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"Tensor analysis" as a book category covers the mathematical theory and practical use of tensors and tensor calculus: the multilinear algebra of tensor objects, coordinate-free and component-based methods, and their manipulation on vector spaces and differentiable manifolds. Titles in this category range from introductory treatments that build on linear algebra and multivariable calculus to advanced texts treating differential geometry, Riemannian geometry, and applications in continuum mechanics, elasticity, fluid dynamics and general relativity. Books often explain index notation, covariant and contravariant components, tensor fields, covariant differentiation, curvature, and conserved quantities, and may include computational and numerical techniques for working with tensors. Intended readers include advanced undergraduates, graduate students, and researchers in mathematics, physics, and engineering who need rigorous foundations as well as applied tools for problems in geometry and field theories.

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