Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques, with large number of problems, from routine manipulative exercises to technically difficult assignments.
Tensor Calculus: A Concise Course by Barry Spain Compact exposition of the fundamental results in the theory of tensors; also illustrates the power of the tensor technique by applications to differential geometry, elasticity, and relativity. 1960 edition.
Differential Forms by Henri Cartan The famous mathematician addresses both pure and applied branches of mathematics in a book equally essential as a text, reference, or a brilliant mathematical exercise. "Superb." — Mathematical Review. 1971 edition.
The Absolute Differential Calculus: Calculus of Tensors by Tullio Levi-Civita This classic was written by a founder in the field, offering a clear, detailed exposition that examines introductory theories, the fundamental quadratic form and absolute differential calculus, and physical applications. 1926 edition.
Cartesian Tensors: An Introduction by G. Temple This undergraduate-level text provides an introduction to isotropic tensors and spinor analysis, with numerous examples that illustrate the general theory and indicate certain extensions and applications. 1960 edition.
Introduction to Differentiable Manifolds by Louis Auslander, Robert E. MacKenzie This text presents basic concepts in the modern approach to differential geometry. Topics include Euclidean spaces, submanifolds, and abstract manifolds; fundamental concepts of Lie theory; fiber bundles; and multilinear algebra. 1963 edition.
