Tensor analysis is used in engineering and science fields. This new edition provides engineers and applied scientists the tools and techniques of tensor analysis for applications in practical problem solving and analysis activities. The geometry is limited to the Euclideanspace/geometry, where the Pythagorean Theorem applies, with well-defined Cartesian coordinate systems as the reference. Quantities defined in curvilinear coordinate systems, like cylindrical, spherical, parabolic, etc. are discussed and several examples and coordinates sketches with related calculations are presented. In addition, the book has several worked-out examples for helping readers with mastering the topics provided in the prior sections.
FEATURES:
Expanded content on the rigid body rotation and Cartesian tensors by including Euler angles and quaternion methods
Easy to understand mathematical concepts through numerous figures, solved examples, andexercises
List of gradient-like operators for major systems of coordinates.
1. Introduction
2. Coordinate systems
3. Curvilinear and oblique coordinate systems
4. Basis vectors and scale factors
5. Contravariantcomponents and transformations
6. Physical components and transformations
7. Tensors mixed and metric
8. Metric tensor operation on tensor indices
9. Dot andcross products of tensors
10. Gradient vector operator-Christoffel symbols
11.Derivative forms-curl, divergence, Laplacian
12. Cartesian tensortransformation-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
Mehrzad Tabatabaian holds a PhD from McGill University and is currently the chairman of the Energy Efficiency and Renewable Energy Division at the British Columbia Institute of Technology. He has written numerous journal articles, has registered patents, and currently teaches courses in renewable energy and thermal engineering.
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