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Tensor Analysis (Hardcover, 1st ed. 2019)
Loot Price: R4,944
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Tensor Analysis (Hardcover, 1st ed. 2019)
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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.
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