Tensor Analysis

Nonfiction, Science & Nature, Science, Physics, Mechanics, Mathematics, Algebra, Technology
Cover of the book Tensor Analysis by Fridtjov Irgens, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Fridtjov Irgens ISBN: 9783030034122
Publisher: Springer International Publishing Publication: December 15, 2018
Imprint: Springer Language: English
Author: Fridtjov Irgens
ISBN: 9783030034122
Publisher: Springer International Publishing
Publication: December 15, 2018
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer International Publishing

Cover of the book Innovative Business Education Design for 21st Century Learning by Fridtjov Irgens
Cover of the book Security Protocols XXIII by Fridtjov Irgens
Cover of the book Framing the EU Global Strategy by Fridtjov Irgens
Cover of the book ADEX Optimized Adaptive Controllers and Systems by Fridtjov Irgens
Cover of the book Asbestos and Mesothelioma by Fridtjov Irgens
Cover of the book Advanced Hybrid Information Processing by Fridtjov Irgens
Cover of the book Methodological Reflections on Practice Oriented Theories by Fridtjov Irgens
Cover of the book Materiality and Managerial Techniques by Fridtjov Irgens
Cover of the book The Quartz Crystal Microbalance in Soft Matter Research by Fridtjov Irgens
Cover of the book Project Management for Facility Constructions by Fridtjov Irgens
Cover of the book The Complementary Roots of Growth and Development by Fridtjov Irgens
Cover of the book Interest Groups, Water Politics and Governance by Fridtjov Irgens
Cover of the book Practical Panarchy for Adaptive Water Governance by Fridtjov Irgens
Cover of the book New Political Economy of Energy in Europe by Fridtjov Irgens
Cover of the book New Trends in Applied Harmonic Analysis by Fridtjov Irgens
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy