Tensor Analysis for Engineers

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.

1. Introduction
2. Coordinate Systems Definition
3. Basic Vectors and Scale Factors
4. Contravariant Components and Transformations
5. Covariant Components and Transformations
6. Physical Componentsand 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. Mechanical Stress Transformation
17. The Worked Examples
18. Exercises
References
Index