Elements of Tensor Calculus

This classic introductory text, geared toward undergraduate students of mathematics, is the work of an internationally renowned authority on tensor calculus. The two-part treatment offers a rigorous presentation of tensor calculus as a development of vector analysis as well as discussions of the most important applications of tensor calculus.
Starting with a chapter on vector spaces, Part I explores affine Euclidean point spaces, tensor algebra, curvilinear coordinates in Euclidean space, and Riemannian spaces. Part II examines the use of tensors in classical analytical dynamics and details the role of tensors in special relativity theory. The book concludes with a brief presentation of the field equations of general relativity theory.

French mathematician Andre Lichnerowicz (1915–98) taught at the University of Paris from 1949 to 1952 and at the College de France until his 1986 retirement. He made significant contributions to several areas of mathematics and mathematical physics.

PrefacePart I: Tensor CalculusI. Vector SpacesII. Affine Euclidean Point SpacesIII. Tensor AlgebraIV. Curvilinear Coordinates in Euclidean SpaceV. Riemannian Spaces Part II: ApplicationsVI. Tensor Calculus and Classical DynamicsVII. Special relativity and Maxwell's EquationsVIII. Elements of the Relativistic Theory of GravitationBibliographyIndex