dimensional data. It also touches problems related to Geometric Algebra.

Tensor Spaces and Numerical Tensor Calculus

Wolfgang Hackbusch
Tensor Spaces and Numerical Tensor Calculus Book PDF

Author : Wolfgang Hackbusch
Publisher : Springer Science & Business Media
Page : 525 pages
File Size : 47,9 Mb
Release : 2012-02-23
Category : Mathematics
ISBN : 9783642280276

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Tensor Spaces and Numerical Tensor Calculus by Wolfgang Hackbusch Pdf

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 Spaces and Numerical Tensor Calculus

W. Hackbusch
Tensor Spaces and Numerical Tensor Calculus Book PDF

Author : W. Hackbusch
Publisher : Unknown
Page : 622 pages
File Size : 40,8 Mb
Release : 2019
Category : Calculus of tensors
ISBN : 3030355551

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Tensor Spaces and Numerical Tensor Calculus by W. Hackbusch Pdf

This book describes the methods by which tensors can be practically treated and shows how numerical operations can be performed. Applications include problems from quantum chemistry, approximation of multivariate functions, solution of pde and more.

Tensor Spaces and Exterior Algebra

Takeo Yokonuma
Tensor Spaces and Exterior Algebra Book PDF

Author : Takeo Yokonuma
Publisher : American Mathematical Soc.
Page : 148 pages
File Size : 51,7 Mb
Release : 1992
Category : Mathematics
ISBN : 0821827960

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Tensor Spaces and Exterior Algebra by Takeo Yokonuma Pdf

This book explains, as clearly as possible, tensors and such related topics as tensor products of vector spaces, tensor algebras, and exterior algebras. You will appreciate Yokonuma's lucid and methodical treatment of the subject. This book is useful in undergraduate and graduate courses in multilinear algebra. Tensor Spaces and Exterior Algebra begins with basic notions associated with tensors. to facilitate understanding of the definitions, Yokonuma often presents two or more different ways of describing one object. Next, the properties and applications of tensors are developed, including the classical definition of tensors and the description of relative tensors. Also discussed are the algebraic foundations of tensor calculus and applications of exterior algebra to determinants and to geometry. This book closes with an examination of algebraic systems with bilinear multiplication. in particular, Yokonuma discusses the theory of replicas of Chevalley and several properties of Lie algebras deduced from them.

Tensor Calculus

J. L. Synge,A. Schild
Tensor Calculus Book PDF

Author : J. L. Synge,A. Schild
Publisher : Courier Corporation
Page : 336 pages
File Size : 43,5 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9780486141398

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Tensor Calculus by J. L. Synge,A. Schild Pdf

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.

Tensor Calculus for Physics

Dwight E. Neuenschwander
Tensor Calculus for Physics Book PDF

Author : Dwight E. Neuenschwander
Publisher : JHU Press
Page : 244 pages
File Size : 46,7 Mb
Release : 2015
Category : Mathematics
ISBN : 9781421415642

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Tensor Calculus for Physics by Dwight E. Neuenschwander Pdf

It is an ideal companion for courses such as mathematical methods of physics, classical mechanics, electricity and magnetism, and relativity.--Gary White, editor of The Physics Teacher "American Journal of Physics"

Introduction to Tensor Analysis and the Calculus of Moving Surfaces

Pavel Grinfeld
Introduction to Tensor Analysis and the Calculus of Moving Surfaces Book PDF

Author : Pavel Grinfeld
Publisher : Springer Science & Business Media
Page : 302 pages
File Size : 54,6 Mb
Release : 2013-09-24
Category : Mathematics
ISBN : 9781461478676

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Introduction to Tensor Analysis and the Calculus of Moving Surfaces by Pavel Grinfeld Pdf

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 and Nonlinear Tensor Functions

Yuriy I. Dimitrienko
Tensor Analysis and Nonlinear Tensor Functions Book PDF

Author : Yuriy I. Dimitrienko
Publisher : Springer Science & Business Media
Page : 680 pages
File Size : 55,7 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401732215

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Tensor Analysis and Nonlinear Tensor Functions by Yuriy I. Dimitrienko Pdf

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.

