What Is Tensor Analysis
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Introduction to Vector and Tensor Analysis
Author: Robert C. Wrede
language: en
Publisher: Courier Corporation
Release Date: 2013-01-30
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.
An Introduction to Tensor Analysis
The subject of Tensor Analysis deals with the problem of the formulation of the relation between various entities in forms which remain invariant when we pass from one system of coordinates to another. The invariant form of equation is necessarily related to the possible system of coordinates with reference to which the equation remains invariant. The primary purpose of this book is the study of the invariance form of equation relative to the totally of the rectangular co-ordinate system in the three-dimensional Euclidean space. We start with the consideration of the way the sets representing various entities are transformed when we pass from one system of rectangular co-ordinates to another. A Tensor may be a physical entity that can be described as a Tensor only with respect to the manner of its representation by means of multi-sux sets associated with different system of axes such that the sets associated with different system of co-ordinate obey the transformation law for Tensor. We have employed sux notation for tensors of any order, we could also employ single letter such A,B to denote Tensors.
Tensor Analysis
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.