Tensor analysis is used in engineering and science fields. Calculations of physical quantities in different systems of coordinates and transformations are required in scientific computations. This requires the use of mathematical concepts and application software. This book is designed to provide the necessary definitions, formulations, and procedures for tensor analysis and transformations to help engineers and scientists to perform their calculations in arbitrary coordinates systems. Companion files include enhanced and animated 4-color figures.
Features:
*Uses AR software to enhance static figures
*Easy to understand mathematical concepts through
numerous figures, solved examples, and exercises
*List of gradient-like operators for major systems of coordinates
*Companion files include animated 4-color figures showing
different perspectives and parameters, etc.
The companion files include (files are also available for downloading from the publisher):
*All images from the text
*Uses AR software to enhance 4-color static figures
1: Introduction.
2: Cartesian Systems Definition.
3: Basis Vectors and Scale Factors.
4: Contravariant Components and Transformations.
5: Covariant Components and Transformations.
6: Physical Components and Transformations.
7: TensorsMixed and Metric.
8: Metric Tensor Operation on Tensor Indices.
9: Dot and Cross Products of Tensors.
10: Gradient Vector OperatorChristoffel Symbols.
11: Derivative FormsCurl, Divergence, Laplacian.
12: Cartesian Tensor TransformationRotations.
13: Coordinate Independent Governing Equations.
14: Collection of Relations for Selected Coordinate Systems.
15: Worked-out Examples.
16: Exercises.
References.
Index.
Mehrzad Tabatabaia is currently a senior faculty member in the Mechanical Engineering Department, School of Energy at the British Columbia Institute of Technology(BCIT) with several years of teaching, research, and industry experiences. He has authored several textbooks and published papers in various scientific journals and conferences. He holds several registered patents in the clean energy field.
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