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. 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. Dover republication of the Methuen & Co., Ltd., London, and John Wiley & Sons, Inc., New York, 1962 edition. See every Dover book in print at www.doverpublications.com 20th century mathematical theory;mathematics;calculus of tensors;tensor fields;differential geometry;vector space;lorentz group;minkowski space time;maxwell lorentz equation;nonfiction;teaching calculus;calculus;fundamental theorems;tensor flow;mathematical development;solving calculus problems;physical sciences;antisymmetric tensor;christoffel symbols;euclidean point;euclidean space;riemannian spaces;analytical dynamics;theoretical;science and math