Tensor Calculus With Applications

Goldberg Vladislav V,Akivis Maks A
Tensor Calculus With Applications Book PDF

Author : Goldberg Vladislav V,Akivis Maks A
Publisher : World Scientific Publishing Company
Page : 380 pages
File Size : 47,7 Mb
Release : 2003-09-29
Category : Science
ISBN : 9789813102255

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Tensor Calculus With Applications by Goldberg Vladislav V,Akivis Maks A Pdf

This textbook presents the foundations of tensor calculus and the elements of tensor analysis. In addition, the authors consider 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 tensor 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.

A Primer in Tensor Analysis and Relativity

Ilya L. Shapiro
A Primer in Tensor Analysis and Relativity Book PDF

Author : Ilya L. Shapiro
Publisher : Springer Nature
Page : 324 pages
File Size : 55,5 Mb
Release : 2019-08-30
Category : Science
ISBN : 9783030268954

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A Primer in Tensor Analysis and Relativity by Ilya L. Shapiro Pdf

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.

Tensor Algebra and Tensor Analysis for Engineers

Mikhail Itskov
Tensor Algebra and Tensor Analysis for Engineers Book PDF

Author : Mikhail Itskov
Publisher : Springer Science & Business Media
Page : 253 pages
File Size : 54,8 Mb
Release : 2009-04-30
Category : Technology & Engineering
ISBN : 9783540939078

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Tensor Algebra and Tensor Analysis for Engineers by Mikhail Itskov Pdf

There is a large gap between engineering courses in tensor algebra on one hand, and the treatment of linear transformations within classical linear algebra on the other. This book addresses primarily engineering students with some initial knowledge of matrix algebra. Thereby, mathematical formalism is applied as far as it is absolutely necessary. Numerous exercises provided in the book are accompanied by solutions enabling autonomous study. The last chapters deal with modern developments in the theory of isotropic and 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.

The Very Basics of Tensors

Nils K. Oeijord
The Very Basics of Tensors Book PDF

Author : Nils K. Oeijord
Publisher : iUniverse
Page : 149 pages
File Size : 50,8 Mb
Release : 2005
Category : Algebras, Linear
ISBN : 9780595356942

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The Very Basics of Tensors by Nils K. Oeijord Pdf

Tensor calculus is a generalization of vector calculus, and comes near of being a universal language in physics. Physical laws must be independent of any particular coordinate system used in describing them. This requirement leads to tensor calculus. The only prerequisites for reading this book are a familiarity with calculus (including vector calculus) and linear algebra, and some knowledge of differential equations.

Tensor Calculus

Uday Chand De,Absos Ali Shaikh,Joydeep Sengupta
Tensor Calculus Book PDF

Author : Uday Chand De,Absos Ali Shaikh,Joydeep Sengupta
Publisher : Alpha Science Int'l Ltd.
Page : 188 pages
File Size : 54,8 Mb
Release : 2005
Category : Computers
ISBN : 1842651900

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Tensor Calculus by Uday Chand De,Absos Ali Shaikh,Joydeep Sengupta Pdf

This work covers all the basic topics of tensor analysis in a lucid and clear language and is aimed at both the undergraduate and postgraduate in Civil, Mechanical and Aerospace Engineering and in Engineering Physics.

Introduction to Vector and Tensor Analysis

Robert C. Wrede
Introduction to Vector and Tensor Analysis Book PDF

Author : Robert C. Wrede
Publisher : Courier Corporation
Page : 418 pages
File Size : 42,5 Mb
Release : 2013-01-30
Category : Mathematics
ISBN : 9780486137117

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Introduction to Vector and Tensor Analysis by Robert C. Wrede Pdf

Examines general Cartesian coordinates, the cross product, Einstein's special theory of relativity, bases in general coordinate systems, maxima and minima of functions of two variables, line integrals, integral theorems, and more. 1963 edition.

Schaums Outline of Tensor Calculus

David C. Kay
Schaums Outline of Tensor Calculus Book PDF

Author : David C. Kay
Publisher : McGraw-Hill Education
Page : 240 pages
File Size : 41,9 Mb
Release : 2011-02-11
Category : Study Aids
ISBN : 0071756035

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Schaums Outline of Tensor Calculus by David C. Kay Pdf

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