Tensor Analysis for Engineers and Physicists - With Application to Continuum Mechanics, Turbulence, and Einstein's Special and General Theory of Relativity

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ABOUT THE BOOK

This book unites 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.

TABLE OF CONTENTS
  1. Vectors and Tensors

    • Meinhard T. Schobeiri
    Pages 1-15
  2. Transformation of Tensors

    • Meinhard T. Schobeiri
    Pages 17-28
  3. Differential Operators in Continuum Mechanics

    • Meinhard T. Schobeiri
    Pages 29-47
  4. Tensors and Kinematics

    • Meinhard T. Schobeiri
    Pages 49-62
  5. Differential Balances in Continuum Mechanics

    • Meinhard T. Schobeiri
    Pages 63-89
  6. Tensor Application, Navier–Stokes Equation

    • Meinhard T. Schobeiri
    Pages 119-131
  7. Curves, Curvature, Surfaces, Geodesics

    • Meinhard T. Schobeiri
    Pages 133-161
  8. Turbulent Flow, Modeling

    • Meinhard T. Schobeiri
    Pages 163-204
  9. Special Theory of Relativity

    • Meinhard T. Schobeiri
    Pages 205-222
  10. Tensors in General Theory of Relativity

    • Meinhard T. Schobeiri
    Pages 223-236

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