The Absolute Differential Calculus (Calculus of Tensors) (Revised) (Dover Books on Mathematics)

Marc Notes:
This translation originally published: London: Blackie and Son, 1926.;Includes bibliographical references and indexes.;Written by a distinguished mathematician, this classic examines the mathematical material necessary for a grasp of relativity theory. Covers introductory theories, fundamental quadratic forms, absolute differential calculus, and physical applications. 1926 edition.;Translated from the Italian.

Biographical Note:
Italian mathematician Tullio Levi-Civita (1873-1941) is most famous for his work on absolute differential calculus and its applications to relativity theory.

Publisher Marketing:
Written by a towering figure of twentieth-century mathematics, this classic examines the mathematical background necessary for a grasp of relativity theory. Tullio Levi-Civita provides a thorough treatment of the introductory theories that form the basis for discussions of fundamental quadratic forms and absolute differential calculus, and he further explores physical applications.
Part one opens with considerations of functional determinants and matrices, advancing to systems of total differential equations, linear partial differential equations, algebraic foundations, and a geometrical introduction to theory. The second part addresses covariant differentiation, curvature-related Riemann's symbols and properties, differential quadratic forms of classes zero and one, and intrinsic geometry. The final section focuses on physical applications, covering gravitational equations and general relativity.