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Tensor Analysis for Engineers Edition 3
Transformations - Mathematics - Applications
Hardback
July 2023
9781683929642
More details
- Publisher
Mercury Learning and Information - Published
18th July 2023 - ISBN 9781683929642
- Language English
- Pages 234 pp.
- Size 7" x 9"
$89.99
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June 2023
9781683929628
More details
- Publisher
Mercury Learning and Information - Published
29th June 2023 - ISBN 9781683929628
- Language English
- Pages 234 pp.
- Size 7" x 9"
$89.99
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June 2023
9781683929635
More details
- Publisher
Mercury Learning and Information - Published
29th June 2023 - ISBN 9781683929635
- Language English
- Pages 234 pp.
- Size 7" x 9"
$159.00
Tensor analysis is used in engineering and science fields. This new edition provides engineers and applied scientists with
the tools and techniques of tensor analysis for applications in practical problem solving and analysis activities. It includes expanded content on the application of mechanical stress transformation. The geometry is limited to the Euclidean space/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 the readers with mastering the topics provided in the prior sections.
FEATURES:
- Expanded content on the application of mechanical stress transformation
- Covers rigid body rotation and Cartesian tensors by including Euler angles and quaternion methods
- Uses easy to understand mathematical concepts through numerous figures, solved examples, and exercises
- Lists gradient-like operators for major systems of coordinates and rotation matrices for proper Euler and Tait-Bryan angles
1. Introduction
2. Coordinate Systems Definition
3. Basic Vectors and Scale Factors
4. Contravariant Components and Transformations
5. Covariant 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. Mechanical Stress Transformation
17. The Worked Examples
18. Exercises
References
Index
Mehrzad Tabatabaian, PhD, PEng
Mehrzad Tabatabaian, PhD, PEng, is currently Chair of the BCIT School of Energy Research Committee. He has published several papers for scientific journals and has written textbooks on multiphysics modelling and thermodynamics. He holds several registered patents in the energy field and teaches courses in renewable energy.
engineering; physics; mathematics; science; electronics; tensors