Tensor Algebra And Tensor Analysis For Engineers Itskov
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Tensor Algebra and Tensor Analysis for Engineers
This is the fourth and revised edition of a well-received book that aims at bridging the gap between the engineering course of tensor algebra on the one side and the mathematical course of classical linear algebra on the other side. In accordance with the contemporary way of scientific publications, a modern absolute tensor notation is preferred throughout. The book provides a comprehensible exposition of the fundamental mathematical concepts of tensor calculus and enriches the presented material with many illustrative examples. In addition, the book also includes advanced chapters dealing with recent developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics. Hence, this monograph addresses graduate students as well as scientists working in this field. In each chapter numerous exercises are included, allowing for self-study and intense practice. Solutions to the exercises are also provided.
Tensor Algebra and Tensor Analysis for Engineers
Author: Mikhail Itskov
language: en
Publisher: Springer Science & Business Media
Release Date: 2009-04-30
This second edition is completed by a number of additional examples and exercises. In response of comments and questions of students using this book, solutions of many exercises have been improved for a better understanding. Some changes and enhancements are concerned with the treatment of sk- symmetric and rotation tensors in the ?rst chapter. Besides, the text and formulae have thoroughly been reexamined and improved where necessary. Aachen, January 2009 Mikhail Itskov Preface to the First Edition Like many other textbooks the present one is based on a lecture course given by the author for master students of the RWTH Aachen University. In spite of a somewhat di?cult matter those students were able to endure and, as far as I know, are still ?ne. I wish the same for the reader of the book. Although the present book can be referred to as a textbook one ?nds only little plain text inside. I tried to explain the matter in a brief way, nevert- lessgoinginto detailwherenecessary.Ialsoavoidedtediousintroductions and lengthy remarks about the signi?cance of one topic or another. A reader - terested in tensor algebra and tensor analysis but preferring, however, words instead of equations can close this book immediately after having read the preface.
Tensor Calculus for Engineers and Physicists
Author: Emil de Souza Sánchez Filho
language: en
Publisher: Springer
Release Date: 2016-05-20
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.