Fundamental introduction for beginning student of absolute differential calculus and for those interested in applications of tensor calculus to mathematical physics and engineering. Topics include spaces and tensors; basic operations in Riemannian space, curvature of space, special types of space, relative tensors, ideas of volume, more.
Here's a sample of other books in this Dover category
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.
Matrix and Tensor Calculus: With Applications to Mechanics, Elasticity and Aeronautics by Aristotle D. Michal This volume offers a working knowledge of the fundamentals of matrix and tensor calculus. Relevant to several fields, particularly aeronautical engineering, the text skillfully combines mathematical statements with practical applications. 1947 edition.
The Malliavin Calculus by Denis R. Bell This introductory text presents detailed accounts of the different forms of the theory developed by Stroock and Bismut, discussions of the relationship between these 2 approaches, and a variety of applications. 1987 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.
The Geometry of Geodesics by Herbert Busemann A comprehensive approach to qualitative problems in intrinsic differential geometry, this text examines Desarguesian spaces, perpendiculars and parallels, covering spaces, the influence of the sign of the curvature on geodesics, more. 1955 edition. Includes 66 figures.
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.
