Skip to main content
SpringerLink
Log in

Tensor Algebra and Tensor Analysis for Engineers

With Applications to Continuum Mechanics

  • Textbook
  • © 2007

Overview

Authors:
  1. Mikhail Itskov

    1. Department of Continuum Mechanics, RWTH Aachen University, Aachen, Germany

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Compact and illustrated introduction for readers of different levels
  • Numerous exercises with solutions
  • Applications to continuum mechanics
  • Tensor algebra in absolute notation
  • Treatment of tensors on the basis of linear algebra
  • Includes supplementary material: sn.pub/extras

  • 17k Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (8 chapters)

  1. Front Matter

    Pages I-XI
    Download chapter PDF

  2. Vectors and Tensors in a Finite-Dimensional Space

    Pages 1-31

  3. Vector and Tensor Analysis in Euclidean Space

    Pages 33-55

  4. Curves and Surfaces in Three-Dimensional Euclidean Space

    Pages 57-77

  5. Eigenvalue Problem and Spectral Decomposition of Second-Order Tensors

    Pages 79-98

  6. Fourth-Order Tensors

    Pages 99-110

  7. Analysis of Tensor Functions

    Pages 111-139

  8. Analytic Tensor Functions

    Pages 141-160

  9. Applications to Continuum Mechanics

    Pages 161-178

  10. Back Matter

    Pages 179-239
    Download chapter PDF
Back to top

Keywords

About this book

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. The reader is assumed to be familiar with the basics of matrix algebra and continuum mechanics and is encouraged to solve at least some of num- ous exercises accompanying every chapter. Having read many other texts on mathematics and mechanics I was always upset vainly looking for solutions to the exercises which seemed to be most interesting for me. For this reason, all the exercises here are supplied with solutions amounting a substantial part of the book. Without doubt, this part facilitates a deeper understanding of the subject. As a research work this book is open for discussion which will certainly contribute to improving the text for further editions. In this sense, I am very gratefulfor comments,suggestionsand constructivecriticismfromthe reader.

Reviews

From the reviews:

"Most books on continuum mechanics begin with a more or less lengthy introduction into this mere mathematical topic. … With the present introduction to tensors, Itskov has filled this gap. … It is written in a clear and modern style … . contains a lot of interesting representations, which will be appreciated by researchers in the field. … All in all, the book can be clearly recommended both for students and researchers in the field of continuum mechanics." (Technische Mechanik, Vol. 28 (3), 2008)

Authors and Affiliations

  • Department of Continuum Mechanics, RWTH Aachen University, Aachen, Germany

    Mikhail Itskov

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation