This book is a comprehensive guide to tensor analysis for engineers and applied scientists, focusing on practical problem-solving in Euclidean space. It covers Cartesian coordinate systems and curvilinear coordinates like cylindrical and spherical, with examples and calculations. Expanded content includes rigid body rotation, Cartesian tensors, Euler angles, and quaternion methods.
The course begins with coordinate systems, moving through curvilinear systems, basis vectors, and scale factors. It covers contravariant and physical components, tensor transformations, and mixed and metric tensors. Advanced topics include gradient operators, derivative forms, Cartesian tensor transformations, and coordinate-independent equations. The book features relations for selected coordinate systems, rigid body rotation methods, and numerous worked-out examples and exercises.
Mastering tensor analysis is crucial for complex engineering and science problems. This book transitions from basic concepts to advanced applications, blending theory with practical examples. Clear explanations, figures, and exercises enhance learning, making this an essential resource for tensor analysis in Euclidean space.

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Spis treści

Tensor Analysis for Engineers. Mastering Coordinate Systems, Transformations and Applications using Mathematics eBook -- spis treści

• 1. Introduction
• 2. Coordinate Systems Definition
• 3. Basis 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. Worked-out Examples
• 17. Exercise Problems