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Tensor Analysis for Engineers: Transformations, Applications
- 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.
- 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.
- 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
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