Tensor Analysis for Engineers
Transformations - Mathematics - Applications
2nd Edition
Published on 27. October 2020
182 pages
978-1-68392-599-6 (ISBN)
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Tabatabaian Mehrzad:
Mehrzad Tabatabaian holds a PhD from McGill University and is currently Chair of the BCIT School of Energy Research Committee. He has published several papers for scientific journals and conferences, and he has written textbooks on multiphysics and turbulent flow modelling, thermodynamics, and direct energy conversion. He holds several registered patents in the energy field and currently teaches courses in renewable energy and thermal engineering.
Mehrzad Tabatabaian holds a PhD from McGill University and is currently Chair of the BCIT School of Energy Research Committee. He has published several papers for scientific journals and conferences, and he has written textbooks on multiphysics and turbulent flow modelling, thermodynamics, and direct energy conversion. He holds several registered patents in the energy field and currently teaches courses in renewable energy and thermal engineering.
Content
1. Introduction
2. Coordinate systems
3. Curvilinear and oblique coordinate systems
4. Basis vectors and scale factors
5. Contravariant components and transformations
6. Physical components and transformations
7. Tensors - mixed and metric
8. Metric tensor operation on tensor indices
9. Dot and cross products of tensors
10. Gradient vector operator-Christoffel symbols
11. Derivative forms-curl, divergence, Laplacian
12. Cartesian tensor transformation-rotations
13. Coordinate independent governing equations
14. Collection of relations for selected coordinate systems
15. Rigid body rotation: Euler angles, quaternions, and rotation matrix
16. Worked-out examples
17. Exercises
References
Index
2. Coordinate systems
3. Curvilinear and oblique coordinate systems
4. Basis vectors and scale factors
5. Contravariant components and transformations
6. Physical components and transformations
7. Tensors - mixed and metric
8. Metric tensor operation on tensor indices
9. Dot and cross products of tensors
10. Gradient vector operator-Christoffel symbols
11. Derivative forms-curl, divergence, Laplacian
12. Cartesian tensor transformation-rotations
13. Coordinate independent governing equations
14. Collection of relations for selected coordinate systems
15. Rigid body rotation: Euler angles, quaternions, and rotation matrix
16. Worked-out examples
17. Exercises
References
Index
