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

Great 20th-century mathematician’s classic work on material necessary for mathematical grasp of theory of relativity. Thorough treatment of introductory theories provides basics for discussion of fundamental quadratic form and absolute differential calculus. Final section deals with physical applications. 1926 ed. 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. Written by a towering figure of 20th-century mathematics, this classic examines the mathematical material necessary for a grasp of relativity theory. Levi-Civita's thorough treatment of introductory theories provides the basis for his discussions of fundamental quadratic forms and absolute differential calculus. Concluding chapters address physical applications. 1926 edition.