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Tensor analysis

Irgens, Fridtjov.

Tensor analysis

Record Type:	Electronic resources : Monograph/item
Title/Author:	Tensor analysisby Fridtjov Irgens.
Author:	Irgens, Fridtjov.
Published:	Cham :Springer International Publishing :2019.
Description:	xxi, 385 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Calculus of tensors.
Online resource:	https://doi.org/10.1007/978-3-030-03412-2
ISBN:	9783030034122$q(electronic bk.)

Tensor analysis
Irgens, Fridtjov.

Tensor analysis[electronic resource] /by Fridtjov Irgens. - Cham :Springer International Publishing :2019. - xxi, 385 p. :ill., digital ;24 cm.

Mathematical Foundation -- Dynamics -- Tensors -- Deformation Analysis -- Constitutive Equations -- General Coordinates in Euclidean Space E3 -- Elements of Continuum Mechanics in General Coordinates -- Surface Geometry. Tensors in Riemannian Space R2 -- Integral Theorems -- Tensor Analysis in n-Dimensional Space -- Appendix Problems with Solutions.

This book presents tensors and tensor analysis as primary mathematical tools for engineering and engineering science students and researchers. The discussion is based on the concepts of vectors and vector analysis in three-dimensional Euclidean space, and although it takes the subject matter to an advanced level, the book starts with elementary geometrical vector algebra so that it is suitable as a first introduction to tensors and tensor analysis. Each chapter includes a number of problems for readers to solve, and solutions are provided in an Appendix at the end of the text. Chapter 1 introduces the necessary mathematical foundations for the chapters that follow, while Chapter 2 presents the equations of motions for bodies of continuous material. Chapter 3 offers a general definition of tensors and tensor fields in three-dimensional Euclidean space. Chapter 4 discusses a new family of tensors related to the deformation of continuous material. Chapter 5 then addresses constitutive equations for elastic materials and viscous fluids, which are presented as tensor equations relating the tensor concept of stress to the tensors describing deformation, rate of deformation and rotation. Chapter 6 investigates general coordinate systems in three-dimensional Euclidean space and Chapter 7 shows how the tensor equations discussed in chapters 4 and 5 are presented in general coordinates. Chapter 8 describes surface geometry in three-dimensional Euclidean space, Chapter 9 includes the most common integral theorems in two- and three-dimensional Euclidean space applied in continuum mechanics and mathematical physics.

ISBN: 9783030034122$q(electronic bk.)

Standard No.: 10.1007/978-3-030-03412-2doiSubjects--Topical Terms:

210256
Calculus of tensors.

LC Class. No.: QA433 / .I744 2019

Dewey Class. No.: 515.63

Tensor analysis
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100 1 $a Irgens, Fridtjov. $3 276531
245 1 0 $a Tensor analysis $h [electronic resource] / $c by Fridtjov Irgens.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2019.
300 $a xxi, 385 p. : $b ill., digital ; $c 24 cm.
505 0 $a Mathematical Foundation -- Dynamics -- Tensors -- Deformation Analysis -- Constitutive Equations -- General Coordinates in Euclidean Space E3 -- Elements of Continuum Mechanics in General Coordinates -- Surface Geometry. Tensors in Riemannian Space R2 -- Integral Theorems -- Tensor Analysis in n-Dimensional Space -- Appendix Problems with Solutions.
520 $a This book presents tensors and tensor analysis as primary mathematical tools for engineering and engineering science students and researchers. The discussion is based on the concepts of vectors and vector analysis in three-dimensional Euclidean space, and although it takes the subject matter to an advanced level, the book starts with elementary geometrical vector algebra so that it is suitable as a first introduction to tensors and tensor analysis. Each chapter includes a number of problems for readers to solve, and solutions are provided in an Appendix at the end of the text. Chapter 1 introduces the necessary mathematical foundations for the chapters that follow, while Chapter 2 presents the equations of motions for bodies of continuous material. Chapter 3 offers a general definition of tensors and tensor fields in three-dimensional Euclidean space. Chapter 4 discusses a new family of tensors related to the deformation of continuous material. Chapter 5 then addresses constitutive equations for elastic materials and viscous fluids, which are presented as tensor equations relating the tensor concept of stress to the tensors describing deformation, rate of deformation and rotation. Chapter 6 investigates general coordinate systems in three-dimensional Euclidean space and Chapter 7 shows how the tensor equations discussed in chapters 4 and 5 are presented in general coordinates. Chapter 8 describes surface geometry in three-dimensional Euclidean space, Chapter 9 includes the most common integral theorems in two- and three-dimensional Euclidean space applied in continuum mechanics and mathematical physics.
650 0 $a Calculus of tensors. $3 210256
650 1 4 $a Solid Mechanics. $3 825700
650 2 4 $a Linear and Multilinear Algebras, Matrix Theory. $3 274063
650 2 4 $a Classical and Continuum Physics. $3 771188
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
856 4 0 $u https://doi.org/10.1007/978-3-030-03412-2
950 $a Engineering (Springer-11647)