Tensor analysis for engineers and physicists : with application to continuum mechanics, turbulence, and Einstein's special and general theory of relativity
著者
書誌事項
Tensor analysis for engineers and physicists : with application to continuum mechanics, turbulence, and Einstein's special and general theory of relativity
Springer, c2021
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
This book unies the common tensor analytical aspects in engineering and physics. Using tensor analysis enables the reader to understand complex physical phenomena from the basic principles in continuum mechanics including the turbulence, its correlations and modeling to the complex Einstein' tensor equation. The development of General Theory of Relativity and the introduction of spacetime geometry would not have been possible without the use of tensor analysis. This textbook is primarily aimed at students of mechanical, electrical, aerospace, civil and other engineering disciplines as well as of theoretical physics. It also covers the special needs of practicing professionals who perform CFD-simulation on a routine basis and would like to know more about the underlying physics of the commercial codes they use. Furthermore, it is suitable for self-study, provided that the reader has a sufficient knowledge of differential and integral calculus. Particular attention was paid to selecting the application examples. The transformation of Cartesian coordinate system into curvilinear one and the subsequent applications to conservation laws of continuum mechanics and the turbulence physics prepares the reader for fully understanding the Einstein tensor equations, which exhibits one of the most complex tensor equation in theoretical physics.
目次
Vectors and Tensors.- Transformation of Tensors.- Differential Operators in Continuum Mechanics.- Tensors and Kinematics.- Differential Balances in Continuum Mechanics.- Tensor Operations in Orthogonal Curvilinear.- Tensor Application, Navier-Stokes Equation.- Curves, Curvature, Surfaces, Geodesics.- Turbulent Flow, Modeling.- Special Theory of Relativity.- Tensors In General Theory of Relativity.
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