Tabatabaian M. Tensor Analysis for Engineers: Transformations-Mathematics-Applications

2nd Edition. — Mercury Learning and Information, 2020. — 196 p. — ISBN 978-1-68392-601-6.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 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 readers with mastering the topics provided in the prior sections.Coordinate systems
Curvilinear and oblique coordinate systems
Basis vectors and scale factors
Contravariant components and transformations
Physical components and transformations
Tensors – mixed and metric
Metric tensor operation on tensor indices
Dot and cross products of tensors
Gradient vector operator-Christoffel symbols
Derivative forms-curl, divergence, Laplacian
Cartesian tensor transformation-rotations
Coordinate independent governing equations
Collection of relations for selected coordinate systems
Rigid body rotation: Euler angles, quaternions, and rotation matrix
Worked-out examples
Exercises

Index