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