Tensor Algebra and Tensor Analysis for Engineers

1. Front Matter

   Pages 1-10

   PDF

2. Vectors and Tensors in a Finite-Dimensional Space

   • Mikhail Itskov

   Pages 1-33

3. Vector and Tensor Analysis in Euclidean Space

   • Mikhail Itskov

   Pages 35-58

4. Curves and Surfaces in Three-Dimensional Euclidean Space

   • Mikhail Itskov

   Pages 59-79

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

   • Mikhail Itskov

   Pages 81-101

6. Fourth-Order Tensors

   • Mikhail Itskov

   Pages 103-114

7. Analysis of Tensor Functions

   • Mikhail Itskov

   Pages 115-144

8. Analytic Tensor Functions

   • Mikhail Itskov

   Pages 145-164

9. Applications to Continuum Mechanics

   • Mikhail Itskov

   Pages 165-183

10. Back Matter

    Pages 1-62

    PDF

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.

• Analysis
• Eigenvalue
• Matrix
• Transformation
• algebra
• computer-aided design (CAD)
• linear algebra
• mechanics

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)

Policies and ethics