Book Name: Tensor Analysis
Author: Fridtjov Irgens
File size: 8.05 MB
File format: PDF
Tensor Analysis Pdf Book Description:
This publication presents tensors and tensor analysis as chief mathematical tools for technology and technology science scientists and students. The conversation is based upon the concepts of vectors and vector analysis in three-dimensional Euclidean area, and though it requires the subject matter to an advanced degree, the novel begins with fundamental geometrical vector algebra so it is appropriate as a primary introduction to tensors and tensor analysis. Every chapter comprises lots of issues for readers to resolve, and solutions can be found in an Appendix at the end of the text.
Chapter 1 presents the required mathematical foundations for the chapters which follow, whilst Chapter two introduces the equations of motions for bodies of constant substance. Chapter 4 discusses a brand new family of tensors regarding the deformation of constant substance. Chapter 5 then addresses constitutive equations for elastic substances and viscous fluids, which can be introduced as tensor equations concerning the tensor notion of pressure into the tensors describing deformation, speed of deformation and spinning. Chapter 6 investigates overall coordinate systems in three dimensional Euclidean distance and Chapter 7 demonstrates how the tensor equations discussed in chapters 4 and 5 are introduced in general coordinates. Chapter 8 describes surface geometry in three-dimensional Euclidean space, Chapter 9 comprises the most frequent integral theorems in 2 – and – three-dimensional Euclidean space employed in continuum mechanics and mathematical physics.